Search results for: stability and convergence analysis

Authors: Sudhakar Kadiyala, Sripad R. Naik

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Large cavern in Bhutan Himalayas is being monitored since the construction period. The behavior of the cavern is being monitored for last 16 years. Instrumentation includes measurement of convergence of high walls by geodetic monitoring, load on the support systems with load cells and instrumented bolts. Analysis of the results of instrumentation showed that during the construction period of the cavern, the convergence of the cavern varied from 181 - 233 mm in the unit bay area with maximum convergence rate of 2.80mm/day. Whereas during the operational period the total convergence observed was in the range of 21 to 45 mm during a period of 11.30 years with convergence rate of 0.005 to 0.011 mm/day. During the last five years, there were no instances of high tensile stress recorded by the instrumented bolts. Load on the rock bolts have shown stabilization trend at most of the locations. This paper discusses in detail the results of long-term monitoring using the geotechnical instruments and how the data is being used in 3D numerical model to confirm the stability of the cavern.

Keywords: convergence, displacements, geodetic monitoring, long-term stability

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Authors: Kwounghee Choi

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Technological convergence between the various sectors is expected to have a very large impact on future industrial and economy. This study attempts to do empirical approach between specific technologies’ classification. For technological convergence classification, it is necessary to set the target technology to be analyzed. This study selected target technology from national research and development plan. At first we found a source technology for analysis. Depending on the weight of source technology, NT-based, BT-based, IT-based, ET-based, CS-based convergence types were classified. This study aims to empirically show the concept of convergence technology and convergence types. If we use the source technology to classify convergence type, it will be useful to make practical strategies of convergence technology.

Keywords: technology convergence, source technology, convergence type, R&D strategy, technology classification

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Authors: César Garza

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In supervised binary classification and regression problems, it is well-known that learnability is equivalent to a uniform convergence of the hypothesis class, and if a problem is learnable, it is learnable by empirical risk minimization. For the general learning setting of unsupervised learning tasks, there are non-trivial learning problems where uniform convergence does not hold. We present here the task of learning centers of mass with an extra feature that “activates” some of the coordinates over the unit ball in a Hilbert space. We show that the learning problem is learnable under a stable RLM rule. We introduce a family of distributions over the domain space with some mild restrictions for which the sample complexity of uniform convergence for these problems must grow logarithmically with the dimension of the Hilbert space. If we take this dimension to infinity, we obtain a learnable problem for which the uniform convergence property fails for a vast family of distributions.

Keywords: statistical learning theory, learnability, uniform convergence, stability, regularized loss minimization

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Authors: Amjad Naveed

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This study analysed the role of structural change in the process of labour productivity convergence at country and regional levels. Many forms of structural changes occurred within the European Union (EU) countries i.e. variation in sectoral employment share, changes in demand for products, variations in trade patterns and advancement in technology which may have an influence on the process of convergence. Earlier studies on convergence have neglected the role of structural changes which can have resulted in different conclusion on the nature of convergence. The contribution of this study is to examine the role of structural change in testing labour productivity convergence at various levels. For the empirical purpose, the data of 19 EU countries, 259 regions and 6 industries is used for the period of 1991-2009. The results indicate that convergence varies across regional and country levels for different industries when considered the role of structural change.

Keywords: labor produvitivty, convergence, structural change, panel unit root

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Authors: Reza Mollapourasl, Majid Haghi

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In this study, we develop local meshfree methods known as radial basis function-generated finite difference (RBF-FD) method and Hermite finite difference (RBF-HFD) method to design stencil weights and spatial discretization for Helmholtz equation. The convergence and stability of schemes are investigated numerically in three dimensions with irregular shaped domain. These localized meshless methods incorporate the advantages of the RBF method, finite difference and Hermite finite difference methods to handle the ill-conditioning issue that often destroys the convergence rate of global RBF methods. Moreover, numerical illustrations show that the proposed localized RBF type methods are efficient and applicable for problems with complex geometries. The convergence and accuracy of both schemes are compared by solving a test problem.

Keywords: radial basis functions, Hermite finite difference, Helmholtz equation, stability

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Authors: Sandeep Kaur Chouhan, Jatinderdeep Kaur, S. S. Bhatia

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The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries.

Keywords: conjugate Dirichlet kernel, Dirichlet kernel, L1-convergence, modified sums

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Authors: Swarn Singh, Suruchi Singh

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In this paper, we present a fourth order two level implicit finite difference scheme for 1D Pennes bio-heat equation. Unconditional stability and convergence of the proposed scheme is discussed. Numerical results are obtained to demonstrate the efficiency of the scheme. In this paper we present a fourth order two level implicit finite difference scheme for 1D Pennes bio-heat equation. Unconditional stability and convergence of the proposed scheme is discussed. Numerical results are obtained to demonstrate the efficiency of the scheme.

