Search results for: joint probability density matrix

Authors: N. A. Salim, M. M. Othman, I. Musirin, M. S. Serwan

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Hidden failure in a protection system has been recognized as one of the main reasons which may cause to a power system instability leading to a system cascading collapse. This paper presents a computationally systematic approach used to obtain the estimated average probability of a system cascading collapse by considering the effect of probability hidden failure in a protection system. The estimated average probability of a system cascading collapse is then used to determine the severe loading condition contributing to the higher risk of critical system cascading collapse. This information is essential to the system utility since it will assist the operator to determine the highest point of increased system loading condition prior to the event of critical system cascading collapse.

Keywords: Critical system cascading collapse, protection system hidden failure, severe loading condition.

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Authors: Long Kim Vu, Ban Dang Nguyen

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In this paper, the finite element method (FEM) is utilized to simulate the comprehensive process including tightening, releasing and self-loosening of a bolt joint under transverse vibration. Following to the accurate geometry of helical threads, an absolutely hexahedral meshing is implemented. The accuracy of simulation process is verified and validated by comparison with the experimental results on clamping force-vibration relationship, which shows the sufficient correlation. Further analysis with different amplitude and frequency of transverse vibration is done to determine the dominant factor inducing the failure.

Keywords: Bolt self-loosening, contact state, FEM, transverse vibration.

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Authors: Yilun Shang

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In this paper we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process. The transition probability matrix and stationary distribution are derived for the Markov chains concerning connectivity and the number of components. We analyze the algorithm for hitting time regarding disconnectivity. In addition to dynamical properties, we also study topological properties for static snapshots. We obtain the degree distributions as well as asymptotic precise bounds and strong law of large numbers for connectivity threshold distance and the largest nearest neighbor distance amongst others. Both exact results and limit theorems are provided in this paper.

Keywords: random geometric graph, autoregressive process, degree, connectivity, Markovian, wireless network.

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Authors: Nao-Aki Noda, Yu Zhang, Ken-Tarou Takaishi, Hiroyuki Shibahara

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In this paper the strength of adhesive joint under tension and bending is discussed on the basis of intensity of singular stress by the application of FEM. A useful method is presented with focusing on the stress at the edge of interface between the adhesive and adherent obtained by FEM. After analyzing the adhesive joint strength with all material combinations, it is found that to improve the interface strength, thin adhesive layers are desirable because the intensity of singular stress decreases with decreasing the thickness.

Keywords: Adhesive, Adherent, Intensity of singular stress, Bonded strip

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Authors: J. P. P. Andrade, V. A. F. Campos

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This work presents an application of Linear Matrix Inequalities (LMI) for the robust control of an F-16 aircraft through an algorithm ensuring the damping factor to the closed loop system. The results show that the zero and gain settings are sufficient to ensure robust performance and stability with respect to various operating points. The technique used is the pole placement, which aims to put the system in closed loop poles in a specific region of the complex plane. Test results using a dynamic model of the F-16 aircraft are presented and discussed.

Keywords: F-16 Aircraft, linear matrix inequalities, pole placement, robust control.

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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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Authors: J.H. Park, S. Lakshmanan, H.Y. Jung, S.M. Lee

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This paper is concerned with the delay-distributiondependent stability criteria for bidirectional associative memory (BAM) neural networks with time-varying delays. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is derived to achieve the globally asymptotically mean square stable of the considered BAM neural networks. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulation is given to demonstrate the usefulness and effectiveness of the proposed results.

Keywords: BAM neural networks, Probabilistic time-varying delays, Stability criteria.

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Authors: Andy Handouyahia, Tony Haddad, Frank Eaton

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Recent quasi-experimental evaluation of the Canadian Active Labour Market Policies (ALMP) by Human Resources and Skills Development Canada (HRSDC) has provided an opportunity to examine alternative methods to estimating the incremental effects of Employment Benefits and Support Measures (EBSMs) on program participants. The focus of this paper is to assess the efficiency and robustness of inverse probability weighting (IPW) relative to kernel matching (KM) in the estimation of program effects. To accomplish this objective, the authors compare pairs of 1,080 estimates, along with their associated standard errors, to assess which type of estimate is generally more efficient and robust. In the interest of practicality, the authorsalso document the computationaltime it took to produce the IPW and KM estimates, respectively.

