Abstract: A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.
Abstract: This paper focuses on the development of bond graph
dynamic model of the mechanical dynamics of an excavating mechanism
previously designed to be used with small tractors, which are
fabricated in the Engineering Workshops of Jomo Kenyatta University
of Agriculture and Technology. To develop a mechanical dynamics
model of the manipulator, forward recursive equations similar to
those applied in iterative Newton-Euler method were used to obtain
kinematic relationships between the time rates of joint variables
and the generalized cartesian velocities for the centroids of the
links. Representing the obtained kinematic relationships in bondgraphic
form, while considering the link weights and momenta as
the elements led to a detailed bond graph model of the manipulator.
The bond graph method was found to reduce significantly the number
of recursive computations performed on a 3 DOF manipulator for a
mechanical dynamic model to result, hence indicating that bond graph
method is more computationally efficient than the Newton-Euler
method in developing dynamic models of 3 DOF planar manipulators.
The model was verified by comparing the joint torque expressions
of a two link planar manipulator to those obtained using Newton-
Euler and Lagrangian methods as analyzed in robotic textbooks. The
expressions were found to agree indicating that the model captures
the aspects of rigid body dynamics of the manipulator. Based on
the model developed, actuator sizing and valve sizing methodologies
were developed and used to obtain the optimal sizes of the pistons
and spool valve ports respectively. It was found that using the pump
with the sized flow rate capacity, the engine of the tractor is able to
power the excavating mechanism in digging a sandy-loom soil.
Abstract: A new, rapidly convergent, numerical procedure for
internal loading distribution computation in statically loaded, singlerow,
angular-contact ball bearings, subjected to a known combined
radial and thrust load, which must be applied so that to avoid tilting
between inner and outer rings, is used to find the load distribution
differences between a loaded unfitted bearing at room temperature,
and the same loaded bearing with interference fits that might
experience radial temperature gradients between inner and outer
rings. For each step of the procedure it is required the iterative
solution of Z + 2 simultaneous nonlinear equations – where Z is the
number of the balls – to yield exact solution for axial and radial
deflections, and contact angles.
Abstract: In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.
Abstract: In this paper we introduce a novel kernel classifier
based on a iterative shrinkage algorithm developed for compressive
sensing. We have adopted Bregman iteration with soft and hard
shrinkage functions and generalized hinge loss for solving l1 norm
minimization problem for classification. Our experimental results
with face recognition and digit classification using SVM as the
benchmark have shown that our method has a close error rate
compared to SVM but do not perform better than SVM. We have
found that the soft shrinkage method give more accuracy and in some
situations more sparseness than hard shrinkage methods.
Abstract: This paper presents an optimal design of linear phase
digital high pass finite impulse response (FIR) filter using Improved
Particle Swarm Optimization (IPSO). In the design process, the filter
length, pass band and stop band frequencies, feasible pass band and
stop band ripple sizes are specified. FIR filter design is a multi-modal
optimization problem. An iterative method is introduced to find the
optimal solution of FIR filter design problem. Evolutionary
algorithms like real code genetic algorithm (RGA), particle swarm
optimization (PSO), improved particle swarm optimization (IPSO)
have been used in this work for the design of linear phase high pass
FIR filter. IPSO is an improved PSO that proposes a new definition
for the velocity vector and swarm updating and hence the solution
quality is improved. A comparison of simulation results reveals the
optimization efficacy of the algorithm over the prevailing
optimization techniques for the solution of the multimodal, nondifferentiable,
highly non-linear, and constrained FIR filter design
problems.
Abstract: This paper presents an iterative algorithm to find a
inverse kinematic solution of 5-DOF robot. The algorithm is to
minimize the iteration number. Since the 5-DOF robot cannot give full
orientation of tool. Only z-direction of tool is satisfied while rotation
of tool is determined by kinematic constraint. This work therefore
described how to specify the tool direction and let the tool rotation free.
The simulation results show that this algorithm effectively worked.
Using the proposed iteration algorithm, error due to inverse kinematics
converged to zero rapidly in 5 iterations. This algorithm was applied in
real welding robot and verified through various practical works.
Abstract: This paper presents the development of a hybrid
thermal model for the EVO Electric AFM 140 Axial Flux Permanent
Magnet (AFPM) machine as used in hybrid and electric vehicles. The
adopted approach is based on a hybrid lumped parameter and finite
difference method. The proposed method divides each motor
component into regular elements which are connected together in a
thermal resistance network representing all the physical connections
in all three dimensions. The element shape and size are chosen
according to the component geometry to ensure consistency. The
fluid domain is lumped into one region with averaged heat transfer
parameters connecting it to the solid domain. Some model parameters
are obtained from Computation Fluid Dynamic (CFD) simulation and
empirical data. The hybrid thermal model is described by a set of
coupled linear first order differential equations which is discretised
and solved iteratively to obtain the temperature profile. The
computation involved is low and thus the model is suitable for
transient temperature predictions. The maximum error in temperature
prediction is 3.4% and the mean error is consistently lower than the
mean error due to uncertainty in measurements. The details of the
model development, temperature predictions and suggestions for
design improvements are presented in this paper.