Keywords: convergence, finite difference scheme, Pennes bio-heat equation, stability

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Authors: Christoph Ramsauer, Jaydeep Karandikar, Tony Schmitz, Friedrich Bleicher

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Machining stability is an important limitation to discrete part machining. In this work, a networked implementation of milling stability optimization with Bayesian learning is presented. The milling process was monitored with a wireless sensory tool holder instrumented with an accelerometer at the Vienna University of Technology, Vienna, Austria. The recorded data from a milling test cut is used to classify the cut as stable or unstable based on the frequency analysis. The test cut result is fed to a Bayesian stability learning algorithm at the University of Tennessee, Knoxville, Tennessee, USA. The algorithm calculates the probability of stability as a function of axial depth of cut and spindle speed and recommends the parameters for the next test cut. The iterative process between two transatlantic locations repeats until convergence to a stable optimal process parameter set is achieved.

Keywords: machining stability, machine learning, sensor, optimization

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Authors: Sonia Sonia

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This paper presents a family of iterative scheme for solving nonlinear systems of equations which have wide application in sciences and engineering. The proposed iterative family is based upon some parameters which generates many different iterative schemes. This family is completely derivative free and uses first of divided difference operator. Moreover some numerical experiments are performed and compared with existing methods. Analysis of convergence shows that the presented family has fourth-order of convergence. The dynamical behaviour of proposed family and local convergence have also been discussed. The numerical performance and convergence region comparison demonstrates that proposed family is efficient.

Keywords: convergence, divided difference operator, nonlinear system, Newton's method

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Authors: Rishikesh Yadav, Ramakanta Meher, Vishnu Narayan Mishra

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The main aim of this article is to investigate the statistical convergence of the summation of integral type operators and to obtain the weighted statistical convergence. The rate of statistical convergence by means of modulus of continuity and function belonging to the Lipschitz class are also studied. We discuss the convergence of the defined operators by graphical representation and put a better rate of convergence than the Szasz-Mirakjan-Kantorovich operators. In the last section, we extend said operators into bivariate operators to study about the rate of convergence in sense of modulus of continuity and by means of Lipschitz class by using function of two variables.

Keywords: The Szasz-Mirakjan-Kantorovich operators, statistical convergence, modulus of continuity, Peeters K-functional, weighted modulus of continuity

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Authors: Firano Zakaria, Filali Adib Fatine

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The issue f convergence in theoretical models (classical or Keynesian) has been widely discussed. The results of the work affirm that most countries are seeking to get as close as possible to a steady state in order to catch up with developed countries. In this paper, we have retested this question whether it is absolute or conditional. The results affirm that the degree of convergence of countries like Morocco is very low and income is still far from its equilibrium state. Moreover, the analysis of financial convergence, of the countries in our panel, states that the pace in this sector is more intense: countries are converging more rapidly in financial terms. The question arises as to why, with a fairly convergent financial system, growth does not respond, yet the financial system should facilitate this economic convergence. Our results confirm that the degree of information exchange between the financial system and the economic system did not change significantly between 1985 and 2017. This leads to the hypothesis that the financial system is failing to serve its role as a creator of information in developing countries despite all the reforms undertaken, thus making the existence of an economic demon in the Maxwell prevail.

Keywords: economic convergence, financial convergence, financial system, entropy

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Authors: Rashid Ahmed , John N. Avaritsiotis

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Many signal subspace-based approaches have already been proposed for determining the fixed Direction of Arrival (DOA) of plane waves impinging on an array of sensors. Two procedures for DOA estimation based neural networks are presented. First, Principal Component Analysis (PCA) is employed to extract the maximum eigenvalue and eigenvector from signal subspace to estimate DOA. Second, minor component analysis (MCA) is a statistical method of extracting the eigenvector associated with the smallest eigenvalue of the covariance matrix. In this paper, we will modify a Minor Component Analysis (MCA(R)) learning algorithm to enhance the convergence, where a convergence is essential for MCA algorithm towards practical applications. The learning rate parameter is also presented, which ensures fast convergence of the algorithm, because it has direct effect on the convergence of the weight vector and the error level is affected by this value. MCA is performed to determine the estimated DOA. Preliminary results will be furnished to illustrate the convergences results achieved.

