Search results for: Linear matrix inequality(LMI).

Authors: S. H. Nasseri, E. Ardil, A. Yazdani, R. Zaefarian

Abstract:

The fuzzy set theory has been applied in many fields, such as operations research, control theory, and management sciences, etc. In particular, an application of this theory in decision making problems is linear programming problems with fuzzy numbers. In this study, we present a new method for solving fuzzy number linear programming problems, by use of linear ranking function. In fact, our method is similar to simplex method that was used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy number linear programming, rankingfunction, simplex method.

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Authors: Roozbeh Mansouri, Hassan Hadidi

Abstract:

Truss spars are used for oil exploitation in deep and ultra-deep water if storage crude oil is not needed. The linear hydrodynamic analysis of truss spar in random sea wave load is necessary for determining the behaviour of truss spar. This understanding is not only important for design of the mooring lines, but also for optimising the truss spar design. In this paper linear hydrodynamic analysis of truss spar is carried out in frequency domain. The hydrodynamic forces are calculated using the modified Morison equation and diffraction theory. Added mass and drag coefficients of truss section computed by transmission matrix and normal acceleration and velocity component acting on each element and for hull section computed by strip theory. The stiffness properties of the truss spar can be separated into two components; hydrostatic stiffness and mooring line stiffness. Then, platform response amplitudes obtained by solved the equation of motion. This equation is non-linear due to viscous damping term therefore linearised by iteration method [1]. Finally computed RAOs and significant response amplitude and results are compared with experimental data.

Keywords: Truss Spar, Hydrodynamic analysis, Wave spectrum, Frequency Domain

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Authors: M. T. Sichani, B. J. Pedersen, S. R. K. Nielsen

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Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper an empirical cross spectral density function for the along-wind turbulence component over the wind field area is taken as the starting point. The spectrum is spatially discretized in terms of a Hermitian cross-spectral density matrix for the turbulence state vector which turns out not to be positive definite. Since the succeeding state space and ARMA modelling of the turbulence rely on the positive definiteness of the cross-spectral density matrix, the problem with the non-positive definiteness of such matrices is at first addressed and suitable treatments regarding it are proposed. From the adjusted positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modelling method is proposed which allows selection of an appropriate model order, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modelling method.

Keywords: Turbulence, wind turbine, complex coherence, state space modelling, ARMA modelling.

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Authors: A. M. Nazari, B. Sepehrian, M. Jabari

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In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvectors are given. At last we study the special cases and get some remarkable results.

Keywords: Householder matrix, nonnegative matrix, Inverse eigenvalue problem.

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Authors: R. B. Ogunrinde, C. C. Jibunoh

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In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: Spectral decomposition, eigenvalues of the Jacobian, linear RHS, homogeneous linear systems.

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Authors: Guiding Gu, Guo Liu

Abstract:

We discuss the convergence property of the minimum residual (MINRES) method for the solution of complex shifted Hermitian system (αI + H)x = f. Our convergence analysis shows that the method has a faster convergence than that for real shifted Hermitian system (Re(α)I + H)x = f under the condition Re(α) + λmin(H) > 0, and a larger imaginary part of the shift α has a better convergence property. Numerical experiments show such convergence properties.

Keywords: complex shifted linear system, Hermitian matrix, MINRES method.

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Authors: Mengzhuo Luo, Shouming Zhong

Abstract:

This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived.

Keywords: Delay-dependent stability, Neural networks, Time varying delay, Linear matrix inequality (LMI).

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Authors: Jianqiao. Yu, Jianbo. Wang, Xinzhen. He

Abstract:

This paper presents a longitudinal quasi-linear model for the ADMIRE model. The ADMIRE model is a nonlinear model of aircraft flying in the condition of high angle of attack. So it can-t be considered to be a linear system approximately. In this paper, for getting the longitudinal quasi-linear model of the ADMIRE, a state transformation based on differentiable functions of the nonscheduling states and control inputs is performed, with the goal of removing any nonlinear terms not dependent on the scheduling parameter. Since it needn-t linear approximation and can obtain the exact transformations of the nonlinear states, the above-mentioned approach is thought to be appropriate to establish the mathematical model of ADMIRE. To verify this conclusion, simulation experiments are done. And the result shows that this quasi-linear model is accurate enough.

