Search results for: Imprecise matrix.

Authors: D. H. Kim, Y. H. Kim, T. Kim

Abstract:

A new method identifies coupled fluid-structure system with a reduced set of state variables is presented. Assuming that the structural model is known a priori either from an analysis or a test and using linear transformations between structural and aeroelastic states, it is possible to deduce aerodynamic information from sampled time histories of the aeroelastic system. More specifically given a finite set of structural modes the method extracts generalized aerodynamic force matrix corresponding to these mode shapes. Once the aerodynamic forces are known, an aeroelastic reduced-order model can be constructed in discrete-time, state-space format by coupling the structural model and the aerodynamic system. The resulting reduced-order model is suitable for constant Mach, varying density analysis.

Keywords: ROM (Reduced-Order Model), aero elasticity, AGARD 445.6 wing.

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Authors: A. Keshavarz, Z. Roosta

Abstract:

In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: Paraxial group transformation, nonlocal nonlinear media, Cos-Gaussian beam, ABCD law.

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Authors: Saman M. Siddiqui, Fang Jiancheng

Abstract:

Robust nonlinear integrated navigation of GPS and low cost MEMS is a hot topic of research these days. A robust filter is required to cope up with the problem of unpredictable discontinuities and colored noises associated with low cost sensors. H∞ filter is previously used in Extended Kalman filter and Unscented Kalman filter frame. Unscented Kalman filter has a problem of Cholesky matrix factorization at each step which is a very unstable operation. To avoid this problem in this research H∞ filter is designed in Square root Unscented filter framework and found 50% more robust towards increased level of colored noises.

Keywords: H∞ filter, MEMS, GPS, Nonlinear system, robust system, Square root unscented filter.

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Authors: Youssef Khmou, Said Safi

Abstract:

In this paper, we investigated the effect of real valued transformation of the spectral matrix of the received data for Angles Of Arrival estimation problem.  Indeed, the unitary transformation of Partial Propagator (UPP) for narrowband sources is proposed and applied on Uniform Linear Array (ULA).

Monte Carlo simulations proved the performance of the UPP spectrum comparatively with Forward Backward Partial Propagator (FBPP) and Unitary Propagator (UP). The results demonstrates that when some of the sources are fully correlated and closer than the Rayleigh angular limit resolution of the broadside array, the UPP method outperforms the FBPP in both of spatial resolution and complexity.

Keywords: DOA, Uniform Linear Array, Narrowband, Propagator, Real valued transformation, Subspace, Unitary Operator.

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Authors: D. Korsacilar, C. Atas

Abstract:

In this study, first thermoplastic composite materials /plates that have high ballistic impact resistance were produced. For this purpose, the thermoplastic prepreg and the vacuum bagging technique were used to produce a composite material. Thermoplastic prepregs (resin-impregnated fiber) that are supplied ready to be used, namely high-density polyethylene (HDPE) was chosen as matrix and unidirectional glass fiber was used as reinforcement. In order to compare the fiber configuration effect on mechanical properties, unidirectional and biaxial prepregs were used. Then the microstructural properties of the composites were investigated with scanning electron microscopy (SEM) analysis. Impact properties of the composites were examined by Charpy impact test and tensile mechanical tests and then the effects of ultraviolet irradiation were investigated on mechanical performance.

Keywords: Ballistic, Composite, Thermoplastic.

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Authors: Antônio P. de Araújo Neto, Ruy D. A. da Silva Neto, Juliana R. de Souza, Salete K. P. de Medeiros, João T. N. de Medeiros

Abstract:

The tribological test with Pin-On-Disc configuration measures friction and wear properties in dry or lubricated sliding surfaces of a variety of materials and coatings. Polymeric matrix composites loaded with mineral filler were used, 1%, 3%, 10%, 30%, and 50% mass percentage of filler, to reduce the material cost by using mineral tailings. Using a pin-on-disc tribometer to quantify coefficient of friction and wear resistance of the specimens. The parameters known to performing the test were 300 rpm rotation, normal load of 16N and duration of 33.5 minutes. The composite with 10% mineral filler performed better, considering that the wear resistance was good when compared to the other compositions and an average low coefficient of friction, in the order of μ ≤ 0.15.