Abstract: The focal spot of a high intensity focused ultrasound
transducer is small. To heat a large target volume, multiple treatment spots are required. If the power of each treatment spot is fixed, it could
results in insufficient heating of initial spots and over-heating of later ones, which is caused by the thermal diffusion. Hence, to produce a
uniform heated volume, the delivered energy of each treatment spot
should be properly adjusted. In this study, we proposed an iterative, extrapolation technique to adjust the required ultrasound energy of
each treatment spot. Three different scanning pathways were used to evaluate the performance of this technique. Results indicate that by using the proposed technique, uniform heating volume could be obtained.
Abstract: A known iterative computational procedure is used for
internal normal ball loads calculation in statically loaded single-row,
angular-contact ball bearings, subjected to a known thrust load,
which is applied in the inner ring at the geometric bearing center line.
Numerical aspects of the iterative procedure are discussed.
Numerical examples results for a 218 angular-contact ball bearing
have been compared with those from the literature. Twenty figures
are presented showing the geometrical features, the behavior of the
convergence variables and the following parameters as functions of
the thrust load: normal ball loads, contact angle, distance between
curvature centers, and normal ball and axial deflections between the
raceways.
Abstract: In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.
Abstract: Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.
Abstract: Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.
Abstract: This study proposes a multi-response surface
optimization problem (MRSOP) for determining the proper choices
of a process parameter design (PPD) decision problem in a noisy
environment of a grease position process in an electronic industry.
The proposed models attempts to maximize dual process responses
on the mean of parts between failure on left and right processes. The
conventional modified simplex method and its hybridization of the
stochastic operator from the hunting search algorithm are applied to
determine the proper levels of controllable design parameters
affecting the quality performances. A numerical example
demonstrates the feasibility of applying the proposed model to the
PPD problem via two iterative methods. Its advantages are also
discussed. Numerical results demonstrate that the hybridization is
superior to the use of the conventional method. In this study, the
mean of parts between failure on left and right lines improve by
39.51%, approximately. All experimental data presented in this
research have been normalized to disguise actual performance
measures as raw data are considered to be confidential.
Abstract: In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.
Abstract: The Spiral development model has been used
successfully in many commercial systems and in a good number of
defense systems. This is due to the fact that cost-effective
incremental commitment of funds, via an analogy of the spiral model
to stud poker and also can be used to develop hardware or integrate
software, hardware, and systems. To support adaptive, semantic
collaboration between domain experts and knowledge engineers, a
new knowledge engineering process, called Spiral_OWL is proposed.
This model is based on the idea of iterative refinement, annotation
and structuring of knowledge base. The Spiral_OWL model is
generated base on spiral model and knowledge engineering
methodology. A central paradigm for Spiral_OWL model is the
concentration on risk-driven determination of knowledge engineering
process. The collaboration aspect comes into play during knowledge
acquisition and knowledge validation phase. Design rationales for the
Spiral_OWL model are to be easy-to-implement, well-organized, and
iterative development cycle as an expanding spiral.
Abstract: This paper describes an automatic algorithm to restore
the shape of three-dimensional (3D) left ventricle (LV) models created
from magnetic resonance imaging (MRI) data using a geometry-driven
optimization approach. Our basic premise is to restore the LV shape
such that the LV epicardial surface is smooth after the restoration. A
geometrical measure known as the Minimum Principle Curvature (κ2)
is used to assess the smoothness of the LV. This measure is used to
construct the objective function of a two-step optimization process.
The objective of the optimization is to achieve a smooth epicardial
shape by iterative in-plane translation of the MRI slices.
Quantitatively, this yields a minimum sum in terms of the magnitude
of κ
2, when κ2 is negative. A limited memory quasi-Newton algorithm,
L-BFGS-B, is used to solve the optimization problem. We tested our
algorithm on an in vitro theoretical LV model and 10 in vivo
patient-specific models which contain significant motion artifacts. The
results show that our method is able to automatically restore the shape
of LV models back to smoothness without altering the general shape of
the model. The magnitudes of in-plane translations are also consistent
with existing registration techniques and experimental findings.
Abstract: The aim of this research is to design a collaborative
framework that integrates risk analysis activities into the geospatial
database design (GDD) process. Risk analysis is rarely undertaken
iteratively as part of the present GDD methods in conformance to
requirement engineering (RE) guidelines and risk standards.
Accordingly, when risk analysis is performed during the GDD, some
foreseeable risks may be overlooked and not reach the output
specifications especially when user intentions are not systematically
collected. This may lead to ill-defined requirements and ultimately in
higher risks of geospatial data misuse. The adopted approach consists
of 1) reviewing risk analysis process within the scope of RE and
GDD, 2) analyzing the challenges of risk analysis within the context
of GDD, and 3) presenting the components of a risk-based
collaborative framework that improves the collection of the
intended/forbidden usages of the data and helps geo-IT experts to
discover implicit requirements and risks.
Abstract: In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.
Abstract: This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.