Keywords: Treatment effect, causal inference, observational studies, Propensity score based matching, Kernel Matching, Inverse Probability Weighting, Estimation methods for incremental effect.

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Authors: P. Mounnarath, U. Schmitz, Ch. Zhang

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Fragility analysis is an effective tool for the seismic vulnerability assessment of civil structures in the last several years. The design of the expansion joints according to various bridge design codes is almost inconsistent, and only a few studies have focused on this problem so far. In this study, the influence of the expansion joint clearances between the girder ends and the abutment backwalls on the seismic fragility assessment of continuous integral bridge frames is investigated. The gaps (ranging from 60 mm, 150 mm, 250 mm and 350 mm) are designed by following two different bridge design code specifications, namely, Caltrans and Eurocode 8-2. Five bridge models are analyzed and compared. The first bridge model serves as a reference. This model uses three-dimensional reinforced concrete fiber beam-column elements with simplified supports at both ends of the girder. The other four models also employ reinforced concrete fiber beam-column elements but include the abutment backfill stiffness and four different gap values. The nonlinear time history analysis is performed. The artificial ground motion sets, which have the peak ground accelerations (PGAs) ranging from 0.1 g to 1.0 g with an increment of 0.05 g, are taken as input. The soil-structure interaction and the P-Δ effects are also included in the analysis. The component fragility curves in terms of the curvature ductility demand to the capacity ratio of the piers and the displacement demand to the capacity ratio of the abutment sliding bearings are established and compared. The system fragility curves are then obtained by combining the component fragility curves. Our results show that in the component fragility analysis, the reference bridge model exhibits a severe vulnerability compared to that of other sophisticated bridge models for all damage states. In the system fragility analysis, the reference curves illustrate a smaller damage probability in the earlier PGA ranges for the first three damage states, they then show a higher fragility compared to other curves in the larger PGA levels. In the fourth damage state, the reference curve has the smallest vulnerability. In both the component and the system fragility analysis, the same trend is found that the bridge models with smaller clearances exhibit a smaller fragility compared to that with larger openings. However, the bridge model with a maximum clearance still induces a minimum pounding force effect.

Keywords: Expansion joint clearance, fiber beam-column element, fragility assessment, time history analysis.

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Authors: S. Mogili, J. S. Kuang, N. Zhang

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Knee joints, the beam column connections found at the roof level of a moment resisting frame buildings, are inherently different from conventional interior and exterior beam column connections in the way that forces from adjoining members are transferred into joint and then resisted by the joint. A knee connection has two distinct load resisting mechanisms, each for closing and opening actions acting simultaneously under reversed cyclic loading. In spite of many distinct differences in the behaviour of shear resistance in knee joints, there are no special design provisions in the major design codes available across the world due to lack of in-depth research on the knee connections. To understand the relative importance of opening and closing actions in design, it is imperative to study knee joints under varying shear stresses, especially at higher opening-to-closing shear stress ratios. Three knee joint specimens, under different input shear stresses, were designed to produce a varying ratio of input opening to closing shear stresses. The design was carried out in such a way that the ratio of flexural strength of beams with consideration of axial forces in opening to closing actions are maintained at 0.5, 0.7, and 1.0, thereby resulting in the required variation of opening to closing joint shear stress ratios among the specimens. The behaviour of these specimens was then carefully studied in terms of closing and opening capacities, hysteretic behaviour, and envelope curves to understand the differences in joint performance based on which an attempt to suggest design guidelines for knee joints is made emphasizing the relative importance of opening and closing actions. Specimens with relatively higher opening stresses were observed to be more vulnerable under the action of seismic loading.

Keywords: Knee-joints, large-scale testing, opening and closing shear stresses, seismic performance.

