Abstract: Most real world systems express themselves formally
as a set of nonlinear algebraic equations. As applications grow, the
size and complexity of these equations also increase. In this work, we
highlight the key concepts in using the homotopy analysis method
as a methodology used to construct efficient iteration formulas for
nonlinear equations solving. The proposed method is experimentally
characterized according to a set of determined parameters which
affect the systems. The experimental results show the potential and
limitations of the new method and imply directions for future work.
Abstract: In the present paper, we present a modification of the
New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari
[J. Math. Anal. Appl. 2006;316:753–763] and use it for solving
systems of nonlinear functional equations. This modification yields
a series with faster convergence. Illustrative examples are presented
to demonstrate the method.
Abstract: The paper addresses a problem of optimal staffing in
open shop environment. The problem is to determine the optimal
number of operators serving a given number of machines to fulfill the
number of independent operations while minimizing staff idle. Using
a Gantt chart presentation of the problem it is modeled as twodimensional
cutting stock problem. A mixed-integer programming
model is used to get minimal job processing time (makespan) for
fixed number of machines' operators. An algorithm for optimal openshop
staffing is developed based on iterative solving of the
formulated optimization task. The execution of the developed
algorithm provides optimal number of machines' operators in the
sense of minimum staff idle and optimal makespan for that number of
operators. The proposed algorithm is tested numerically for a real life
staffing problem. The testing results show the practical applicability
for similar open shop staffing problems.
Abstract: Unified Speech Audio Coding (USAC), the latest MPEG standardization for unified speech and audio coding, uses a speech/audio classification algorithm to distinguish speech and audio segments of the input signal. The quality of the recovered audio can be increased by well-designed orchestra/percussion classification and subsequent processing. However, owing to the shortcoming of the system, introducing an orchestra/percussion classification and modifying subsequent processing can enormously increase the quality of the recovered audio. This paper proposes an orchestra/percussion classification algorithm for the USAC system which only extracts 3 scales of Mel-Frequency Cepstral Coefficients (MFCCs) rather than traditional 13 scales of MFCCs and use Iterative Dichotomiser 3 (ID3) Decision Tree rather than other complex learning method, thus the proposed algorithm has lower computing complexity than most existing algorithms. Considering that frequent changing of attributes may lead to quality loss of the recovered audio signal, this paper also design a modified subsequent process to help the whole classification system reach an accurate rate as high as 97% which is comparable to classical 99%.
Abstract: An iterative definition of any n variable mean function is given in this article, which iteratively uses the two-variable form of the corresponding two-variable mean function. This extension method omits recursivity which is an important improvement compared with certain recursive formulas given before by Ando-Li-Mathias, Petz- Temesi. Furthermore it is conjectured here that this iterative algorithm coincides with the solution of the Riemann centroid minimization problem. Certain simulations are given here to compare the convergence rate of the different algorithms given in the literature. These algorithms will be the gradient and the Newton mehod for the Riemann centroid computation.
Abstract: In this paper, we have proposed a Haar wavelet quasilinearization
method to solve the well known Blasius equation. The
method is based on the uniform Haar wavelet operational matrix
defined over the interval [0, 1]. In this method, we have proposed the
transformation for converting the problem on a fixed computational
domain. The Blasius equation arises in the various boundary layer
problems of hydrodynamics and in fluid mechanics of laminar
viscous flows. Quasi-linearization is iterative process but our
proposed technique gives excellent numerical results with quasilinearization
for solving nonlinear differential equations without any
iteration on selecting collocation points by Haar wavelets. We have
solved Blasius equation for 1≤α ≤ 2 and the numerical results are
compared with the available results in literature. Finally, we
conclude that proposed method is a promising tool for solving the
well known nonlinear Blasius equation.
Abstract: This paper presents kinematic and dynamic analysis of a novel 8-DOF hybrid robot manipulator. The hybrid robot manipulator under consideration consists of a parallel robot which
is followed by a serial mechanism. The parallel mechanism has three translational DOF, and the serial mechanism has five DOF so that the overall degree of freedom is eight. The introduced
manipulator has a wide workspace and a high capability to reduce
the actuating energy. The inverse and forward kinematic solutions are described in closed form. The theoretical results are verified by
a numerical example. Inverse dynamic analysis of the robot is presented by utilizing the Iterative Newton-Euler and Lagrange dynamic formulation methods. Finally, for performing a multi-step
arc welding process, results have indicated that the introduced manipulator is highly capable of reducing the actuating energy.
Abstract: The paper presents a simple and an accurate formula
that has been developed for the conduction angle (δ) of a single
phase half-wave or full-wave controlled rectifier with RL load. This
formula can be also used for calculating the conduction angle (δ) in
case of A.C. voltage regulator with inductive load under
discontinuous current mode. The simulation results shows that the
conduction angle calculated from the developed formula agree very
well with that obtained from the exact solution arrived from the
iterative method. Applying the developed formula can reduce the
computational time and reduce the time for manual classroom
calculation. In addition, the proposed formula is attractive for real
time implementations.