Keywords: Direction of Arrival, neural networks, Principle Component Analysis, Minor Component Analysis

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Authors: F. Berna Benli, Özgür Keskin

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Lately, many mathematicians have been studied the statistical convergence of a sequence of fuzzy numbers. We know that Lambda-statistically convergence is a kind of convergence between ordinary convergence and statistical convergence. In this paper, we will introduce the new kind of convergence such as λ-levelwise statistical convergence. Then, we will define the concept of the λ-levelwise statistical cluster and limit points of a sequence of fuzzy numbers. Also, we will discuss the relations between the sets of λ-levelwise statistical cluster points and λ-levelwise statistical limit points of sequences of fuzzy numbers. This work has been extended in this paper, where some relations have been considered such that when lambda-statistical limit inferior and lambda-statistical limit superior for lambda-statistically convergent sequences of fuzzy numbers are equal. Furthermore, lambda-statistical boundedness condition for different sequences of fuzzy numbers has been studied.

Keywords: fuzzy number, λ-levelwise statistical cluster points, λ-levelwise statistical convergence, λ-levelwise statistical limit points, λ-statistical cluster points, λ-statistical convergence, λ-statistical limit points

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Authors: H. C. Nguyen

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This contribution considers seismic effects on the stability of slope and footing resting on a slope. The seismic force is simply treated as static inertial force through the values of acceleration factor. All domains are assumed to be plasticity deformations approximated using node-based smoothed finite element method (NS-FEM). The failure mechanism and safety factor were then explored using numerical procedure based on upper bound approach in which optimization problem was formed as second order cone programming (SOCP). The data obtained confirm that upper bound procedure using NS-FEM and SOCP can give stable and rapid convergence results of seismic stability factors.

Keywords: upper bound analysis, safety factor, slope stability, footing resting on slope

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Authors: Prashant Pandey

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In the present article, an effective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diffusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution profiles of the coupled system are presented graphically for different particular cases. The salient feature of the present article is finding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher efficiency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs confirms the super-linearly convergence rate of the proposed method.

Keywords: fractional coupled PDE, stability and convergence analysis, diffusion equation, Laguerre polynomials, spectral method

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Authors: Z. Bouchama, N. Essounbouli, A. Hamzaoui, M. N. Harmas

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A new robust finite time synergetic controller is presented based on recently developed synergetic control methodology and a terminal attractor technique. A Fast Terminal Synergetic Control (FTSC) is proposed for controlling DC-DC buck converter. Unlike Synergetic Control (SC) and sliding mode control, the proposed control scheme has the characteristics of finite time convergence and chattering free phenomena. Simulation of stabilization and reference tracking for buck converter systems illustrates the approach effectiveness while stability is assured in the Lyapunov sense and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability.

Keywords: dc-dc buck converter, synergetic control, finite time convergence, terminal synergetic control, fast terminal synergetic control, Lyapunov

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Authors: Neha Bhardwaj

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In this paper, we consider positive linear operators and study the Voronovskaya type result of the operator then obtain an error estimate in terms of the higher order modulus of continuity of the function being approximated and its A-statistical convergence. Also, we compute the corresponding rate of A-statistical convergence for the linear positive operators.

Keywords: Poisson distribution, Voronovskaya, modulus of continuity, a-statistical convergence

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Authors: Berkay Buluş, Aytekin İşman, Kübra Yüzüncüyıl

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Developments in media and communication technologies have changed the way we use media. The importance of convergence culture has been increasing day by day within the framework of these developments. With new media, it is possible to say that social networks are the most powerful platforms that are integrated to this digitalization process. Although social networks seem like the place that people can socialize, they can also be utilized as places of production. On the other hand, audience has become users within the framework of transformation from national to global broadcasting. User generated contents make conventional media and new media collide. In this study, these communication platforms will be examined not as platforms that replace one another but mediums that unify each other. In the light of this information, information that is produced by users regarding new media platforms and all new media use practices are called convergence culture. In other words, convergence culture means intersections of conventional and new media. In this study, examples of convergence culture will be analyzed in detail.

Keywords: new media, convergence culture, convergence, use of new media, user generated content

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Authors: Ali Al-Zughaibi

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The purpose of this paper is to present a modeling and control of the quarter car active suspension system with unknown mass, unknown time-delay and road disturbance. The objective of designing the controller by deriving a control law to achieve stability of the system and convergence that can considerably improve the ride comfort and road disturbance handling. Thus is accomplished by using Routh-Herwitz criterion and based on some assumptions. A mathematical proof is given to show the ability of the designed controller to ensure stability and convergence of the active suspension system and dispersion oscillation of system with unknown mass, time-delay and road disturbances. Simulations were also performed for controlling quarter car suspension, where the results obtained from these simulations verify the validity of the proposed design.