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Authors: Kong Fah Tee, Lutfor Rahman Khan, Hongshuang Li

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An advanced Monte Carlo simulation method, called Subset Simulation (SS) for the time-dependent reliability prediction for underground pipelines has been presented in this paper. The SS can provide better resolution for low failure probability level with efficient investigating of rare failure events which are commonly encountered in pipeline engineering applications. In SS method, random samples leading to progressive failure are generated efficiently and used for computing probabilistic performance by statistical variables. SS gains its efficiency as small probability event as a product of a sequence of intermediate events with larger conditional probabilities. The efficiency of SS has been demonstrated by numerical studies and attention in this work is devoted to scrutinise the robustness of the SS application in pipe reliability assessment. It is hoped that the development work can promote the use of SS tools for uncertainty propagation in the decision-making process of underground pipelines network reliability prediction.

Keywords: Underground pipelines, Probability of failure, Reliability and Subset Simulation.

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Authors: Fenglong Guo, Dingcheng Wang

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This paper studies ruin probabilities in two discrete-time risk models with premiums, claims and rates of interest modelled by three autoregressive moving average processes. Generalized Lundberg inequalities for ruin probabilities are derived by using recursive technique. A numerical example is given to illustrate the applications of these probability inequalities.

Keywords: Lundberg inequality, NWUC, Renewal recursive technique, Ruin probability

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Authors: Shenq Yih Luo, Chung Hsien Lu

Abstract:

The aluminum bronze matrix alumina composites using hot press and resin infiltration were investigated to study their porosities, hardness, bending strengths, and microstructures. The experiment results show that the hardness of the sintered composites with the decrease of porosity increases. The composites without and with resin infiltration have about HRF 42-61 of about 34-40% of porosity and about HRF 62-83 of about 30-36% of porosity, respectively. Besides, the alumina composites contain a more amount of iron and nickel powders would cause a lower bending strength due to forming some weaker bonding among the iron, nickel, copper, aluminum under this hot pressing of shorter time.

Keywords: Aluminum bronze matrix composite, bending strength, hot pressing, porosity.

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Authors: J. Prakash, K. Rajesh

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In this paper we propose a novel method for human face segmentation using the elliptical structure of the human head. It makes use of the information present in the edge map of the image. In this approach we use the fact that the eigenvalues of covariance matrix represent the elliptical structure. The large and small eigenvalues of covariance matrix are associated with major and minor axial lengths of an ellipse. The other elliptical parameters are used to identify the centre and orientation of the face. Since an Elliptical Hough Transform requires 5D Hough Space, the Circular Hough Transform (CHT) is used to evaluate the elliptical parameters. Sparse matrix technique is used to perform CHT, as it squeeze zero elements, and have only a small number of non-zero elements, thereby having an advantage of less storage space and computational time. Neighborhood suppression scheme is used to identify the valid Hough peaks. The accurate position of the circumference pixels for occluded and distorted ellipses is identified using Bresenham-s Raster Scan Algorithm which uses the geometrical symmetry properties. This method does not require the evaluation of tangents for curvature contours, which are very sensitive to noise. The method has been evaluated on several images with different face orientations.

Keywords: Circular Hough Transform, Covariance matrix, Eigenvalues, Elliptical Hough Transform, Face segmentation, Raster Scan Algorithm.

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Authors: Tawiwat V., Tosapolporn P., Kedit J.

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This research proposes the state of art on how to control or find the trajectory paths of the RRP robot when the prismatic joint is malfunction. According to this situation, the minimum energy of the dynamic optimization is applied. The RRP robot or similar systems have been used in many areas such as fire fighter truck, laboratory equipment and military truck for example a rocket launcher. In order to keep on task that assigned, the trajectory paths must be computed. Here, the open loop control is applied and the result of an example show the reasonable solution which can be applied to the controllable system.

Keywords: RRP robot, Optimal Control, Minimum Energy and Under Actuator.

