Search results for: inverse dynamics

Authors: Takashi Shimizu, Tomoaki Hashimoto

Abstract:

Recently, crystal growth technologies have made progress by the requirement for the high quality of crystal materials. To control the crystal growth dynamics actively by external forces is useuful for reducing composition non-uniformity. In this study, a control method based on model predictive control using thermal inputs is proposed for crystal growth dynamics of semiconductor materials. The control system of crystal growth dynamics considered here is governed by the continuity, momentum, energy, and mass transport equations. To establish the control method for such thermal fluid systems, we adopt model predictive control known as a kind of optimal feedback control in which the control performance over a finite future is optimized with a performance index that has a moving initial time and terminal time. The objective of this study is to establish a model predictive control method for crystal growth dynamics of semiconductor materials.

Keywords: Model predictive control, optimal control, crystal growth, process control.

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Authors: Magdi M. Nabi, Ding-Li Yu

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Control of a semi-batch polymerization reactor using an adaptive radial basis function (RBF) neural network method is investigated in this paper. A neural network inverse model is used to estimate the valve position of the reactor; this method can identify the controlled system with the RBF neural network identifier. The weights of the adaptive PID controller are timely adjusted based on the identification of the plant and self-learning capability of RBFNN. A PID controller is used in the feedback control to regulate the actual temperature by compensating the neural network inverse model output. Simulation results show that the proposed control has strong adaptability, robustness and satisfactory control performance and the nonlinear system is achieved.

Keywords: Chylla-Haase polymerization reactor, RBF neural networks, feed-forward and feedback control.

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Authors: Sanwu Wang, Hongli Dang, Wenhua Xue, Darwin Shields, Xin Liu, Friederike C. Jentoft, Daniel E. Resasco

Abstract:

The bonding configuration and the heat of adsorption of a furfural molecule on the Pd(111) surface were determined by ab initio density-functional-theory calculations. The dynamics of pure liquid water, the liquid-solid interface formed by liquid water and the Pd(111) surface, as well as furfural at the water-Pd interface, were investigated by ab initio molecular dynamics simulations at finite temperatures. Calculations and simulations suggest that the bonding configurations at the water-Pd interface promote decarbonylation of furfural.

Keywords: Ab initio molecular dynamics simulations, bio-fuels, density functional theory, liquid-solid interfaces.

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Authors: Jan Rychtar, Brian Stadler

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We study how the outcome of evolutionary dynamics on graphs depends on a randomness on the graph structure. We gradually change the underlying graph from completely regular (e.g. a square lattice) to completely random. We find that the fixation probability increases as the randomness increases; nevertheless, the increase is not significant and thus the fixation probability could be estimated by the known formulas for underlying regular graphs.

Keywords: evolutionary dynamics, small-world networks

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Authors: Sidshchadhaa Aumted, Shuhei Shiina, Hiroshi Takami

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In this paper, we propose an advanced ILQ control for the buck-converter via two-degrees of freedom servo-system. Our presented strategy is based on Inverse Linear Quadratic (ILQ) servo-system controller without solving Riccati-s equation directly. The optimal controller of the current and voltage control system is designed. The stability and robust control are analyzed. A conscious and persistent effort has been made to improve ILQ control via two-degrees of freedom guarantees the optimal gains on the basis of polynomial pole assignment, which our results of the proposed strategy shows that the advanced ILQ control can be controlled independently the step response and the disturbance response by appending a feed-forward compensator.

Keywords: Optimal voltage control, inverse LQ design method, second order polynomial, two-degrees of freedom.

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Authors: Arturo Ayala-Hernandez, Humberto H´ıjar

Abstract:

We propose a new alternative method for imposing fluid-solid boundary conditions in simulations of Multiparticle Collision Dynamics. Our method is based on the introduction of an explicit potential force acting between the fluid particles and a surface representing a solid boundary. We show that our method can be used in simulations of plane Poiseuille flows. Important quantities characterizing the flow and the fluid-solid interaction like the slip coefficient at the solid boundary and the effective viscosity of the fluid, are measured in terms of the set of independent parameters defining the numerical implementation. We find that our method can be used to simulate the correct hydrodynamic flow within a wide range of values of these parameters.

