Search results for: singular perturbation problem

Authors: Meng Koon Lee, Mohammad Hosseini Fouladi, Satesh Narayana Namasivayam

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Research is focused on the response of soundboards of Classical guitars at frequencies up to 5 kHz as the soundboard is a major contributor to acoustic radiation at high frequencies when compared to the bridge and sound hole. A thin rectangular plate of variable thickness that is simply-supported on all sides is used as an analytical model of the research. This model is used to study the response of the guitar soundboard as the latter can be considered as a modified form of a rectangular plate. Homotopy Perturbation Method (HPM) is selected as a mathematical method to obtain an analytical solution of the 4th-order parabolic partial differential equation of motion of the rectangular plate of constant thickness viewed as a linear problem. This procedure is generalized to the nonlinear problem of the rectangular plate with variable thickness and an analytical solution can also be obtained. Sound power is used as a parameter to investigate the acoustic radiation of soundboards made from spruce using various bracing patterns. The sound power of soundboards made from Malaysian softwood such as damar minyak, sempilor or podo are investigated to determine the viability of replacing spruce as future materials for soundboards of Classical guitars.

Keywords: rectangular plates, analytical solution, homotopy perturbation, natural frequencies

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Authors: Orhun Aydin, Mark V. Janikas, Rodrigo Alves, Renato Assuncao

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In this paper, a tree-based perturbation methodology for regionalization inference is presented. Regionalization is a constrained optimization problem that aims to create groups with similar attributes while satisfying spatial contiguity constraints. Similar to any constrained optimization problem, the spatial constraint may hinder convergence to some global minima, resulting in spatially contiguous members of a group with dissimilar attributes. This paper presents a general methodology for rigorously perturbing spatial constraints through the use of random spanning trees. The general framework presented can be used to quantify the effect of the spatial constraints in the overall regionalization result. We compare several types of stochastic spanning trees used in inference problems such as fuzzy regionalization and determining the number of regions. Performance of stochastic spanning trees is juxtaposed against the traditional permutation-based hypothesis testing frequently used in spatial statistics. Inference results for fuzzy regionalization and determining the number of regions is presented on the Local Area Personal Incomes for Texas Counties provided by the Bureau of Economic Analysis.

Keywords: regionalization, constrained clustering, probabilistic inference, fuzzy clustering

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Sasiwimol Auepong, Raywat Tanadkithirun

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In this work, the problem that squirrels ruin durian, which is an economical fruit in Thailand, is considered. We seek the strategy for the durian farmers to eliminate the squirrels under the consideration that squirrels also provide ecosystem service. The population dynamics of squirrels are constructed to have carrying capacity since we consider the population in a confined area. A performance index indicating the total benefit of a given elimination strategy is provided. It comprises the cost of countermeasures, the loss of resources, and the ecosystem service provided by squirrels. The optimal performance index is numerically solved through the variational inequality using the finite difference method. The optimal strategy to control the squirrel population is also given numerically.

Keywords: controlled stochastic differential equation, durian, finite difference method, performance index, singular stochastic control model, squirrel

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Authors: Myunggon Yoon, Jung-Ho Moon

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In this paper, we present a transfer function representation of a general one-dimensional combustor. The input of the transfer function is a heat rate perturbation of a burner and the output is a flow velocity perturbation at the burner. This paper considers a general combustor model composed of multiple cans with different cross sectional areas, along with a non-zero flow rate.