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Authors: Ju-Hong Lee, Ching-Wei Liao, Kun-Che Lee

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This paper deals with the problem of using antenna sensors for adaptive beamforming in the presence of random steering mismatch. We present an efficient adaptive array beamformer with robustness to deal with the considered problem. The robustness of the proposed beamformer comes from the efficient designation of the steering vector. Using the received array data vector, we construct an appropriate correlation matrix associated with the received array data vector and a correlation matrix associated with signal sources. Then, the eigenvector associated with the largest eigenvalue of the constructed signal correlation matrix is designated as an appropriate estimate of the steering vector. Finally, the adaptive weight vector required for adaptive beamforming is obtained by using the estimated steering vector and the constructed correlation matrix of the array data vector. Simulation results confirm the effectiveness of the proposed method.

Keywords: Adaptive beamforming, antenna array, linearly constrained minimum variance, robustness, steering vector.

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Authors: Yu T. Tsai, Jin H. Huang

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In this paper, the specific sound Transmission Loss (TL) of the Laminated Composite Plate (LCP) with different material properties in each layer is investigated. The numerical method to obtain the TL of the LCP is proposed by using elastic plate theory. The transfer matrix approach is novelty presented for computational efficiency in solving the numerous layers of dynamic stiffness matrix (D-matrix) of the LCP. Besides the numerical simulations for calculating the TL of the LCP, the material properties inverse method is presented for the design of a laminated composite plate analogous to a metallic plate with a specified TL. As a result, it demonstrates that the proposed computational algorithm exhibits high efficiency with a small number of iterations for achieving the goal. This method can be effectively employed to design and develop tailor-made materials for various applications.

Keywords: Sound transmission loss, laminated composite plate, transfer matrix approach, inverse problem, elastic plate theory, material properties.

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Authors: Tudor Petreuş, Andrei Neamţu, Cristina Dascălu, Paul Dan Sîrbu, Carmen E. Cotrutz

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Matrix metalloproteinases (MMP) are a class of structural and functional related enzymes involved in altering the natural elements of the extracellular matrix. Most of the MMP structures are cristalographycally determined and published in WorldWide ProteinDataBank, isolated, in full structure or bound to natural or synthetic inhibitors. This study proposes an algorithm to replace missing crystallographic structures in PDB database. We have compared the results of a chosen docking algorithm with a known crystallographic structure in order to validate enzyme sites reconstruction there where crystallographic data are missing.

Keywords: matrix metalloproteinases, molecular docking, structure superposition, surface complementarity.

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Authors: K. Kalaiselvan, Naresh Subramania Warrier, S. Elavarasi

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Several situations arise in industrial practice which calls for joining of dissimilar metals. With increasing demand in the application requirements, dissimilar metal joining becomes inevitable in modern engineering industries. The metals employed are the structure for effective and utilization of the special properties of each metal. The purpose of this paper is to present the research and development status of titanium (Ti) and aluminium (Al) dissimilar alloys weldment by the researchers worldwide. The detailed analysis of problems faced during welding of dissimilar metal joint for Ti/Al metal combinations are discussed. Microstructural variations in heat affected zone (HAZ), fusion zone (FZ), Intermetallic compound (IMC) layer and surface fracture of weldments are analysed. Additionally, mechanical property variations and microstructural feature have been studied by the researchers. The paper provides a detailed literature review of Ti/Al dissimilar metal joint microchemistry and property variation across the weldment.

Keywords: Laser beam welding, titanium, aluminium, metallurgical properties.

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Authors: T. N. Janakiraman, P. V. S. S. R. Chandra Mouli

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A color image edge detection algorithm is proposed in this paper using Pseudo-complement and matrix rotation operations. First, pseudo-complement method is applied on the image for each channel. Then, matrix operations are applied on the output image of the first stage. Dominant pixels are obtained by image differencing between the pseudo-complement image and the matrix operated image. Median filtering is carried out to smoothen the image thereby removing the isolated pixels. Finally, the dominant or core pixels occurring in at least two channels are selected. On plotting the selected edge pixels, the final edge map of the given color image is obtained. The algorithm is also tested in HSV and YCbCr color spaces. Experimental results on both synthetic and real world images show that the accuracy of the proposed method is comparable to other color edge detectors. All the proposed procedures can be applied to any image domain and runs in polynomial time.

Keywords: Color edge detection, dominant pixels, matrixrotation/shift operations, pseudo-complement.

