Abstract: In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.
Abstract: Structures of eye bottom were extracted using multiscale texture gradient method and color characteristics of macular zone and vessels were verified in CIELAB scale. The difference of average values of L*, a* and b* coordinates of CIE (International Commision of Illumination) scale in patients with diabetes and healthy volunteers was compared. The average value of L* in diabetic patients exceeded such one in the group of practically healthy persons by 2.71 times (P
Abstract: Several techniques exist for determining stress-intensity factors in linear elastic fracture mechanics analysis. These techniques are based on analytical, numerical, and empirical approaches that have been well documented in literature and engineering handbooks. However, not all techniques share the same merit. In addition to overly-conservative results, the numerical methods that require extensive computational effort, and those requiring copious user parameters hinder practicing engineers from efficiently evaluating stress-intensity factors. This paper investigates the prospects of reducing the complexity and required variables to determine stress-intensity factors through the utilization of the stress gradient and a weighting function. The heart of this work resides in the understanding that fracture emanating from stress concentration locations cannot be explained by a single maximum stress value approach, but requires use of a critical volume in which the crack exists. In order to understand the effectiveness of this technique, this study investigated components of different notch geometry and varying levels of stress gradients. Two forms of weighting functions were employed to determine stress-intensity factors and results were compared to analytical exact methods. The results indicated that the “exponential” weighting function was superior to the “absolute” weighting function. An error band +/- 10% was met for cases ranging from a steep stress gradient in a sharp v-notch to the less severe stress transitions of a large circular notch. The incorporation of the proposed method has shown to be a worthwhile consideration.
Abstract: A two-step multigrid approach is proposed to solve the inverse heat conduction problem in a 3-D object under laser irradiation. In the first step, the location of the laser center is estimated using a coarse and uniform grid system. In the second step, the front-surface temperature is recovered in good accuracy using a multiple grid system in which fine mesh is used at laser spot center to capture the drastic temperature rise in this region but coarse mesh is employed in the peripheral region to reduce the total number of sensors required. The effectiveness of the two-step approach and the multiple grid system are demonstrated by the illustrative inverse solutions. If the measurement data for the temperature and heat flux on the back surface do not contain random error, the proposed multigrid approach can yield more accurate inverse solutions. When the back-surface measurement data contain random noise, accurate inverse solutions cannot be obtained if both temperature and heat flux are measured on the back surface.
Abstract: Gradient boosting methods have been proven to be a very important strategy. Many successful machine learning solutions were developed using the XGBoost and its derivatives. The aim of this study is to investigate and compare the efficiency of three gradient methods. Home credit dataset is used in this work which contains 219 features and 356251 records. However, new features are generated and several techniques are used to rank and select the best features. The implementation indicates that the LightGBM is faster and more accurate than CatBoost and XGBoost using variant number of features and records.
Abstract: Modeling sediment transport processes by means of numerical approach often poses severe challenges. In this way, a number of techniques have been suggested to solve flow and sediment equations in decoupled, semi-coupled or fully coupled forms. Furthermore, in order to capture flow discontinuities, a number of techniques, like artificial viscosity and shock fitting, have been proposed for solving these equations which are mostly required careful calibration processes. In this research, a numerical scheme for solving shallow water and Exner equations in fully coupled form is presented. First-Order Centered scheme is applied for producing required numerical fluxes and the reconstruction process is carried out toward using Monotonic Upstream Scheme for Conservation Laws to achieve a high order scheme. In order to satisfy C-property of the scheme in presence of bed topography, Surface Gradient Method is proposed. Combining the presented scheme with fourth order Runge-Kutta algorithm for time integration yields a competent numerical scheme. In addition, to handle non-prismatic channels problems, Cartesian Cut Cell Method is employed. A trained Multi-Layer Perceptron Artificial Neural Network which is of Feed Forward Back Propagation (FFBP) type estimates sediment flow discharge in the model rather than usual empirical formulas. Hydrodynamic part of the model is tested for showing its capability in simulation of flow discontinuities, transcritical flows, wetting/drying conditions and non-prismatic channel flows. In this end, dam-break flow onto a locally non-prismatic converging-diverging channel with initially dry bed conditions is modeled. The morphodynamic part of the model is verified simulating dam break on a dry movable bed and bed level variations in an alluvial junction. The results show that the model is capable in capturing the flow discontinuities, solving wetting/drying problems even in non-prismatic channels and presenting proper results for movable bed situations. It can also be deducted that applying Artificial Neural Network, instead of common empirical formulas for estimating sediment flow discharge, leads to more accurate results.