Keywords: Microcomposites, microparticles tailings of scheelite, PTFE, tribology.

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Authors: Choon Ki Ahn, Jung Hun Park, Wook Hyun Kwon

Abstract:

CEMTool is a command style design and analyzing package for scientific and technological algorithm and a matrix based computation language. In this paper, we present new 2D & 3D finite element method (FEM) packages for CEMTool. We discuss the detailed structures and the important features of pre-processor, solver, and post-processor of CEMTool 2D & 3D FEM packages. In contrast to the existing MATLAB PDE Toolbox, our proposed FEM packages can deal with the combination of the reserved words. Also, we can control the mesh in a very effective way. With the introduction of new mesh generation algorithm and fast solving technique, our FEM packages can guarantee the shorter computational time than MATLAB PDE Toolbox. Consequently, with our new FEM packages, we can overcome some disadvantages or limitations of the existing MATLAB PDE Toolbox.

Keywords: CEMTool, Finite element method (FEM), Numericalanalysis, Partial differential equation (PDE)

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Authors: Adil AL-Rammahi

Abstract:

When we prefer to make the data secure from various attacks and fore integrity of data, we must encrypt the data before it is transmitted or stored. This paper introduces a new effective and lossless image encryption algorithm using a natural logarithmic function. The new algorithm encrypts an image through a three stage process. In the first stage, a reference natural logarithmic function is generated as the foundation for the encryption image. The image numeral matrix is then analyzed to five integer numbers, and then the numbers’ positions are transformed to matrices. The advantages of this method is useful for efficiently encrypting a variety of digital images, such as binary images, gray images, and RGB images without any quality loss. The principles of the presented scheme could be applied to provide complexity and then security for a variety of data systems such as image and others.

Keywords: Linear Systems, Image Encryption, Calculus.

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Authors: Jihyung Kim, Taejin Kim, Sungho Park, Jun-Dong Cho

Abstract:

In this paper, the problem of reducing switching activity in on-chip buses at the stage of high-level synthesis is considered, and a high-level low power bus binding based on dynamic bit reordering is proposed. Whereas conventional methods use a fixed bit ordering between variables within a bus, the proposed method switches a bit ordering dynamically to obtain a switching activity reduction. As a result, the proposed method finds a binding solution with a smaller value of total switching activity (TSA). Experimental result shows that the proposed method obtains a binding solution having 12.0-34.9% smaller TSA compared with the conventional methods.

Keywords: bit reordering, bus binding, low power, switching activity matrix

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Authors: J. Wozniak, M. Kostecki, K. Broniszewski, W. Bochniak, A. Olszyna

Abstract:

The influence of extrusion parameters on surface quality and properties of AA6061+x% vol. SiC (x = 0; 2,5; 5; 7,5;10) composites was discussed in this paper. The averages size of AA6061 and SiC particles were 10.6 μm and 0.42 μm, respectively. Two series of composites (I - compacts were preheated at extrusion temperature through 0.5 h and cooled by water directly after process; II - compacts were preheated through 3 hours and were not cooled) were consolidated via powder metallurgy processing and extruded by KoBo method. High values of density for both series of composites were achieved. Better surface quality was observed for II series of composites. Moreover, for these composites lower (compared to I series) but more uniform strength properties over the cross-section of the bar were noticed. Microstructure and Young-s modulus investigations were made.

Keywords: aluminum alloy, extrusion, metal matrix composites, microstructure

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Authors: Xinhui Wang, Xiuyong Ding

Abstract:

This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.

Keywords: Switched copositive Lyapunov functions, positive linear systems, switched systems, time-varying delays, stabilization.