Keywords: active suspension system, time-delay, disturbance rejection, dynamic uncertainty

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Authors: Zhifeng Kong

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Over-parameterized neural networks have attracted a great deal of attention in recent deep learning theory research, as they challenge the classic perspective of over-fitting when the model has excessive parameters and have gained empirical success in various settings. While a number of theoretical works have been presented to demystify properties of such models, the convergence properties of such models are still far from being thoroughly understood. In this work, we study the convergence properties of training two-hidden-layer partially over-parameterized fully connected networks with the Rectified Linear Unit activation via gradient descent. To our knowledge, this is the first theoretical work to understand convergence properties of deep over-parameterized networks without the equally-wide-hidden-layer assumption and other unrealistic assumptions. We provide a probabilistic lower bound of the widths of hidden layers and proved linear convergence rate of gradient descent. We also conducted experiments on synthetic and real-world datasets to validate our theory.

Keywords: over-parameterization, rectified linear units ReLU, convergence, gradient descent, neural networks

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

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Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas.

Keywords: conjugate gradient method, conjugate gradient coefficient, global convergence

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Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

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In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Holder continuity condition, Frechet derivative, fifth order convergence, recurrence relations

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Authors: Salah Al-Din I. Badran, Samad Ahmadi, Ismail Shahin

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A blind source separation method is proposed; in this method we use a non-uniform filter bank and a novel normalisation. This method provides a reduced computational complexity and increased convergence speed comparing to the full-band algorithm. Recently, adaptive sub-band scheme has been recommended to solve two problems: reduction of computational complexity and increase the convergence speed of the adaptive algorithm for correlated input signals. In this work the reduction in computational complexity is achieved with the use of adaptive filters of orders less than the full-band adaptive filters, which operate at a sampling rate lower than the sampling rate of the input signal. The decomposed signals by analysis bank filter are less correlated in each sub-band than the input signal at full bandwidth, and can promote better rates of convergence.

Keywords: blind source separation, computational complexity, subband, convergence speed, mixture

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Authors: Salah Al-Din I. Badran, Samad Ahmadi, Ismail Shahin

Abstract:

A blind source separation method is proposed; in this method, we use a non-uniform filter bank and a novel normalisation. This method provides a reduced computational complexity and increased convergence speed comparing to the full-band algorithm. Recently, adaptive sub-band scheme has been recommended to solve two problems: reduction of computational complexity and increase the convergence speed of the adaptive algorithm for correlated input signals. In this work, the reduction in computational complexity is achieved with the use of adaptive filters of orders less than the full-band adaptive filters, which operate at a sampling rate lower than the sampling rate of the input signal. The decomposed signals by analysis bank filter are less correlated in each subband than the input signal at full bandwidth, and can promote better rates of convergence.

Keywords: blind source separation, computational complexity, subband, convergence speed, mixture

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Authors: Seyed Abolhassan Naeini, Azam Kouhpeyma

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Reduction of water level at which a slope is submerged with it is called drawdown. Draw down can took place rapidly or slowly and in both situations, it can affect slope stability. Using coupled analysis (seepage and stability analysis) causes more accurate results. In this study, the stability of homogeneous embankment is investigated numerically. Slope safety factor changes due to changes in three factors of height, slope and drawdown rate have been investigated and compared. It was found that with increasing height and slope, the safety factor decreases, and with increasing the discharge rate, the safety factor increases.

Keywords: drawdown, slope stability, coupled seepage and stability analysis

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Authors: Burak Yildirim, Muhsin Tunay Gençoğlu

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A microgrid (MG) is a small power grid composed of localized medium or low level power generation, storage systems, and loads. In this paper, the effects of a MG on power systems voltage stability are shown. The MG model, designed to demonstrate the effects of the MG, was applied to the IEEE 14 bus power system which is widely used in power system stability studies. Eigenvalue and modal analysis methods were used in simulation studies. In the study results, it is seen that MGs affect system voltage stability positively by increasing system voltage instability limit value for buses of a power system in which MG are placed.