Keywords: quasi-linear model, simulation, state transformation approach, the ADMIRE model.

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Authors: Julian Iliev

Abstract:

Currently, philosophical interpretations of The Matrix trilogy have seen a decline. This study examines the human pods and growing fields in The Matrix trilogy. Their functionality is juxtaposed to Michel Foucault’s concept of docile bodies, linking fictional and contemporary worlds. The comparison illustrates the effects of body manipulation. This paradigm is scrutinized through the power of invisibility. The invisibility of the human pods and fields parallels the hidden algorithms employed by contemporary tech giants. The utilization and secondary manipulation of user’s data are further veiled in secrecy.

Keywords: Docile bodies, film trilogies, Matrix movies, Michel Foucault, visibility, invisibility.

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Authors: Watcharakorn Thongchuay, Puntip Toghaw, Montri Maleewong

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The Wavelet-Galerkin finite element method for solving the one-dimensional heat equation is presented in this work. Two types of basis functions which are the Lagrange and multi-level wavelet bases are employed to derive the full form of matrix system. We consider both linear and quadratic bases in the Galerkin method. Time derivative is approximated by polynomial time basis that provides easily extend the order of approximation in time space. Our numerical results show that the rate of convergences for the linear Lagrange and the linear wavelet bases are the same and in order 2 while the rate of convergences for the quadratic Lagrange and the quadratic wavelet bases are approximately in order 4. It also reveals that the wavelet basis provides an easy treatment to improve numerical resolutions that can be done by increasing just its desired levels in the multilevel construction process.

Keywords: Galerkin finite element method, Heat equation , Lagrange basis function, Wavelet basis function.

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Authors: Ratchada Sopakayang, Gerhard A. Holzapfel

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In this study, a new constitutive model is developed to describe the hyperelastic behavior of collagenous tissues with a parallel arrangement of collagen fibers such as ligaments and tendons. The model is formulated using a continuum approach incorporating the structural changes of the main tissue components: collagen fibers, proteoglycan-rich matrix and fiber-matrix interaction. The mechanical contribution of the interaction between the fibers and the matrix is simply expressed by a coupling term. The structural change of the collagen fibers is incorporated in the constitutive model to describe the activation of the fibers under tissue straining. Finally, the constitutive model can easily describe the stress-stretch nonlinearity which occurs when a ligament/tendon is axially stretched. This study shows that the interaction between the fibers and the matrix contributes to the mechanical tissue response. Therefore, the model may lead to a better understanding of the physiological mechanisms of ligaments and tendons under axial loading.

Keywords: Hyperelasticity, constitutive model, fiber-matrix interaction, ligament, tendon.

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Authors: R. N. Rao, S. L. Tulasi Devi

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Tribological behavior and wear regimes of ascast and heattreted Al-Cu-Mg matrix composites containing SiC particles were studied using a pin-on-disc wear testing apparatus against an EN32 steel counterface giving emphasis on wear rate as a function of applied pressures (0.2, 0.6, 1.0 and 1.4 MPa) at different sliding distances (1000, 2000, 3000, 4000 and 5000 meters) and at a fixed sliding speed of 3.35m/s. The results showed that the composite exhibited lower wear rate than that of the matrix alloy and the wear rate of the composites is noted to be invariant to the sliding distance and is reducing by heat treatment. Wear regimes such as low, mild and severe wear were observed as per the Archard-s wear calculations. It is very interesting to note that the mild wear is almost constant in all the wear regimes.

Keywords: Aluminum, matrix, regimes, wear.

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Authors: P.-W. Tsai, W.-L. Hong, C.-W. Chen, C.-Y. Chen

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In this paper, we present a neural-network (NN) based approach to represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov Stability, Parallel Particle Swarm Optimization, Linear Differential Inclusion, Artificial Intelligence.