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Authors: Jung-Ho Moon, Tae Kwon Ha

Abstract:

High temperature deformation behavior of cast Fe-20Cr-5Al alloy has been investigated in this study by performing tensile and compression tests at temperatures from 1100 to 1200oC. Rectangular ingots of which the dimensions were 300×300×100 in millimeter were cast using vacuum induction melting. Phase equilibrium was calculated using the FactSage®, thermodynamic software and database. Tensile strength of cast Fe-20Cr-5Al alloy was 4 MPa at 1200oC. With temperature decreased, tensile strength increased rapidly and reached up to 13 MPa at 1100oC. Elongation also increased from 18 to 80% with temperature decreased from 1200oC to 1100oC. Microstructure observation revealed that M23C6 carbide was precipitated along the grain boundary and within the matrix.

Keywords: Fe-20Cr-5Al alloy, high temperature deformation, aging treatment, microstructure, mechanical properties.

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Authors: Li Xu, Shouming Zhong

Abstract:

The reachable set bounding estimation for distributed delay systems with disturbances is a new problem. In this paper,we consider this problem subject to not only time varying delay and polytopic uncertainties but also distributed delay systems which is not studied fully untill now. we can obtain improved non-ellipsoidal reachable set estimation for neural networks with time-varying delay by the maximal Lyapunov-Krasovskii fuctional which is constructed as the pointwise maximum of a family of Lyapunov-Krasovskii fuctionals corresponds to vertexes of uncertain polytope.On the other hand,matrix inequalities containing only one scalar and Matlabs LMI Toolbox is utilized to give a non-ellipsoidal description of the reachable set.finally,numerical examples are given to illustrate the existing results.

Keywords: Reachable set, Distributed delay, Lyapunov-Krasovskii function, Polytopic uncertainties.

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Authors: Caigen Zhou, Haibo Jiang

Abstract:

The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive singular perturbed systems with time-varying delay is investigated by employing Lyapunov functions. The nonlinear delay system is built based on the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for global exponential stability of the closed-loop system are derived in terms of linear matrix inequalities (LMIs), which can be easily solved by LMI technique. Some simulations illustrate the effectiveness of the proposed method.

Keywords: T–S fuzzy model, singular perturbed systems, time-varying delay, robust control.

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Authors: M.Z. Norashikin, M.Z. Ibrahim

Abstract:

This report shows the performance of composite biodegradable film from chitosan, starch and sawdust fiber. The main objectives of this research are to fabricate and characterize composite biodegradable film in terms of morphology and physical properties. The film was prepared by casting method. Sawdust fiber was used as reinforcing agent and starch as polymer matrix in the casting solution. The morphology of the film was characterized using atomic force microscope (AFM). The result showed that the film has smooth structure. Chemical composition of the film was investigated using Fourier transform infrared (FTIR) where the result revealed present of starch in the film. The thermal properties were characterized using thermal gravimetric analyzer (TGA) and differential scanning calorimetric (DSC) where the results showed that the film has small difference in melting and degradation temperature.

Keywords: Sawdust, composite, film, biodegradable.

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Authors: M. Stefanovska, S. Risteska, B. Samakoski, G. Maneski, B. Kostadinoska

Abstract:

Aim of this work is to determine the theoretical and experimental properties of filament wound glass fiber/epoxy resin composite pipes with different winding design subjected under bending. For determination of bending strength of composite samples three point bending tests were conducted. Good correlation between theoretical and experimental results has been obtained, where sample No4 has shown the highest value of bending strength. All samples have demonstrated matrix cracking and fiber failure followed by layers delamination during testing. Also, it was found that smaller winding angles lead to an increase in bending stress. From presented results good merger between glass fibers and epoxy resin was confirmed by SEM analysis.

Keywords: Bending properties, composite pipe, winding design.

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Authors: Anuj Abraham, N. Pappa, Daniel Honc, Rahul Sharma

Abstract:

In this paper, an analysis of some model order reduction techniques is presented. A new hybrid algorithm for model order reduction of linear time invariant systems is compared with the conventional techniques namely Balanced Truncation, Hankel Norm reduction and Dominant Pole Algorithm (DPA). The proposed hybrid algorithm is known as Clustering Dominant Pole Algorithm (CDPA), is able to compute the full set of dominant poles and its cluster center efficiently. The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. The effectiveness of this novel technique is shown through the simulation results.