Keywords: Multiparticle Collision Dynamics, Fluid-Solid Boundary Conditions, Molecular Dynamics.

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Authors: E. Barkanov, E. Skukis, M. Wesolowski, A. Chate

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New nondestructive technique, namely an inverse technique based on vibration tests, to characterize nonlinear mechanical properties of adhesive layers in sandwich composites is developed. An adhesive layer is described as a viscoelastic isotropic material with storage and loss moduli which are both frequency dependent values in wide frequency range. An optimization based on the planning of experiments and response surface technique to minimize the error functional is applied to decrease considerably the computational expenses. The developed identification technique has been tested on aluminum panels and successfully applied to characterize viscoelastic material properties of 3M damping polymer ISD-112 used as a core material in sandwich panels.

Keywords: Adhesive layer, finite element method, inverse technique, sandwich panel, vibration test, viscoelastic material properties.

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Authors: A. Cho, H. Sanyal, J. Cataldo

Abstract:

A quantitative analysis of the different variables on both the South and North green roofs of the Jacob K. Javits Convention Center was taken to find mathematical relationships between net radiation and evapotranspiration (ET), average outside temperature, and the lysimeter weight. Groups of datasets were analyzed, and the relationships were plotted on linear and semi-log graphs to find consistent relationships. Antecedent conditions for each rainstorm were also recorded and plotted against the volumetric water difference within the lysimeter. The first relation was the inverse parabolic relationship between the lysimeter weight and the net radiation and ET. The peaks and valleys of the lysimeter weight corresponded to valleys and peaks in the net radiation and ET respectively, with the 8/22/15 and 1/22/16 datasets showing this trend. The U-shaped and inverse U-shaped plots of the two variables coincided, indicating an inverse relationship between the two variables. Cross variable relationships were examined through graphs with lysimeter weight as the dependent variable on the y-axis. 10 out of 16 of the plots of lysimeter weight vs. outside temperature plots had R² values > 0.9. Antecedent conditions were also recorded for rainstorms, categorized by the amount of precipitation accumulating during the storm. Plotted against the change in the volumetric water weight difference within the lysimeter, a logarithmic regression was found with large R² values. The datasets were compared using the Mann Whitney U-test to see if the datasets were statistically different, using a significance level of 5%; all datasets compared showed a U test statistic value, proving the null hypothesis of the datasets being different from being true.

Keywords: Green roof, green infrastructure, Javits Center, evapotranspiration, net radiation, lysimeter.

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Authors: Yongxin Yuan

Abstract:

In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find nontrivial real-valued symmetric arrow-head matrices A and B such that AXΛ = BX. We then consider an optimal approximation problem: Given real-valued symmetric arrow-head matrices A, ˜ B˜ ∈ Rn×n, find (A, ˆ Bˆ) ∈ SE such that Aˆ − A˜2 + Bˆ − B˜2 = min(A,B)∈SE (A−A˜2 +B −B˜2), where SE is the solution set of IEP. We show that the optimal approximation solution (A, ˆ Bˆ) is unique and derive an explicit formula for it.

Keywords: Partially prescribed spectral information, symmetric arrow-head matrix, inverse problem, optimal approximation.

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Authors: S. Jakšić, B. Žmuk

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The paper investigates the key factors of export dynamics for a set of Central and Southeast European (CSEE) countries in the context of current economic and financial crisis. In order to model the export dynamics a Global Vector Auto Regressive (GVAR) model is defined. As opposed to models which model each country separately, the GVAR combines all country models in a global model which enables obtaining important information on spillover effects in the context of globalisation and rising international linkages. The results of the study indicate that for most of the CSEE countries, exports are mainly driven by domestic shocks, both in the short run and in the long run. This study is the first application of the GVAR model to studying the export dynamics in the CSEE countries and therefore the results of the study present an important empirical contribution.

Keywords: Export, GFEVD, Global VAR, International trade, weak exogeneity.

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Authors: Tatiana A. Dolenko, Sergey A. Burikov, Alexander O. Efitorov, Sergey A. Dolenko

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In this study, a comparative analysis of the approaches associated with the use of neural network algorithms for effective solution of a complex inverse problem – the problem of identifying and determining the individual concentrations of inorganic salts in multicomponent aqueous solutions by the spectra of Raman scattering of light – is performed. It is shown that application of artificial neural networks provides the average accuracy of determination of concentration of each salt no worse than 0.025 M. The results of comparative analysis of input data compression methods are presented. It is demonstrated that use of uniform aggregation of input features allows decreasing the error of determination of individual concentrations of components by 16-18% on the average.