Keywords: combustor, dynamics, thermoacoustics, transfer function

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Authors: Solaine Hachem, Frédéric Bourquin, Dominique Siegert

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The brutal collapse of bridges is mainly due to scour. Indeed, the soil erosion in the riverbed around a pier modifies the embedding conditions of the structure, reduces its overall stiffness and threatens its stability. Hence, finding an efficient technique that allows early scour detection becomes mandatory. Vibration analysis is an indirect method for scour detection that relies on real-time monitoring of the bridge. It tends to indicate the presence of a scour based on its consequences on the stability of the structure and its dynamic response. Most of the research in this field has focused on the dynamic behavior of a single pile and has examined the depth of the scour. In this paper, a bridge is fully modeled with all piles and spans and the scour is represented by a reduction in the foundation's stiffnesses. This work aims to identify the vibration modes sensitive to the rigidity’s loss in the foundations so that their variations can be considered as a scour indicator: the decrease in soil-structure interaction rigidity leads to a decrease in the natural frequencies’ values. By using the first-order perturbation method, the expression of sensitivity, which depends only on the selected vibration modes, is established to determine the deficiency of foundations stiffnesses. The solutions are obtained by using the singular value decomposition method for the regularization of the inverse problem. The propagation of uncertainties is also calculated to verify the efficiency of the inverse problem method. Numerical simulations describing different scenarios of scour are investigated on a simplified model of a real composite steel-concrete bridge located in France. The results of the modal analysis show that the modes corresponding to in-plane and out-of-plane piers vibrations are sensitive to the loss of foundation stiffness. While the deck bending modes are not affected by this damage.

Keywords: bridge’s piers, inverse problems, modal sensitivity, scour detection, vibration analysis

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Authors: Linyu Wang, Mingjun Zhu, Jianhong Xiang, Hanyu Jiang

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Aiming at the problem that the spectral efficiency of hybrid precoding (HP) is too low in the current millimeter wave (mmWave) massive multiple input multiple output (MIMO) system, this paper proposes a digital joint equivalent channel hybrid precoding algorithm, which is based on the introduction of digital encoding matrix iteration. First, the objective function is expanded to obtain the relation equation, and the pseudo-inverse iterative function of the analog encoder is derived by using the pseudo-inverse method, which solves the problem of greatly increasing the amount of computation caused by the lack of rank of the digital encoding matrix and reduces the overall complexity of hybrid precoding. Secondly, the analog coding matrix and the millimeter-wave sparse channel matrix are combined into an equivalent channel, and then the equivalent channel is subjected to Singular Value Decomposition (SVD) to obtain a digital coding matrix, and then the derived pseudo-inverse iterative function is used to iteratively regenerate the simulated encoding matrix. The simulation results show that the proposed algorithm improves the system spectral efficiency by 10~20%compared with other algorithms and the stability is also improved.

Keywords: mmWave, massive MIMO, hybrid precoding, singular value decompositing, equivalent channel

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Authors: G. M. Komaki, S. Mobin, E. Teymourian, S. Sheikh

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This paper addresses minimizing the makespan of the distributed permutation flow shop scheduling problem. In this problem, there are several parallel identical factories or flowshops each with series of similar machines. Each job should be allocated to one of the factories and all of the operations of the jobs should be performed in the allocated factory. This problem has recently gained attention and due to NP-Hard nature of the problem, metaheuristic algorithms have been proposed to tackle it. Majority of the proposed algorithms require large computational time which is the main drawback. In this study, a general variable neighborhood search algorithm (GVNS) is proposed where several time-saving schemes have been incorporated into it. Also, the GVNS uses the sophisticated method to change the shaking procedure or perturbation depending on the progress of the incumbent solution to prevent stagnation of the search. The performance of the proposed algorithm is compared to the state-of-the-art algorithms based on standard benchmark instances.

Keywords: distributed permutation flow shop, scheduling, makespan, general variable neighborhood search algorithm

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Authors: Natalia D. Vaysfel’d, Zinaida Y. Zhuravlova

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The loaded plane elastic semistrip, the lateral boundaries of which are fixed, is considered. The integral transformations are applied directly to Lame’s equations. It leads to one dimensional boundary value problem in the transformations’ domain which is formulated as a vector one. With the help of the matrix differential calculation’s apparatus and apparatus of Green matrix function the exact solution of a vector problem is constructed. After the satisfying the boundary condition at the semi strip’s edge the problem is reduced to the solving of the integral singular equation with regard of the unknown stress at the semis trip’s edge. The equation is solved with the orthogonal polynomials method that takes into consideration the real singularities of the solution at the ends of integration interval. The normal stress at the edge of the semis trip were calculated and analyzed.