Keywords: Balanced truncation, Clustering, Dominant pole, Hankel norm, Model reduction.

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Authors: Suheyla Kocaman, Gulnare Ahmetli

Abstract:

In this study, acrylated soybean oil (AESO) was used as modifying agent for DGEBF-type epoxy resin (ER). AESO was used as a co-matrix in 50 wt % with ER. Composites with eco-friendly natural fillers-banana bark and seashell were prepared. MNA was used as a hardener. Effect of banana peel (BP) and seashell (SSh) fillers on mechanical properties, such as tensile strength, elongation at break, and hardness of M-ERs were investigated. The structure epoxy resins (M-ERs) cured with MNA and sebacic acid (SAc) hardeners were characterized by Fourier transform infrared spectroscopy (FTIR). Tensile test results show that Young’s (elastic) modulus, tensile strength and hardness of SSh particles reinforced with M-ERs were higher than the M-ERs reinforced with banana bark.

Keywords: Biobased composite, epoxy resin, mechanical properties, natural fillers.

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Authors: Z. Pavlík, J. Fořt, J. Žumár, M. Pavlíková, R. Černý

Abstract:

The cup method is applied for the measurement of water vapor transport properties of porous materials worldwide. However, in practical applications the experimental results are often used without taking into account some secondary effects which can play an important role under specific conditions. In this paper, the effect of temperature on water vapor transport properties of cellular concrete is studied, together with the influence of sample thickness. At first, the bulk density, matrix density, total open porosity and sorption and desorption isotherms are measured for material characterization purposes. Then, the steady state cup method is used for determination of water vapor transport properties, whereas the measurements are performed at several temperatures and for three different sample thicknesses.

Keywords: Water vapor transport, cellular concrete, cup method, temperature, sample thickness.

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Authors: Buntara Sthenly Gan

Abstract:

A novel and versatile numerical technique to solve a self-stress equilibrium state is adopted herein as a form-finding procedure for an irregular tensegrity structure. The numerical form-finding scheme of a tensegrity structure uses only the connectivity matrix and prototype tension coefficient vector as the initial guess solution. Any information on the symmetrical geometry or other predefined initial structural conditions is not necessary to get the solution in the form-finding process. An eight-node initial condition example is presented to demonstrate the efficiency and robustness of the proposed method in the form-finding of an irregular tensegrity structure. Based on the conception from the form-finding of an eight-node irregular tensegrity structure, a monumental object is designed by considering the real world situation such as self-weight, wind and earthquake loadings.

Keywords: Tensegrity, Form-finding, Design, Irregular, Self-stress, Force density method.

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Authors: Michael P. Herring, Lavrent Khachatryan, Barry Dellinger

Abstract:

Low Temperature Matrix Isolation - Electron Paramagnetic Resonance (LTMI-EPR) Spectroscopy was utilized to identify the species of iron oxide nanoparticles generated during the oxidative pyrolysis of 1-methylnaphthalene (1-MN). The otherwise gas-phase reactions of 1--MN were impacted by a polypropylenimine tetra-hexacontaamine dendrimer complexed with iron (III) nitrate nonahydrate diluted in air under atmospheric conditions. The EPR fine structure of Fe (III)2O3 nanoparticles clusters, characterized by gfactors of 2.00, 2.28, 3.76 and 4.37 were detected on a cold finger maintained at 77 K after accumulation over a multitude of experiments. Additionally, a high valence Fe (IV) paramagnetic intermediate and superoxide anion-radicals, O2•- adsorbed on nanoparticle surfaces in the form of Fe (IV) --- O2•- were detected from the quenching area of Zone 1 in the gas-phase.

Keywords: Cryogenic trapping, EPFRs, dendrimer, Fe2O3 doped silica, soot.

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Authors: M. De la Sen, O. Barambones

Abstract:

This paper presents an indirect adaptive stabilization scheme for first-order continuous-time systems under saturated input which is described by a sigmoidal function. The singularities are avoided through a modification scheme for the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be non-singular and then the estimated plant model is controllable. The modification mechanism involves the use of a hysteresis switching function. An alternative hybrid scheme, whose estimated parameters are updated at sampling instants is also given to solve a similar adaptive stabilization problem. Such a scheme also uses hysteresis switching for modification of the parameter estimates so as to ensure the controllability of the estimated plant model.