Keywords: Inverse problems, multi-component solutions, neural networks, Raman spectroscopy.

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Authors: Xie Kefeng, Zhang He

Abstract:

For the stability and control demand of offshore small floating platform, a 2-HUS/U parallel mechanism was presented as offshore platform. Inverse kinematics was obtained by institutional constraint equation, and the dynamic model of offshore 2-HUS/U parallel platform was derived based on rigid body’s Lagrangian method. The equivalent moment of inertia, damping and driving force/torque variation of offshore 2-HUS/U parallel platform were analyzed. A numerical example shows that, for parallel platform of given motion, system’s equivalent inertia changes 1.25 times maximally. During the movement of platform, they change dramatically with the system configuration and have coupling characteristics. The maximum equivalent drive torque is 800 N. At the same time, the curve of platform’s driving force/torque is smooth and has good sine features. The control system needs to be adjusted according to kinetic equation during stability and control and it provides a basis for the optimization of control system.

Keywords: 2-HUS/U platform, Dynamics, Lagrange, Parallel platform.

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Authors: Rohit Suryawanshi

Abstract:

In this study, the commercial Computational Fluid Dynamics (CFD), ANSYS-Fluent, has been used to optimize the marine propeller with the design of experiment (DOE) method. At the initial stage, different propeller parameters ware selected for the three different levels. The four characteristics factors are: no. of the blade, camber value, pitch delta & chord at the hub. Then, CAD modelling is performed by considering the selected factor and level. In this investigation, a total of 9 test models are simulated with the Reynolds-Averaged Navier-Stokes (RANS) equations. The standard, realizable

Keywords: Marine propeller, Computational Fluid Dynamics, optimization, DOE, propeller thrust.

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Authors: J. G. Batista, L. J. de Bessa Neto, M. A. F. B. Lima, J. R. Leite, J. I. de Andrade Nunes

Abstract:

The robot manipulator is an equipment that stands out for two reasons: Firstly because of its characteristics of movement and reprogramming, resembling the arm; secondly, by adding several areas of knowledge of science and engineering. The present work shows the development of the prototype of a robotic manipulator driven by a Programmable Logic Controller (PLC), having two degrees of freedom, which allows the movement and displacement of mechanical parts, tools, and objects in general of small size, through an electronic system. The aim is to study direct and inverse kinematics of the robotic manipulator to describe the translation and rotation between two adjacent links of the robot through the Denavit-Hartenberg parameters. Currently, due to the many resources that microcomputer systems offer us, robotics is going through a period of continuous growth that will allow, in a short time, the development of intelligent robots with the capacity to perform operations that require flexibility, speed and precision.

Keywords: Direct and inverse kinematics, Denavit-Hartenberg, microcontrollers, robotic manipulator.

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Authors: I. V. Kuzminov

Abstract:

The proposed article is an analytical review of previously published articles in the series "Physics of Gravity", "The Picture of the World by Second Law of Thermodynamics" and others. The article shows the key role of the forces of gravity and the action of the second law of thermodynamics in shaping the picture of the world. In other words, the second law of thermodynamics can be called the law of matter cooling. The action in the compartment of the inverse temperature dependence of the forces of gravity and the second law of thermodynamics is carried out by the processes of separation, condensation, phase transitions, and transformation of matter. On the basis of the proposed concept, along the way, completely new versions of the development of events in the biography of the Earth are put forward. For example, new versions of the origin of planets, the origin of continents and others are being put forward. This article contains a list of articles and videos that are somehow related to the proposed topic. Articles and videos are presented in English and Russian.

Keywords: Gravity, the second law of thermodynamics, electron rotation, inverse temperature dependence, inertia forces, centrifugal forces.