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Authors: Viriyavudh Sim, Woo Young Jung

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The failure of roof cladding mostly occurs due to the failing of the connection between claddings and purlins, which is the pull-out of the screw connecting the two parts when the pull-out load, i.e. typhoon, is higher than the resistance of the connection screw. As typhoon disasters in Korea are constantly on the rise, probability risk assessment (PRA) has become a vital tool to evaluate the performance of civil structures. In this study, we attempted to determine the fragility of roof cladding with the screw connection. Experimental study was performed to evaluate the pull-out resistance of screw joints between honeycomb panels and back frames. Subsequently, by means of Monte Carlo Simulation method, probability of failure for these types of roof cladding was determined. The results that the failure of roof cladding was depends on their location on the roof, for example, the edge most panel has the highest probability of failure.

Keywords: Monte Carlo Simulation, roof cladding, screw pull-out strength, wind fragility

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Authors: Biao Qin, Jin Huang, Jiaojiao Ren, Wei Kang

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This paper deals with the problem of passivity analysis for stochastic neural networks with leakage, discrete and distributed delays. By using delay partitioning technique, free weighting matrix method and stochastic analysis technique, several sufficient conditions for the passivity of the addressed neural networks are established in terms of linear matrix inequalities (LMIs), in which both the time-delay and its time derivative can be fully considered. A numerical example is given to show the usefulness and effectiveness of the obtained results.

Keywords: Passivity, Stochastic neural networks, Multiple time delays, Linear matrix inequalities (LMIs).

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Authors: Wen Liu

Abstract:

With the rapid progress of modern cities, the railway construction must be developing quickly in China.As a typical high-density country, shopping center on the subway should be one important factor during the process of urban development. The paper discusses the influence of the layout of shopping center on the subway, and put it in the time and space’s axis of Shanghai urban development. We usethe digital technology to establish the database of relevant information. And then get the change role about shopping center on subway in Shanghaiby the Kernel density estimate.The result shows the development of shopping center on subway has a relationship with local economic strength, population size, policysupport, and city construction. And the suburbanization trend of shopping center would be increasingly significant.By this case research, we could see the Kernel density estimate is an efficient analysis method on the spatial layout. It could reveal the characters of layout form of shopping center on subway in essence. And it can also be applied to the other research of space form.

Keywords: Shanghai, Shopping center on the subway, Layout form, The Kernel density estimate.

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Authors: Armando Calabrese, Roberta Costa, Tamara Menichini, Francesco Rosati

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As a company competitiveness depends more and more on the relationship with its stakeholders, the topic of companystakeholder fit is becoming increasingly important. This fit affects the extent to which a stakeholder perceives CSR company commitment, values and behaviors and, therefore, stakeholder identification in a company and his/her loyalty to it. Consequently, it is important to measure the alignment or the gap between stakeholder CSR demands, values, preferences and perceptions, and the company CSR disclosed commitment, values and policies. In this paper, in order to assess the company-stakeholder fit about corporate responsibility, an innovative CSR fit positioning matrix is proposed. This matrix is based on the measurement of a company CSR disclosed commitment and stakeholder perceived and required commitment. The matrix is part of a more complex methodology based on Global Reporting Initiative (GRI) indicators, content analysis and stakeholder questionnaires. This methodology provides appropriate indications for helping companies to achieve CSR company-stakeholder fit, by leveraging both CSR commitment and communication. Moreover, it could be used by top management for comparing different companies and stakeholders, and for planning specific CSR strategies, policies and activities.

Keywords: Company-Stakeholder fit, Corporate Social Responsibility (CSR), CSR Positioning Matrix, Global Reporting Initiative (GRI), Stakeholder Orientation.