Keywords: Hybrid dynamic systems, discrete systems, saturated input, control, stabilization.

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Authors: O. Alizadeh Sahraei, A. Khodadadi, Y. Mortazavi, M. Vesali Naseh, S. Mosadegh

Abstract:

A composite made of plasma functionalized multiwall carbon nanotubes (MWNTs) coated with SnO2 was synthesized by sonochemical precipitation method. Thick layer of this nanocomposite material was used as ethanol sensor at low temperatures. The composite sensitivity for ethanol has increased by a factor of 2 at room temperature and by a factor of 13 at 250°C in comparison to that of pure SnO2. SEM image of nanocomposite material showed MWNTs were embedded in SnO2 matrix and also a higher surface area was observed in the presence of functionalized MWNTs. Greatly improved sensitivity of the composite material to ethanol can be attributed to new gas accessing passes through MWNTs and higher specific surface area.

Keywords: Carbon nanotube, Functionalized, Gas sensor, Low temperature, Nanocomposite, Tin oxide.

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Authors: Sidharth Talan, Sanjay Kumar Sharma, Eoin Joseph Wallace, Nikita Agrawal

Abstract:

Underground mining is at the core of rapidly evolving metals and minerals sector due to the increasing mineral consumption globally. Even though the surface mines are still more abundant on earth, the scales of industry are slowly tipping towards underground mining due to rising depth and complexities of orebodies. Thus, the efficient and productive functioning of underground operations depends significantly on the synchronized performance of key elements such as operating site, mining equipment, manpower and mine services. Production drilling is the process of conducting long hole drilling for the purpose of charging and blasting these holes for the production of ore in underground metal mines. Thus, production drilling is the crucial segment in the underground metal mining value chain. This paper presents the process mapping tool to evaluate the production drilling process in the underground metal mining operation by dividing the given process into three segments namely Input, Process and Output. The three segments are further segregated into factors and sub-factors. As per the study, the major input factors crucial for the efficient functioning of production drilling process are power, drilling water, geotechnical support of the drilling site, skilled drilling operators, services installation crew, oils and drill accessories for drilling machine, survey markings at drill site, proper housekeeping, regular maintenance of drill machine, suitable transportation for reaching the drilling site and finally proper ventilation. The major outputs for the production drilling process are ore, waste as a result of dilution, timely reporting and investigation of unsafe practices, optimized process time and finally well fragmented blasted material within specifications set by the mining company. The paper also exhibits the drilling loss matrix, which is utilized to appraise the loss in planned production meters per day in a mine on account of availability loss in the machine due to breakdowns, underutilization of the machine and productivity loss in the machine measured in drilling meters per unit of percussion hour with respect to its planned productivity for the day. The given three losses would be essential to detect the bottlenecks in the process map of production drilling operation so as to instigate the action plan to suppress or prevent the causes leading to the operational performance deficiency. The given tool is beneficial to mine management to focus on the critical factors negatively impacting the production drilling operation and design necessary operational and maintenance strategies to mitigate them. 

Keywords: Process map, drilling loss matrix, availability, utilization, productivity, percussion rate.

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Authors: Theodor D. Popescu

Abstract:

The paper presents a method for multivariate time series forecasting using Independent Component Analysis (ICA), as a preprocessing tool. The idea of this approach is to do the forecasting in the space of independent components (sources), and then to transform back the results to the original time series space. The forecasting can be done separately and with a different method for each component, depending on its time structure. The paper gives also a review of the main algorithms for independent component analysis in the case of instantaneous mixture models, using second and high-order statistics. The method has been applied in simulation to an artificial multivariate time series with five components, generated from three sources and a mixing matrix, randomly generated.