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Authors: G.H. Farrahi, S.A. Faghidian, D.J. Smith

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A thin layer on the component surface can be found with high tensile residual stresses, due to turning operations, which can dangerously affect the fatigue performance of the component. In this paper an analytical approach is presented to reconstruct the residual stress field from a limited incomplete set of measurements. Airy stress function is used as the primary unknown to directly solve the equilibrium equations and satisfying the boundary conditions. In this new method there exists the flexibility to impose the physical conditions that govern the behavior of residual stress to achieve a meaningful complete stress field. The analysis is also coupled to a least squares approximation and a regularization method to provide stability of the inverse problem. The power of this new method is then demonstrated by analyzing some experimental measurements and achieving a good agreement between the model prediction and the results obtained from residual stress measurement.

Keywords: Residual stress, Limited measurements, Inverse problems, Turning process.

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Authors: Win Win Tun, Han Su Yin, Ohn Zin Lin

Abstract:

Transmission networks are an important part of an electric power system. The transmission lines not only have high power transmission capacity but also they are prone of larger magnitudes. Different types of faults occur in transmission lines such as single line to ground (L-G) fault, double line to ground (L-L-G) fault, line to line (L-L) fault and three phases (L-L-L) fault. These faults are needed to be cleared quickly in order to reduce damage caused to the system and they have high impact on the electrical power system equipment’s which are connected in transmission line. The main fault in transmission line is L-G fault. Therefore, protection relays are needed to protect transmission line. Overcurrent and earth fault relay is an important relay used to protect transmission lines, distribution feeders, transformers and bus couplers etc. Sometimes these relays can be used as main protection or backup protection. The modeling of protection relays is important to indicate the effects of network parameters and configurations on the operation of relays. Therefore, the modeling of overcurrent and earth fault relay is described in this paper. The overcurrent and earth fault relays with standard inverse definite minimum time are modeled and simulated by using MATLAB/Simulink software. The developed model was tested with L-G, L-L-G, L-L and L-L-L faults with various fault locations and fault resistance (0.001Ω). The simulation results are obtained by MATLAB software which shows the feasibility of analysis of transmission line protection with overcurrent and earth fault relay.

Keywords: Transmission line, overcurrent and earth fault relay, standard inverse definite minimum time, various faults, MATLAB Software.

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Authors: Athanasios T. Alexiou, Maria M. Psiha, John A. Rekkas, Panayiotis M. Vlamos

Abstract:

Mitochondria are dynamic organelles, capable to interact with each other. While the number of mitochondria in a cell varies, their quality and functionality depends on the operation of fusion, fission, motility and mitophagy. Nowadays, several researches declare as an important factor in neurogenerative diseases the disruptions in the regulation of mitochondrial dynamics. In this paper a stochastic model in BioAmbients calculus is presented, concerning mitochondrial fusion and its distribution in the renewal of mitochondrial population in a cell. This model describes the successive and dependent stages of protein synthesis, protein-s activation and merging of two independent mitochondria.

Keywords: Mitochondrial Dynamics, P-Calculus, StochasticModeling.

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Authors: Nashrawan N. Taha, Andrew M. Cox

Abstract:

In a multi-cultural learning context, where ties are weak and dynamic, combining qualitative with quantitative research methods may be more effective. Such a combination may also allow us to answer different types of question, such as about people’s perception of the network. In this study the use of observation, interviews and photos were explored as ways of enhancing data from social network questionnaires. Integrating all of these methods was found to enhance the quality of data collected and its accuracy, also providing a richer story of the network dynamics and the factors that shaped these changes over time.

Keywords: Mixed Methods, Social Network Analysis, multi-cultural learning, Social Network Dynamics.

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Authors: A. Ito, S. Okamoto

Abstract:

We constructed an atomic structure model for a PAN-based carbon fiber containing amorphous structures using molecular dynamics methods. It was found that basic physical properties such as crystallinity, Young’s modulus, and thermal conductivity of our model were nearly identical to those of real carbon fibers. We then obtained the tensile strength of a carbon fiber, which has no macro defects. We finally determined that the limitation of the tensile strength was 19 GPa.

Keywords: Amorphous, carbon fiber, molecular dynamics, tensile strength.