Keywords: eigenvalue analysis, microgrid, modal analysis, voltage stability

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Authors: Andreas Aceranti, Guido Bighiani, Francesca Crotto, Marco Colorato, Stefania Zaghi, Marino Zanetti, Simonetta Vernocchi

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The management of eye parameters such as convergence, accommodation, and miosis is very complex; in fact, both the neurovegetative system and the complex Oculocephalgiria system come into play. We have found the effectiveness of the "highvelocity low amplitude" technique directed on C7-T1 (where the cilio-spinal nucleus of the budge is located) in improving the convergence parameter through the measurement of the point of maximum convergence. With this research, we set out to investigate whether the improvement obtained through the High Velocity Low Amplitude maneuver lasts over time, carrying out a pre-manipulation measurement, one immediately after manipulation and one month after manipulation. We took a population of 30 subjects with both refractive and non-refractive problems. Of the 30 patients tested, 27 gave a positive result after the High Velocity Low Amplitude maneuver, giving an improvement in the point of maximum convergence. After a month, we retested all 27 subjects: some further improved the result, others kept, and three subjects slightly lost the gain obtained. None of the re-tested patients returned to the point of maximum convergence starting pre-manipulation. This result opens the door to a multidisciplinary approach between ophthalmologists and osteopaths with the aim of addressing oculomotricity and convergence deficits that increasingly afflict our society due to the massive use of devices and for the conduct of life in closed and restricted environments.

Keywords: point of maximum convergence, HVLA, improvement in PPC, convergence

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Authors: Seyed Reza Mirdehghan, Mohammad Reza Haeri Yazdi

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In this paper, the stability and the performance of a two-degree-of-freedom robot under an interaction with a unknown environment has been investigated. The time when the robot returns to its initial position after an interaction and the primary resistance of the robot against the impact must be reduced. Thus, the applied torque on the motor will be reduced. The impedance control is an appropriate method for robot control in these conditions. The stability of the robot at interaction moment was transformed to be a robust stability problem. The dynamic of the unknown environment was modeled as a weight function and the stability of the robot under an interaction with the environment has been investigated using the robust control concept. To improve the performance of the system, a force controller has been designed which the normalized impedance after interaction has been reduced. The resistance of the robot has been considered as a normalized cost function and its value was 0.593. The results has showed reduction of resistance of the robot against impact and the reduction of convergence time by lower than one second.

Keywords: impedance control, control system, robots, interaction

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Authors: Bharti Gupta, V. K. Kukreja

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A comprehensive numerical study is presented for the solution of time-dependent advection diffusion problems by using cubic B-spline collocation method. The linear combination of cubic B-spline basis, taken as approximating function, is evaluated using the zeros of shifted Chebyshev polynomials as collocation points in each element to obtain the best approximation. A comparison, on the basis of efficiency and accuracy, with the previous techniques is made which confirms the superiority of the proposed method. An asymptotic convergence analysis of technique is also discussed, and the method is found to be of order two. The theoretical analysis is supported with suitable examples to show second order convergence of technique. Different numerical examples are simulated using MATLAB in which the 3-D graphical presentation has taken at different time steps as well as different domain of interest.

Keywords: cubic B-spline basis, spectral norms, shifted Chebyshev polynomials, collocation points, error estimates

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Authors: Kuniyoshi Abe

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Bi-conjugate gradient (Bi-CG) is a well-known method for solving linear equations Ax = b, for x, where A is a given n-by-n matrix, and b is a given n-vector. Typically, the dimension of the linear equation is high and the matrix is sparse. A number of hybrid Bi-CG methods such as conjugate gradient squared (CGS), Bi-CG stabilized (Bi-CGSTAB), BiCGStab2, and BiCGstab(l) have been developed to improve the convergence of Bi-CG. Bi-CGSTAB has been most often used for efficiently solving the linear equation, but we have seen the convergence behavior with a long stagnation phase. In such cases, it is important to have Bi-CG coefficients that are as accurate as possible, and the stabilization strategy, which stabilizes the computation of the Bi-CG coefficients, has been proposed. It may avoid stagnation and lead to faster computation. Motivated by a large number of processors in present petascale high-performance computing hardware, the scalability of Krylov subspace methods on parallel computers has recently become increasingly prominent. The main bottleneck for efficient parallelization is the inner products which require a global reduction. The resulting global synchronization phases cause communication overhead on parallel computers. The parallel variants of Krylov subspace methods reducing the number of global communication phases and hiding the communication latency have been proposed. However, the numerical stability, specifically, the convergence speed of the parallel variants of Bi-CGSTAB may become worse than that of the standard Bi-CGSTAB. In this paper, therefore, we compare the convergence speed between the standard Bi-CGSTAB and the parallel variants by numerical experiments and show that the convergence speed of the standard Bi-CGSTAB is faster than the parallel variants. Moreover, we propose the stabilization strategy for the parallel variants.

Keywords: bi-conjugate gradient stabilized method, convergence speed, Krylov subspace methods, linear equations, parallel variant

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