Keywords: semi strip, Green's Matrix, fourier transformation, orthogonal polynomials method

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Authors: Susy Thomas, Sajju Thomas, Varghese Vaidyan

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This paper considers SMCs using linear feedback with switched gains and proposes a method which can minimize the pole perturbation. The method is able to enhance the robustness property of the controller. A pre-assigned neighborhood of the ‘nominal’ positions is assigned and the system poles are not allowed to stray out of these bounds even when parameters variations/uncertainties act upon the system. A quasi SMM is maintained within the assigned boundaries of the sliding surface.

Keywords: parameter variations, pole perturbation, sliding mode control, switching surface, robust switching vector

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Authors: Alhadi Bustaman, Soeganda Formalidin, Titin Siswantining

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DNA microarray technology is used to analyze thousand gene expression data simultaneously and a very important task for drug development and test, function annotation, and cancer diagnosis. Various clustering methods have been used for analyzing gene expression data. However, when analyzing very large and heterogeneous collections of gene expression data, conventional clustering methods often cannot produce a satisfactory solution. Biclustering algorithm has been used as an alternative approach to identifying structures from gene expression data. In this paper, we introduce a transform technique based on singular value decomposition to identify normalized matrix of gene expression data followed by Mixed-Clustering algorithm and the Lift algorithm, inspired in the node-deletion and node-addition phases proposed by Cheng and Church based on Agglomerative Hierarchical Clustering (AHC). Experimental study on standard datasets demonstrated the effectiveness of the algorithm in gene expression data.

Keywords: agglomerative hierarchical clustering (AHC), biclustering, gene expression data, lymphoma, singular value decomposition (SVD)

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Authors: M. H. M. Rashid

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A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl's Theorem, Weyl Spectrum, Polaroid operators, property (gm)

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Authors: Fatemah A. Alqallaf, Debasis Kundu

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The aim of this paper is to introduce a bivariate inverse generalized exponential distribution which has a singular component. The proposed bivariate distribution can be used when the marginals have heavy-tailed distributions, and they have non-monotone hazard functions. Due to the presence of the singular component, it can be used quite effectively when there are ties in the data. Since it has four parameters, it is a very flexible bivariate distribution, and it can be used quite effectively for analyzing various bivariate data sets. Several dependency properties and dependency measures have been obtained. The maximum likelihood estimators cannot be obtained in closed form, and it involves solving a four-dimensional optimization problem. To avoid that, we have proposed to use an EM algorithm, and it involves solving only one non-linear equation at each `E'-step. Hence, the implementation of the proposed EM algorithm is very straight forward in practice. Extensive simulation experiments and the analysis of one data set have been performed. We have observed that the proposed bivariate inverse generalized exponential distribution can be used for modeling dependent competing risks data. One data set has been analyzed to show the effectiveness of the proposed model.

Keywords: Block and Basu bivariate distributions, competing risks, EM algorithm, Marshall-Olkin bivariate exponential distribution, maximum likelihood estimators

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Authors: Prawal Sinha, Peeyush Singh, Pravir Dutt

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Problems in elastohydrodynamic lubrication have attracted a lot of attention in the last few decades. Solving a two-dimensional problem has always been a big challenge. In this paper, a new discontinuous finite volume method (DVM) for two-dimensional point contact Elastohydrodynamic Lubrication (EHL) problem has been developed and analyzed. A complete algorithm has been presented for solving such a problem. The method presented is robust and easily parallelized in MPI architecture. GMRES technique is implemented to solve the matrix obtained after the formulation. A new approach is followed in which discontinuous piecewise polynomials are used for the trail functions. It is natural to assume that the advantages of using discontinuous functions in finite element methods should also apply to finite volume methods. The nature of the discontinuity of the trail function is such that the elements in the corresponding dual partition have the smallest support as compared with the Classical finite volume methods. Film thickness calculation is done using singular quadrature approach. Results obtained have been presented graphically and discussed. This method is well suited for solving EHL point contact problem and can probably be used as commercial software.