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Authors: Yeongyu Choi, Ju H. Park, Ho-Youl Jung

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In this paper, we propose labeling based RANSAC algorithm for lane detection. Advanced driver assistance systems (ADAS) have been widely researched to avoid unexpected accidents. Lane detection is a necessary system to assist keeping lane and lane departure prevention. The proposed vision based lane detection method applies Canny edge detection, inverse perspective mapping (IPM), K-means algorithm, mathematical morphology operations and 8 connected-component labeling. Next, random samples are selected from each labeling region for RANSAC. The sampling method selects the points of lane with a high probability. Finally, lane parameters of straight line or curve equations are estimated. Through the simulations tested on video recorded at daytime and nighttime, we show that the proposed method has better performance than the existing RANSAC algorithm in various environments.

Keywords: Canny edge detection, k-means algorithm, RANSAC, inverse perspective mapping.

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Authors: Yul Y. Nazaruddin, Anas Y. Widiaribowo, Satriyo Nugroho

Abstract:

Boiler is one of the critical unit in a petrochemical plant. Steam produced by the boiler is used for various processes in the plant such as urea and ammonia plant. An alternative method to optimize the boiler combustion system is presented in this paper. Adaptive Neuro-Fuzzy Inference System (ANFIS) approach is applied to model the boiler using real-time operational data collected from a boiler unit of the petrochemical plant. Nonlinear equation obtained is then used to optimize the air to fuel ratio using Genetic Algorithm, resulting an optimal ratio of 15.85. This optimal ratio is then maintained constant by ratio controller designed using inverse dynamics based on ANFIS. As a result, constant value of oxygen content in the flue gas is obtained which indicates more efficient combustion process.

Keywords: ANFIS, boiler, combustion process, genetic algorithm, optimization.

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Authors: Sufian Ashraf Mazhari, Surendra Kumar

Abstract:

This paper compares the heuristic Global Search Techniques; Genetic Algorithm, Particle Swarm Optimization, Simulated Annealing, Generalized Pattern Search, genetic algorithm hybridized with Nelder–Mead and Generalized pattern search technique for tuning of fuzzy PID controller for Puma 560. Since the actual control is in joint space ,inverse kinematics is used to generate various joint angles correspoding to desired cartesian space trajectory. Efficient dynamics and kinematics are modeled on Matlab which takes very less simulation time. Performances of all the tuning methods with and without disturbance are compared in terms of ITSE in joint space and ISE in cartesian space for spiral trajectory tracking. Genetic Algorithm hybridized with Generalized Pattern Search is showing best performance.

Keywords: Controller tuning, Fuzzy Control, Genetic Algorithm, Heuristic search, Robot control.

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Authors: N. Jinesh, K. Shankar

Abstract:

This article presents a method of using the one dimensional piezo-electric patch on beam model for structural identification. A hybrid element constituted of one dimensional beam element and a PZT sensor is used with reduced material properties. This model is convenient and simple for identification of beams. Accuracy of this element is first verified against a corresponding 3D finite element model (FEM). The structural identification is carried out as an inverse problem whereby parameters are identified by minimizing the deviation between the predicted and measured voltage response of the patch, when subjected to excitation. A non-classical optimization algorithm Particle Swarm Optimization is used to minimize this objective function. The signals are polluted with 5% Gaussian noise to simulate experimental noise. The proposed method is applied on beam structure and identified parameters are stiffness and damping. The model is also validated experimentally.

Keywords: Structural identification, PZT patches, inverse problem, particle swarm optimization.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang

Abstract:

Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually the effects of blurred edges and jagged artifacts in the image to some extent. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to sharpen edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (“jaggies") along the tangent directions. In order to preserve image features such as edges, corners and textures, the nonlinear diffusion coefficients are locally adjusted according to the directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

Keywords: anisotropic diffusion, bidirectional flow, directional derivatives, edge enhancement, image interpolation, inverse flow, shock filter.

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Authors: Chen-Yu Wang, Tsung-Chien Chen, Ming-Hui Lee, Jen-Feng Huang

Abstract:

In this paper, the innovative intelligent fuzzy weighted input estimation method (FWIEM) can be applied to the inverse heat transfer conduction problem (IHCP) to estimate the unknown time-varying heat flux efficiently as presented. The feasibility of this method can be verified by adopting the temperature measurement experiment. We would like to focus attention on the heat flux estimation to three kinds of samples (Copper, Iron and Steel/AISI 304) with the same 3mm thickness. The temperature measurements are then regarded as the inputs into the FWIEM to estimate the heat flux. The experiment results show that the proposed algorithm can estimate the unknown time-varying heat flux on-line.