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Authors: M. Chandrasekaran, D. Devarasiddappa

Abstract:

Metal matrix composites have been increasingly used as materials for components in automotive and aerospace industries because of their improved properties compared with non-reinforced alloys. During machining the selection of appropriate machining parameters to produce job for desired surface roughness is of great concern considering the economy of manufacturing process. In this study, a surface roughness prediction model using fuzzy logic is developed for end milling of Al-SiCp metal matrix composite component using carbide end mill cutter. The surface roughness is modeled as a function of spindle speed (N), feed rate (f), depth of cut (d) and the SiCp percentage (S). The predicted values surface roughness is compared with experimental result. The model predicts average percentage error as 4.56% and mean square error as 0.0729. It is observed that surface roughness is most influenced by feed rate, spindle speed and SiC percentage. Depth of cut has least influence.

Keywords: End milling, fuzzy logic, metal matrix composites, surface roughness

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Authors: Ping He, Heng-You Lan, Gong-Quan Tan

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The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matrix theory. An illustrative example and the simulation result, show that the approach to linear systems with multiple time-delays is effective.

Keywords: Linear system, Delay-independent stabilization, Lyapunovfunctional, Riccati algebra matrix equation.

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Authors: Muhammad Salam, Nasir Rashid, Shah Khalid, Muhammad Raees Khan

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In this paper a modified version NXM of traditional 5X5 playfair cipher is introduced which enable the user to encrypt message of any Natural language by taking appropriate size of the matrix depending upon the size of the natural language. 5X5 matrix has the capability of storing only 26 characters of English language and unable to store characters of any language having more than 26 characters. To overcome this limitation NXM matrix is introduced which solve this limitation. In this paper a special case of Urdu language is discussed. Where # is used for completing odd pair and * is used for repeating letters.

Keywords: cryptography, decryption, encryption, playfair cipher, traditional cipher.

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Authors: J. P. Dubois

Abstract:

This paper reports the feasibility of the ARMA model to describe a bursty video source transmitting over a AAL5 ATM link (VBR traffic). The traffic represents the activity of the action movie "Lethal Weapon 3" transmitted over the ATM network using the Fore System AVA-200 ATM video codec with a peak rate of 100 Mbps and a frame rate of 25. The model parameters were estimated for a single video source and independently multiplexed video sources. It was found that the model ARMA (2, 4) is well-suited for the real data in terms of average rate traffic profile, probability density function, autocorrelation function, burstiness measure, and the pole-zero distribution of the filter model.

Keywords: ARMA, ATM networks, burstiness, multimediatraffic, VBR video.

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Authors: Nasrul Amri Mohd Amin, Martin Belusko, Frank Bruno

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PCMs have always been viewed as a suitable candidate for off peak thermal storage, particularly for refrigeration systems, due to the high latent energy densities of these materials. However, due to the need to have them encapsulated within a container this density is reduced. Furthermore, PCMs have a low thermal conductivity which reduces the useful amount of energy which can be stored. To consider these factors, the true energy storage density of a PCM system was proposed and optimised for PCMs encapsulated in slabs. Using a validated numerical model of the system, a parametric study was undertaken to investigate the impact of the slab thickness, gap between slabs and the mass flow rate. The study showed that, when optimised, a PCM system can deliver a true energy storage density between 53% and 83% of the latent energy density of the PCM.

Keywords: Phase change material, refrigeration, sustainability, thermal energy storage.

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Authors: Mohammed H. Rady, Mohd Sukri Mustapa, S Shamsudin, M. A. Lajis, A. Wagiman

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The present study is aimed at investigating microhardness and density of aluminium alloy chips when subjected to various settings of preheating temperature and preheating time. Three values of preheating temperature were taken as 450 °C, 500 °C, and 550 °C. On the other hand, three values of preheating time were chosen (1, 2, 3) hours. The influences of the process parameters (preheating temperature and time) were analyzed using Design of Experiments (DOE) approach whereby full factorial design with center point analysis was adopted. The total runs were 11 and they comprise of two factors of full factorial design with 3 center points. The responses were microhardness and density. The results showed that the density and microhardness increased with decreasing the preheating temperature. The results also found that the preheating temperature is more important to be controlled rather than the preheating time in microhardness analysis while both the preheating temperature and preheating time are important in density analysis. It can be concluded that setting temperature at 450 °C for 1 hour resulted in the optimum responses.

Keywords: AA6061, density, DOE, hot extrusion, microhardness.

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