Keywords: elastohydrodynamic, lubrication, discontinuous finite volume method, GMRES technique

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Authors: Kambiz Rasoulkhani, Jeanne Cole, Sybil Sharvelle, Ali Mostafavi

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Dual water distribution systems have been proposed as solutions to enhance the sustainability and resilience of urban water systems by improving performance and decreasing energy consumption. The objective of this study was to evaluate the long-term resilience and robustness of dual water distribution systems versus singular water distribution systems under various stressors such as demand fluctuation, aging infrastructure, and funding constraints. To this end, the long-term dynamics of these infrastructure systems was captured using a simulation model that integrates institutional agency decision-making processes with physical infrastructure degradation to evaluate the long-term transformation of water infrastructure. A set of model parameters that varies for dual and singular distribution infrastructure based on the system attributes, such as pipes length and material, energy intensity, water demand, water price, average pressure and flow rate, as well as operational expenditures, were considered and input in the simulation model. Accordingly, the model was used to simulate various scenarios of demand changes, funding levels, water price growth, and renewal strategies. The long-term resilience and robustness of each distribution infrastructure were evaluated based on various performance measures including network average condition, break frequency, network leakage, and energy use. An ecologically-based resilience approach was used to examine regime shifts and tipping points in the long-term performance of the systems under different stressors. Also, Classification and Regression Tree analysis was adopted to assess the robustness of each system under various scenarios. Using data from the City of Fort Collins, the long-term resilience and robustness of the dual and singular water distribution systems were evaluated over a 100-year analysis horizon for various scenarios. The results of the analysis enabled: (i) comparison between dual and singular water distribution systems in terms of long-term performance, resilience, and robustness; (ii) identification of renewal strategies and decision factors that enhance the long-term resiliency and robustness of dual and singular water distribution systems under different stressors.

Keywords: complex systems, dual water distribution systems, long-term resilience performance, multi-agent modeling, sustainable and resilient water systems

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Authors: Sameena Tarannum, S. Pranesh

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The effect of linear stability analysis of triple diffusive convection in a vertically oscillating viscoelastic liquid of Oldroyd-B type is studied. The correction Rayleigh number is obtained by using perturbation method which gives prospect to control the convection. The eigenvalue is obtained by using perturbation method by adopting Venezian approach. From the study, it is observed that gravity modulation advances the onset of triple diffusive convection.

Keywords: gravity modulation, Oldroyd-b liquid, triple diffusive convection, venezian approach

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Authors: T. H. Young, S. J. Huang, Y. S. Chiu

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This paper investigates the parametric stability of an axially moving web subjected to nonuniform in-plane edge excitations on two opposite, simply-supported edges. The web is modeled as a viscoelastic plate whose constitutive relation obeys the Kelvin-Voigt model, and the in-plane edge excitations are expressed as the sum of a static tension and a periodical perturbation. Due to the in-plane edge excitations, the moving plate may bring about parametric instability under certain situations. First, the in-plane stresses of the plate due to the nonuniform edge excitations are determined by solving the in-plane forced vibration problem. Then, the dependence on the spatial coordinates in the equation of transverse motion is eliminated by the generalized Galerkin method, which results in a set of discretized system equations in time. Finally, the method of multiple scales is utilized to solve the set of system equations analytically if the periodical perturbation of the in-plane edge excitations is much smaller as compared with the static tension of the plate, from which the stability boundaries of the moving plate are obtained. Numerical results reveal that only combination resonances of the summed-type appear under the in-plane edge excitations considered in this work.