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Authors: A. G. Sifalakis, E. P. Papadopoulou, Y. G. Saridakis

Abstract:

A generalized Dirichlet to Neumann map is one of the main aspects characterizing a recently introduced method for analyzing linear elliptic PDEs, through which it became possible to couple known and unknown components of the solution on the boundary of the domain without solving on its interior. For its numerical solution, a well conditioned quadratically convergent sine-Collocation method was developed, which yielded a linear system of equations with the diagonal blocks of its associated coefficient matrix being point diagonal. This structural property, among others, initiated interest for the employment of iterative methods for its solution. In this work we present a conclusive numerical study for the behavior of classical (Jacobi and Gauss-Seidel) and Krylov subspace (GMRES and Bi-CGSTAB) iterative methods when they are applied for the solution of the Dirichlet to Neumann map associated with the Laplace-s equation on regular polygons with the same boundary conditions on all edges.

Keywords: Elliptic PDEs, Dirichlet to Neumann Map, Global Relation, Collocation, Iterative Methods, Jacobi, Gauss-Seidel, GMRES, Bi-CGSTAB.

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Authors: Minto Rattan, Tania Bose, Neeraj Chamoli

Abstract:

The present paper investigates the effect of linear thermal gradient on the steady-state creep behavior of rotating isotropic disc using threshold stress based Sherby’s creep law. The composite discs made of aluminum matrix reinforced with silicon carbide particulate has been taken for analysis. The stress and strain rate distributions have been calculated for discs rotating at linear thermal gradation using von Mises’ yield criterion. The material parameters have been estimated by regression fit of the available experimental data. The results are displayed and compared graphically in designer friendly format for the above said temperature profile with the disc operating under uniform temperature profile. It is observed that radial and tangential stresses show minor variation and the strain rates vary significantly in the presence of thermal gradation as compared to disc having uniform temperature.

Keywords: Creep, isotropic, steady-state, thermal gradient.

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Authors: K. Krishna Veni, S. Raja Balachandar

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This paper presents a heuristic to solve large size 0-1 Multi constrained Knapsack problem (01MKP) which is NP-hard. Many researchers are used heuristic operator to identify the redundant constraints of Linear Programming Problem before applying the regular procedure to solve it. We use the intercept matrix to identify the zero valued variables of 01MKP which is known as redundant variables. In this heuristic, first the dominance property of the intercept matrix of constraints is exploited to reduce the search space to find the optimal or near optimal solutions of 01MKP, second, we improve the solution by using the pseudo-utility ratio based on surrogate constraint of 01MKP. This heuristic is tested for benchmark problems of sizes upto 2500, taken from literature and the results are compared with optimum solutions. Space and computational complexity of solving 01MKP using this approach are also presented. The encouraging results especially for relatively large size test problems indicate that this heuristic can successfully be used for finding good solutions for highly constrained NP-hard problems.

Keywords: 0-1 Multi constrained Knapsack problem, heuristic, computational complexity, NP-Hard problems.

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Authors: Soltani Amir, Hu Jiaxin

Abstract:

Determination of optimal parameters of a passive  control system device is the primary objective of this study.  Expanding upon the use of control devices in wind and earthquake  hazard reduction has led to development of various control systems.  The advantage of non-linearity characteristics in a passive control  device and the optimal control method using LQR algorithm are  explained in this study. Finally, this paper introduces a simple  approach to determine optimum parameters of a nonlinear viscous  damper for vibration control of structures. A MATLAB program is  used to produce the dynamic motion of the structure considering the  stiffness matrix of the SDOF frame and the non-linear damping  effect. This study concluded that the proposed system (variable  damping system) has better performance in system response control  than a linear damping system. Also, according to the energy  dissipation graph, the total energy loss is greater in non-linear  damping system than other systems.

 

Keywords: Passive Control System, Damping Devices, Viscous Dampers, Control Algorithm.

