Abstract: Most of self-tuning fuzzy systems, which are
automatically constructed from learning data, are based on the
steepest descent method (SDM). However, this approach often
requires a large convergence time and gets stuck into a shallow
local minimum. One of its solutions is to use fuzzy rule modules
with a small number of inputs such as DIRMs (Double-Input Rule
Modules) and SIRMs (Single-Input Rule Modules). In this paper,
we consider a (generalized) DIRMs model composed of double
and single-input rule modules. Further, in order to reduce the
redundant modules for the (generalized) DIRMs model, pruning and
generative learning algorithms for the model are suggested. In order
to show the effectiveness of them, numerical simulations for function
approximation, Box-Jenkins and obstacle avoidance problems are
performed.
Abstract: Steepest descent method is a simple gradient method
for optimization. This method has a slow convergence in heading to
the optimal solution, which occurs because of the zigzag form of the
steps. Barzilai and Borwein modified this algorithm so that it
performs well for problems with large dimensions. Barzilai and
Borwein method results have sparked a lot of research on the method
of steepest descent, including alternate minimization gradient method
and Yuan method. Inspired by previous works, we modified the step
size of the steepest descent method. We then compare the
modification results against the Barzilai and Borwein method,
alternate minimization gradient method and Yuan method for
quadratic function cases in terms of the iterations number and the
running time. The average results indicate that the steepest descent
method with the new step sizes provide good results for small
dimensions and able to compete with the results of Barzilai and
Borwein method and the alternate minimization gradient method for
large dimensions. The new step sizes have faster convergence
compared to the other methods, especially for cases with large
dimensions.
Abstract: An optimal control problem for a mathematical model of efficiency of antiviral therapy in hepatitis B virus infections is considered. The aim of the study is to control the new viral production, block the new infection cells and maintain the number of uninfected cells in the given range. The optimal controls represent the efficiency of antiviral therapy in inhibiting viral production and preventing new infections. Defining the cost functional, the optimal control problem is converted into the constrained optimization problem and the first order optimality system is derived. For the numerical simulation, we propose the steepest descent algorithm based on the adjoint variable method. A computer program in MATLAB is developed for the numerical simulations.
Abstract: Image Compression using Artificial Neural Networks
is a topic where research is being carried out in various directions
towards achieving a generalized and economical network.
Feedforward Networks using Back propagation Algorithm adopting
the method of steepest descent for error minimization is popular and
widely adopted and is directly applied to image compression.
Various research works are directed towards achieving quick
convergence of the network without loss of quality of the restored
image. In general the images used for compression are of different
types like dark image, high intensity image etc. When these images
are compressed using Back-propagation Network, it takes longer
time to converge. The reason for this is, the given image may
contain a number of distinct gray levels with narrow difference with
their neighborhood pixels. If the gray levels of the pixels in an image
and their neighbors are mapped in such a way that the difference in
the gray levels of the neighbors with the pixel is minimum, then
compression ratio as well as the convergence of the network can be
improved. To achieve this, a Cumulative distribution function is
estimated for the image and it is used to map the image pixels. When
the mapped image pixels are used, the Back-propagation Neural
Network yields high compression ratio as well as it converges
quickly.
Abstract: The optimal control problem for the viscoelastic melt
spinning process has not been reported yet in the literature. In this
study, an optimal control problem for a mathematical model of a
viscoelastic melt spinning process is considered. Maxwell-Oldroyd
model is used to describe the rheology of the polymeric material, the
fiber is made of. The extrusion velocity of the polymer at the spinneret
as well as the velocity and the temperature of the quench air and the
fiber length serve as control variables. A constrained optimization
problem is derived and the first–order optimality system is set up
to obtain the adjoint equations. Numerical solutions are carried out
using a steepest descent algorithm. A computer program in MATLAB
is developed for simulations.
Abstract: This paper presents the determination of the proper
quality costs parameters which provide the optimum return. The
system dynamics simulation was applied. The simulation model was
constructed by the real data from a case of the electronic devices
manufacturer in Thailand. The Steepest Descent algorithm was
employed to optimise. The experimental results show that the
company should spend on prevention and appraisal activities for 850
and 10 Baht/day respectively. It provides minimum cumulative total
quality cost, which is 258,000 Baht in twelve months. The effect of
the step size in the stage of improving the variables to the optimum
was also investigated. It can be stated that the smaller step size
provided a better result with more experimental runs. However, the
different yield in this case is not significant in practice. Therefore, the
greater step size is recommended because the region of optima could
be reached more easily and rapidly.
Abstract: Inverse kinematics analysis plays an important role in developing a robot manipulator. But it is not too easy to derive the inverse kinematic equation of a robot manipulator especially robot manipulator which has numerous degree of freedom. This paper describes an application of Artificial Neural Network for modeling the inverse kinematics equation of a robot manipulator. In this case, the robot has three degree of freedoms and the robot was implemented for drilling a printed circuit board. The artificial neural network architecture used for modeling is a multilayer perceptron networks with steepest descent backpropagation training algorithm. The designed artificial neural network has 2 inputs, 2 outputs and varies in number of hidden layer. Experiments were done in variation of number of hidden layer and learning rate. Experimental results show that the best architecture of artificial neural network used for modeling inverse kinematics of is multilayer perceptron with 1 hidden layer and 38 neurons per hidden layer. This network resulted a RMSE value of 0.01474.