Keywords: axially moving viscoelastic plate, in-plane periodic excitation, nonuniformly distributed edge tension, dynamic stability

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Authors: Hamid Reza Pakzad

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In this paper, the properties of dust-ion-acoustic (DIA) shock waves in an unmagnetized dusty plasma, whose constituents are inertial ions, superthermal electrons, and stationary dust particles, are investigated by employing the reductive perturbation method. The dissipation is taken into account the kinematic viscosity among the plasma constituents. It is shown that the basic features of DIA shock waves are significantly modified by the effects of electron superthermality and ion kinematic viscosity.

Keywords: reductive perturbation method, dust ion acoustic shock wave, superthermal electron, dissipative plasmas

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Authors: Flavia Smarrazzo

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Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

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Authors: Song Ni, Junxiang Xu

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This paper concerns quasi-periodic perturbations with parameters of 2-dimensional degenerate systems. If the equilibrium point of the unperturbed system is elliptic-type degenerate. Assume that the perturbation is real analytic quasi-periodic with diophantine frequency. Without imposing any assumption on the perturbation, we can use a path of equilibrium points to tackle with the Melnikov non-resonance condition, then by the Leray-Schauder Continuation Theorem and the Kolmogorov-Arnold-Moser technique, it is proved that the equation has a small response solution for many sufficiently small parameters.

Keywords: quasi-periodic systems, KAM-iteration, degenerate equilibrium point, response solution

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Reza Mohammadi

Abstract:

Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Naser Alajmi, Ali Alobaidly, Mubarak Alhajri, Salem Salamah, Muhammad Alsubaie

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Iterative Learning Control (ILC) known to be a controlling tool to overcome periodic disturbances for repetitive systems. This technique is required to let the error signal tends to zero as the number of operation increases. The learning process that lies within this context is strongly dependent on the initial input which if selected properly tends to let the learning process be more effective compared to the case where a system starts from blind. ILC uses previous recorded execution data to update the following execution/trial input such that a reference trajectory is followed to a high accuracy. Error convergence in ILC is generally highly dependent on the input applied to a plant for trial $1$, thus a good choice of initial starting input signal would make learning faster and as a consequence the error tends to zero faster as well. In the work presented within, an upper limit based on the Singular Values Principle (SV) is derived for the initial input signal applied at trial $1$ such that the system follow the reference in less number of trials without responding aggressively or exceeding the working envelope where a system is required to move within in a robot arm, for example. Simulation results presented illustrate the theory introduced within this paper.

Keywords: initial input, iterative learning control, maximum input, singular values

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Authors: Siraa Ben Ftima, Mourad Talbi, Tahar Ezzedine

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In this paper, we present a technique of secure watermarking of grayscale and color images. This technique consists in applying the Singular Value Decomposition (SVD) in LWT (Lifting Wavelet Transform) domain in order to insert the watermark image (grayscale) in the host image (grayscale or color image). It also uses signature in the embedding and extraction steps. The technique is applied on a number of grayscale and color images. The performance of this technique is proved by the PSNR (Pick Signal to Noise Ratio), the MSE (Mean Square Error) and the SSIM (structural similarity) computations.

Keywords: lifting wavelet transform (LWT), sub-space vectorial decomposition, secure, image watermarking, watermark

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Authors: Mehdi Jalalpour, Mazdak Tootkaboni

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We present a computationally efficient method for reliability-based topology optimization under material properties uncertainty, which is assumed to be lognormally distributed and correlated within the domain. Computational efficiency is achieved through estimating the response statistics with stochastic perturbation of second order, using these statistics to fit an appropriate distribution that follows the empirical distribution of the response, and employing an efficient gradient-based optimizer. The proposed algorithm is utilized for design of new structures and the changes in the optimized topology is discussed for various levels of target reliability and correlation strength. Predictions were verified thorough comparison with results obtained using Monte Carlo simulation.