Keywords: Independent Component Analysis, second order statistics, simulation, time series forecasting

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Authors: Zixin Liu, Huawei Yang, Fangwei Chen

Abstract:

This paper studies the mean square exponential synchronization problem of a class of stochastic neutral type chaotic neural networks with mixed delay. On the Basis of Lyapunov stability theory, some sufficient conditions ensuring the mean square exponential synchronization of two identical chaotic neural networks are obtained by using stochastic analysis and inequality technique. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. The feedback controller used in this paper is more general than those used in previous literatures. One simulation example is presented to demonstrate the effectiveness of the derived results.

Keywords: Exponential synchronization, stochastic analysis, chaotic neural networks, neutral type system.

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Authors: Fatima Setti, Ezziane Karim, Setti Bakhti, Negadi Kheira

Abstract:

The objective of this study is to present and to analyze the feasibility of using steel fibers as reinforcement in the cementations matrix to minimize the effect of free shrinkage which is a major cause of cracks that have can observe on concrete structures, also to improve the mechanical resistances of this concrete reinforced. The experimental study was performed on specimens with geometric characteristics adapted to the testing. The tests of shrinkage apply on prismatic specimens, equipped with rods fixed to the ends with different dosages of fibers, it should be noted that the fibers used are hooked end of 50mm length and 67 slenderness. The results show that the compressive strength and flexural strength increases as the degree of incorporation of fibbers increases. And the shrinkage deformations are generally less important for fibers-reinforced concrete to those appearing in the concrete without fibers.

Keywords: Concrete, Steel fibers, Compression, Flexural, Deformation.

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Authors: Jing Zhang, Yongqin Chang, Yongwei Wang, Xiaolin Li, Shaoning Jiang, Farong Wan, Yi Long

Abstract:

Microstructural and hardening changes of Fe-0.2wt.%V alloy and pure Fe irradiated with 100 keV hydrogen ions at room temperature were investigated. It was found that dislocation density varies dramatically after irradiation, ranging from dislocation free to dense areas with tangled and complex dislocation configuration. As the irradiated Fe-0.2wt.%V samples were annealed at 773 K, the irradiation-induced dislocation loops disappear, while many small precipitates with enriched C distribute in the matrix. Some large precipitates with enriched V were also observed. The hardness of Fe-0.2wt.%V alloy and pure Fe increases after irradiation, which ascribes to the formation of dislocation loops in the irradiated specimens. Compared with pure Fe, the size of the irradiation-introduced dislocation loops in Fe-0.2wt.%V alloy decreases and the density increases, the change of the hardness also decreases.

Keywords: Irradiation, Fe-0.2wt.%V alloy, microstructures, hardness.

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Authors: Jasna Dragosavac, Žarko Janda, J.V. Milanović, Dušan Arnautović

Abstract:

This paper discusses coordinated reactive power - voltage (Q-V) control in a multi machine steam power plant. The drawbacks of manual Q-V control are briefly listed, and the design requirements for coordinated Q-V controller are specified. Theoretical background and mathematical model of the new controller are presented next followed by validation of developed Matlab/Simulink model through comparison with recorded responses in real steam power plant and description of practical realisation of the controller. Finally, the performance of commissioned controller is illustrated on several examples of coordinated Q-V control in real steam power plant and compared with manual control.

Keywords: Coordinated Voltage Control, Power Plant Control, Reactive Power Control, Sensitivity Matrix

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Authors: Dharmveer Singh Rajput , P. K. Singh, Mahua Bhattacharya

Abstract:

Clustering in high dimensional space is a difficult problem which is recurrent in many fields of science and engineering, e.g., bioinformatics, image processing, pattern reorganization and data mining. In high dimensional space some of the dimensions are likely to be irrelevant, thus hiding the possible clustering. In very high dimensions it is common for all the objects in a dataset to be nearly equidistant from each other, completely masking the clusters. Hence, performance of the clustering algorithm decreases. In this paper, we propose an algorithmic framework which combines the (reduct) concept of rough set theory with the k-means algorithm to remove the irrelevant dimensions in a high dimensional space and obtain appropriate clusters. Our experiment on test data shows that this framework increases efficiency of the clustering process and accuracy of the results.

Keywords: High dimensional clustering, sub-space, k-means, rough set, discernibility matrix.

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