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Authors: Luis Arias, Jorge E. Pezoa, Daniel Sbárbaro

Abstract:

In this paper, an automated algorithm to estimate and remove the continuous baseline from measured spectra containing both continuous and discontinuous bands is proposed. The algorithm uses previous information contained in a Continuous Database Spectra (CDBS) to obtain a linear basis, with minimum number of sampled vectors, capable of representing a continuous baseline. The proposed algorithm was tested by using a CDBS of flame spectra where Principal Components Analysis and Non-negative Matrix Factorization were used to obtain linear bases. Thus, the radical emissions of natural gas, oil and bio-oil flames spectra at different combustion conditions were obtained. In order to validate the performance in the baseline estimation process, the Goodness-of-fit Coefficient and the Root Mean-squared Error quality metrics were evaluated between the estimated and the real spectra in absence of discontinuous emission. The achieved results make the proposed method a key element in the development of automatic monitoring processes strategies involving discontinuous spectral bands.

Keywords: Flame spectra, removing baseline, recovering spectrum.

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Authors: L. Lancaster, M. H. Lung, D. Sujan

Abstract:

The application of agro-industrial waste in Aluminum Metal Matrix Composites has been getting more attention as they can reinforce particles in metal matrix which enhance the strength properties of the composites. In addition, by applying these agroindustrial wastes in useful way not only save the manufacturing cost of products but also reduce the pollutions on environment. This paper represents a literature review on a range of industrial wastes and their utilization in metal matrix composites. The paper describes the synthesis methods of agro-industrial waste filled metal matrix composite materials and their mechanical, wear, corrosion, and physical properties. It also highlights the current application and future potential of agro-industrial waste reinforced composites in aerospace, automotive and other construction industries.

Keywords: Bond layer, Interfacial shear stress, Bi-layered assembly, Thermal mismatch, Flip Chip Ball Grid Array.

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Authors: R. Kazemzadeh, J. M. Kauffmann

Abstract:

This research deals with investigations on the “Active Generator" under rotor speed variations and output frequency control. It runs at turbine speed and it is connected to a three phase electrical power grid which has its own frequency different from turbine frequency. In this regard the set composed of a four phase synchronous generator and a natural commutated matrix converter (NCMC) made with thyristors, is called active generator. It replaces a classical mechanical gearbox which introduces many drawbacks. The main idea in this article is the presentation of frequency control at grid side when turbine runs at variable speed. Frequency control has been done by linear and step variations of the turbine speed. Relation between turbine speed (frequency) and main grid zero sequence voltage frequency is presented.

Keywords: Power Generation, Energy Conversion, FrequencyControl, Matrix Converter.

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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: Hazem Al-Mofleh, John Daniels, Joseph McKean

Abstract:

Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

Keywords: Non-Linear Wilcoxon, robust estimation, Variogram estimation.

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Authors: M. E. Turan, H. Zengin, E. Cevik, Y. Sun, Y. Turen, H. Ahlatci

Abstract:

In this study, the effects of B₄C and SiC particle reinforcements on wear properties of magnesium matrix metal composites produced by pressure infiltration method were investigated. AZ91 (9%Al-1%Zn) magnesium alloy was used as a matrix. AZ91 magnesium alloy was melted under an argon atmosphere. The melt was infiltrated to the particles with an appropriate pressure. Wear tests, hardness tests were performed respectively. Microstructure characterizations were examined by light optical (LOM) and scanning electron microscope (SEM). The results showed that uniform particle distributions were achieved in both B₄C and SiC reinforced composites. Wear behaviors of magnesium matrix metal composites changed as a function of type of particles. SiC reinforced composite has better wear performance and higher hardness than B₄C reinforced composite.

Keywords: Magnesium matrix composite, pressure infiltration, SEM, wear.

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Authors: Dursun Aydın, Bilgin Senel

Abstract:

In this paper, the sum of squares in linear regression is reduced to sum of squares in semi-parametric regression. We indicated that different sums of squares in the linear regression are similar to various deviance statements in semi-parametric regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the semi-parametric regression model. Then, it is made an application in order to support the theory of the linear regression and semi-parametric regression. In this way, study is supported with a simulated data example.