Keywords: material uncertainty, stochastic perturbation, structural reliability, topology optimization

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Authors: Subhayan Maity

Abstract:

Complete scenario of cosmic evolution from emergent phase to late time acceleration (i.e. non-singular ever expanding Universe) is a popular preference in the recent cosmology. Yet one can’t exclude the idea that other type of evolution pattern of the Universe may also be possible. Especially, the bouncing scenario is becoming a matter of interest now a days. The present work is an exhibition of such a different pattern of cosmic evolution where the evolution of Universe has been shown as a cyclic thermodynamic process. Under diffusion mechanism (non-equilibrium thermodynamic process), the cosmic evolution has been modelled as [ emergent - accelerated expansion - decelerated expansion - decelerated contraction - accelerated contraction - emergent] .

Keywords: non-equilibrium thermodynamics, non singular evolution of universe, cyclic evolution, diffusive fluid

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Authors: H. Bensouilah, H. Boucherit, M. Lahmar

Abstract:

A theoretical investigation on the effects of both steady-state and dynamic deformations of the foils on the dynamic performance characteristics of a self-acting air foil journal bearing operating under small harmonic vibrations is proposed. To take into account the dynamic deformations of foils, the perturbation method is used for determining the gas-film stiffness and damping coefficients for given values of excitation frequency, compressibility number, and compliance factor of the bump foil. The nonlinear stationary Reynolds’ equation is solved by means of the Galerkins’ finite element formulation while the finite differences method are used to solve the first order complex dynamic equations resulting from the perturbation of the nonlinear transient compressible Reynolds’ equation. The stiffness of a bump is uniformly distributed throughout the bearing surface (generation I bearing). It was found that the dynamic properties of the compliant finite length journal bearing are significantly affected by the compliance of foils especially when the dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition.

Keywords: elasto-aerodynamic lubrication, air foil bearing, steady-state deformation, dynamic deformation, stiffness and damping coefficients, perturbation method, fluid-structure interaction, Galerk infinite element method, finite difference method

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Authors: Reza Mohammadi

Abstract:

Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Jose D. Herrera, Mario A. Rios

Abstract:

This paper deals with the coordinated tuning of the Power System Stabilizer (PSS) controller and Power Oscillation Damping (POD) Controller of Flexible AC Transmission System (FACTS) in a multi-machine power systems. The coordinated tuning is based on the critical eigenvalues of the power system and a model reduction technique where the Hankel Singular Value method is applied. Through the linearized system model and the parameter-constrained nonlinear optimization algorithm, it can compute the parameters of both controllers. Moreover, the parameters are optimized simultaneously obtaining the gains of both controllers. Then, the nonlinear simulation to observe the time response of the controller is performed.

Keywords: electromechanical oscillations, power system stabilizers, power oscillation damping, hankel singular values

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Authors: Bandar Alahmadi, Manohar Mareboyana, Lethia Jackson

Abstract:

Today, there are many applications that are using computer vision models, such as face recognition, image classification, and object detection. The accuracy of these models is very important for the performance of these applications. One challenge that facing the computer vision models is the adversarial examples attack. In computer vision, the adversarial example is an image that is intentionally designed to cause the machine learning model to misclassify it. One of very well-known method that is used to attack the Convolution Neural Network (CNN) is Fast Gradient Sign Method (FGSM). The goal of this method is to find the perturbation that can fool the CNN using the gradient of the cost function of CNN. In this paper, we introduce a novel model that can attack Regional-Convolution Neural Network (R-CNN) that use FGSM. We first extract the regions that are detected by R-CNN, and then we resize these regions into the size of regular images. Then, we find the best perturbation of the regions that can fool CNN using FGSM. Next, we add the resulted perturbation to the attacked region to get a new region image that looks similar to the original image to human eyes. Finally, we placed the regions back to the original image and test the R-CNN with the attacked images. Our model could drop the accuracy of the R-CNN when we tested with Pascal VOC 2012 dataset.

Keywords: adversarial examples, attack, computer vision, image processing

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