Abstract: The study of a real function of two real variables can be supported by visualization using a Computer Algebra System (CAS). One type of constraints of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the function and can provide strange plots, not compatible with the mathematics. In recent years, point based geometry has gained increasing attention as an alternative surface representation, both for efficient rendering and for flexible geometry processing of complex surfaces. In this paper we present different artifacts created by mesh surfaces near discontinuities and propose a point based method that controls and reduces these artifacts. A least squares penalty method for an automatic generation of the mesh that controls the behavior of the chosen function is presented. The special feature of this method is the ability to improve the accuracy of the surface visualization near a set of interior points where the function may be discontinuous. The present method is formulated as a minimax problem and the non uniform mesh is generated using an iterative algorithm. Results show that for large poorly conditioned matrices, the new algorithm gives more accurate results than the classical preconditioned conjugate algorithm.
Abstract: This paper evaluates performances of an adaptive noise
cancelling (ANC) based target detection algorithm on a set of real test
data supported by the Defense Evaluation Research Agency (DERA
UK) for multi-target wideband active sonar echolocation system. The
hybrid algorithm proposed is a combination of an adaptive ANC
neuro-fuzzy scheme in the first instance and followed by an iterative
optimum target motion estimation (TME) scheme. The neuro-fuzzy
scheme is based on the adaptive noise cancelling concept with the
core processor of ANFIS (adaptive neuro-fuzzy inference system) to
provide an effective fine tuned signal. The resultant output is then
sent as an input to the optimum TME scheme composed of twogauge
trimmed-mean (TM) levelization, discrete wavelet denoising
(WDeN), and optimal continuous wavelet transform (CWT) for
further denosing and targets identification. Its aim is to recover the
contact signals in an effective and efficient manner and then determine
the Doppler motion (radial range, velocity and acceleration) at very
low signal-to-noise ratio (SNR). Quantitative results have shown that
the hybrid algorithm have excellent performance in predicting targets-
Doppler motion within various target strength with the maximum
false detection of 1.5%.
Abstract: This paper presents a new heuristic algorithm useful
for long-term planning of survivable WDM networks. A multi-period
model is formulated that combines network topology design and
capacity expansion. The ability to determine network expansion
schedules of this type becomes increasingly important to the
telecommunications industry and to its customers. The solution
technique consists of a Genetic Algorithm that allows generating
several network alternatives for each time period simultaneously and
shortest-path techniques to deduce from these alternatives a least-cost
network expansion plan over all time periods. The multi-period
planning approach is illustrated on a realistic network example.
Extensive simulations on a wide range of problem instances are
carried out to assess the cost savings that can be expected by
choosing a multi-period planning approach instead of an iterative
network expansion design method.
Abstract: Installation of power compensation equipment in
some cases places additional buses into the system. Therefore, a total
number of power flow equations and voltage unknowns increase due
to additional locations of installed devices. In this circumstance, power flow calculation is more complicated. It may result in a
computational convergence problem. This paper presents a power flow calculation by using Newton-Raphson iterative method together
with the proposed load transfer technique. This concept is to eliminate additional buses by transferring installed loads at the new buses to existing two adjacent buses. Thus, the total number of power
flow equations is not changed. The overall computational speed is
expectedly shorter than that of solving the problem without applying the load transfer technique. A 15-bus test system is employed for test
to evaluate the effectiveness of the proposed load transfer technique. As a result, the total number of iteration required and execution time
is significantly reduced.
Abstract: Repetitive systems stand for a kind of systems that
perform a simple task on a fixed pattern repetitively, which are
widely spread in industrial fields. Hence, many researchers have been
interested in those systems, especially in the field of iterative learning
control (ILC). In this paper, we propose a finite-horizon tracking
control scheme for linear time-varying repetitive systems with uncertain
initial conditions. The scheme is derived both analytically
and numerically for state-feedback systems and only numerically for
output-feedback systems. Then, it is extended to stable systems with
input constraints. All numerical schemes are developed in the forms
of linear matrix inequalities (LMIs). A distinguished feature of the
proposed scheme from the existing iterative learning control is that
the scheme guarantees the tracking performance exactly even under
uncertain initial conditions. The simulation results demonstrate the
good performance of the proposed scheme.
Abstract: In the last few years, three multivariate spectral
analysis techniques namely, Principal Component Analysis (PCA),
Independent Component Analysis (ICA) and Non-negative Matrix
Factorization (NMF) have emerged as effective tools for oscillation
detection and isolation. While the first method is used in determining
the number of oscillatory sources, the latter two methods
are used to identify source signatures by formulating the detection
problem as a source identification problem in the spectral domain.
In this paper, we present a critical drawback of the underlying linear
(mixing) model which strongly limits the ability of the associated
source separation methods to determine the number of sources
and/or identify the physical source signatures. It is shown that the
assumed mixing model is only valid if each unit of the process gives
equal weighting (all-pass filter) to all oscillatory components in its
inputs. This is in contrast to the fact that each unit, in general, acts
as a filter with non-uniform frequency response. Thus, the model
can only facilitate correct identification of a source with a single
frequency component, which is again unrealistic. To overcome
this deficiency, an iterative post-processing algorithm that correctly
identifies the physical source(s) is developed. An additional issue
with the existing methods is that they lack a procedure to pre-screen
non-oscillatory/noisy measurements which obscure the identification
of oscillatory sources. In this regard, a pre-screening procedure
is prescribed based on the notion of sparseness index to eliminate
the noisy and non-oscillatory measurements from the data set used
for analysis.