Keywords: Semi-parametric regression, Penalized LeastSquares, Residuals, Deviance, Smoothing Spline.

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Authors: Qian-Ping Guo, Hou-Biao Li

Abstract:

The generalized Higham matrix is a complex symmetric matrix A = B + iC, where both B ∈ Cn×n and C ∈ Cn×n are Hermitian positive definite, and i = √−1 is the imaginary unit. The growth factor in Gaussian elimination is less than 3√2 for this kind of matrices. In this paper, we give a new brief proof on this result by different techniques, which can be understood very easily, and obtain some new findings.

Keywords: CSPD matrix, positive definite, Schur complement, Higham matrix, Gaussian elimination, Growth factor.

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Authors: M. Khajezadeh, M. Saied Fallah Niasar, S. Ali Asli, D. Davani Davari, M. Godarzi, Y. Asgari

Abstract:

This study aims to explore the joint application of both Boston and Ansoff matrices in the operational development of the product. We conduct deep analysis, by utilizing the Artificial Neural Network, to predict the position of the product in the market while the company is interested in increasing its share. The data are gathered from two industries, called hygiene and detergent. In doing so, the effort is being made by investigating the behavior of top player companies and, recommend strategic orientations. In conclusion, this combination analysis is appropriate for operational development; as well, it plays an important role in providing the position of the product in the market for both hygiene and detergent industries. More importantly, it will elaborate on the company’s strategies to increase its market share related to a combination of the Boston Consulting Group (BCG) Matrix and Ansoff Matrix.

Keywords: Artificial neural network, portfolio analysis, BCG matrix, Ansoff matrix.

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Authors: Khalide Jbilou

Abstract:

In the present paper, we propose numerical methods for solving the Stein equation AXC - X - D = 0 where the matrix A is large and sparse. Such problems appear in discrete-time control problems, filtering and image restoration. We consider the case where the matrix D is of full rank and the case where D is factored as a product of two matrices. The proposed methods are Krylov subspace methods based on the block Arnoldi algorithm. We give theoretical results and we report some numerical experiments.

Keywords: IEEEtran, journal, LATEX, paper, template.

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Authors: A. Gürses, Z. Eroğlu, E. Şahin, K. Güneş, Ç. Doğar

Abstract:

In recent years, polymer/clay nanocomposites have generated great interest in the polymer industry as a new type of composite material because of their superior properties, which includes high heat deflection temperature, gas barrier performance, dimensional stability, enhanced mechanical properties, optical clarity and flame retardancy when compared with the pure polymer or conventional composites. The investigation of change of the tensile properties of organoclay/linear low density polyethylene (LLDPE) nanocomposites with the use of Dioctyl terephthalate (DOTP) (as plasticizer) and calcite (as filler) has been aimed. The composites and organoclay synthesized were characterized using the techniques such as XRD, HRTEM and FTIR techniques. The spectroscopic results indicate that platelets of organoclay were well dispersed within the polymeric matrix. The tensile properties of the composites were compared considering the stress-strain curve drawn for each composite and pure polymer. It was observed that the composites prepared by adding the plasticizer at different ratios and a certain amount of calcite exhibited different tensile behaviors compared to pure polymer.

Keywords: Linear low density polyethylene, nanocomposite, organoclay, plasticizer.

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Authors: Mahdi Nouri

Abstract:

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

Keywords: Riccati, matrix equation, eigenvalue problem, symmetric, bisymmetric, persymmetric, decomposition, canonical forms, Graphs theory, adjacency and Laplacian matrices.

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Authors: Guangbin Wang, Xue Li, Fuping Tan

Abstract:

In this paper, we present some new upper bounds for the spectral radius of iterative matrices based on the concept of doubly α diagonally dominant matrix. And subsequently, we give two examples to show that our results are better than the earlier ones.

Keywords: doubly α diagonally dominant matrix, eigenvalue, iterative matrix, spectral radius, upper bound.

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