Keywords: Fuzzy Weighted Input Estimation Method, IHCP andHeat Flux.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang

Abstract:

Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to enhance edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (''jaggies'') along the tangent directions. In order to preserve image features such as edges, angles and textures, the nonlinear diffusion coefficients are locally adjusted according to the first and second order directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

Keywords: anisotropic diffusion, bidirectional flow, directionalderivatives, edge enhancement, image interpolation, inverse flow, shock filter.

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Authors: Gülçin Tekin, Fethi Kadıoğlu

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In this study, the dynamic analysis of viscoelastic plates with variable thickness is examined. The solutions of dynamic response of viscoelastic thin plates with variable thickness have been obtained by using the functional analysis method in the conjunction with the Gâteaux differential. The four-node serendipity element with four degrees of freedom such as deflection, bending, and twisting moments at each node is used. Additionally, boundary condition terms are included in the functional by using a systematic way. In viscoelastic modeling, Three-parameter Kelvin solid model is employed. The solutions obtained in the Laplace-Carson domain are transformed to the real time domain by using MDOP, Dubner & Abate, and Durbin inverse transform techniques. To test the performance of the proposed mixed finite element formulation, numerical examples are treated.

Keywords: Dynamic analysis, inverse Laplace transform techniques, mixed finite element formulation, viscoelastic plate with variable thickness.

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Authors: Sylvain Amailland, Jean-Hugh Thomas, Charles Pézerat, Romuald Boucheron, Jean-Claude Pascal

Abstract:

The noise requirements for naval and research vessels have seen an increasing demand for quieter ships in order to fulfil current regulations and to reduce the effects on marine life. Hence, new methods dedicated to the characterization of propeller noise, which is the main source of noise in the far-field, are needed. The study of cavitating propellers in closed-section is interesting for analyzing hydrodynamic performance but could involve significant difficulties for hydroacoustic study, especially due to reverberation and boundary layer noise in the tunnel. The aim of this paper is to present a numerical methodology for the identification of hydroacoustic sources on marine propellers using hydrophone arrays in a large hydrodynamic tunnel. The main difficulties are linked to the reverberation of the tunnel and the boundary layer noise that strongly reduce the signal-to-noise ratio. In this paper it is proposed to estimate the reflection coefficients using an inverse method and some reference transfer functions measured in the tunnel. This approach allows to reduce the uncertainties of the propagation model used in the inverse problem. In order to reduce the boundary layer noise, a cleaning algorithm taking advantage of the low rank and sparse structure of the cross-spectrum matrices of the acoustic and the boundary layer noise is presented. This approach allows to recover the acoustic signal even well under the boundary layer noise. The improvement brought by this method is visible on acoustic maps resulting from beamforming and DAMAS algorithms.

Keywords: Acoustic imaging, boundary layer noise denoising, inverse problems, model adaptation.

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Authors: Yongxin Yuan

Abstract:

Let R ∈ Cm×m and S ∈ Cn×n be nontrivial unitary involutions, i.e., RH = R = R−1 = ±Im and SH = S = S−1 = ±In. A ∈ Cm×n is said to be a generalized reflexive (anti-reflexive) matrix if RAS = A (RAS = −A). Let ρ be the set of m × n generalized reflexive (anti-reflexive) matrices. Given X ∈ Cn×p, Z ∈ Cm×p, Y ∈ Cm×q and W ∈ Cn×q, we characterize the matrices A in ρ that minimize AX−Z2+Y HA−WH2, and, given an arbitrary A˜ ∈ Cm×n, we find a unique matrix among the minimizers of AX − Z2 + Y HA − WH2 in ρ that minimizes A − A˜. We also obtain sufficient and necessary conditions for existence of A ∈ ρ such that AX = Z, Y HA = WH, and characterize the set of all such matrices A if the conditions are satisfied. These results are applied to solve a class of left and right inverse eigenproblems for generalized reflexive (anti-reflexive) matrices.

Keywords: approximation, generalized reflexive matrix, generalized anti-reflexive matrix, inverse eigenvalue problem.

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