Abstract: Statement of the automatic speech recognition
problem, the assignment of speech recognition and the application
fields are shown in the paper. At the same time as Azerbaijan speech,
the establishment principles of speech recognition system and the
problems arising in the system are investigated. The computing algorithms of speech features, being the main part
of speech recognition system, are analyzed. From this point of view,
the determination algorithms of Mel Frequency Cepstral Coefficients
(MFCC) and Linear Predictive Coding (LPC) coefficients expressing
the basic speech features are developed. Combined use of cepstrals of
MFCC and LPC in speech recognition system is suggested to
improve the reliability of speech recognition system. To this end, the
recognition system is divided into MFCC and LPC-based recognition
subsystems. The training and recognition processes are realized in
both subsystems separately, and recognition system gets the decision
being the same results of each subsystems. This results in decrease of
error rate during recognition. The training and recognition processes are realized by artificial
neural networks in the automatic speech recognition system. The
neural networks are trained by the conjugate gradient method. In the
paper the problems observed by the number of speech features at
training the neural networks of MFCC and LPC-based speech
recognition subsystems are investigated. The variety of results of neural networks trained from different
initial points in training process is analyzed. Methodology of
combined use of neural networks trained from different initial points
in speech recognition system is suggested to improve the reliability
of recognition system and increase the recognition quality, and
obtained practical results are shown.
Abstract: In this paper, we consider a geometric inverse source
problem for the heat equation with Dirichlet and Neumann boundary
data. We will reconstruct the exact form of the unknown source
term from additional boundary conditions. Our motivation is to
detect the location, the size and the shape of source support.
We present a one-shot algorithm based on the Kohn-Vogelius
formulation and the topological gradient method. The geometric
inverse source problem is formulated as a topology optimization
one. A topological sensitivity analysis is derived from a source
function. Then, we present a non-iterative numerical method for the
geometric reconstruction of the source term with unknown support
using a level curve of the topological gradient. Finally, we give
several examples to show the viability of our presented method.
Abstract: Since the advances in digital imaging technologies have led to
development of high quality digital devices, there are a lot of illegal copies
of copyrighted video content on the Internet. Also, unauthorized editing is
occurred frequently. Thus, we propose an editing prevention technique for
high-quality (HQ) video that can prevent these illegally edited copies from
spreading out. The proposed technique is applied spatial and temporal gradient
methods to improve the fidelity and detection performance. Also, the scheme
duplicates the embedding signal temporally to alleviate the signal reduction
caused by geometric and signal-processing distortions. Experimental results
show that the proposed scheme achieves better performance than previously
proposed schemes and it has high fidelity. The proposed scheme can be used
in unauthorized access prevention method of visual communication or traitor
tracking applications which need fast detection process to prevent illegally
edited video content from spreading out.
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: The sound pressure level (SPL) of the moving-coil
loudspeaker (MCL) is often simulated and analyzed using the lumped
parameter model. However, the SPL of a MCL cannot be simulated
precisely in the high frequency region, because the value of cone
effective area is changed due to the geometry variation in different
mode shapes, it is also related to affect the acoustic radiation mass and
resistance. Herein, the paper presents the inverse method which has a
high ability to measure the value of cone effective area in various
frequency points, also can estimate the MCL electroacoustic
parameters simultaneously. The proposed inverse method comprises
the direct problem, adjoint problem, and sensitivity problem in
collaboration with nonlinear conjugate gradient method. Estimated
values from the inverse method are validated experimentally which
compared with the measured SPL curve result. Results presented in
this paper not only improve the accuracy of lumped parameter model
but also provide the valuable information on loudspeaker cone design.
Abstract: We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.
Abstract: 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.
Abstract: The purpose of this study is to derive optimal shapes of
a body located in viscous flows by the finite element method using the
acoustic velocity and the four-step explicit scheme. The formulation
is based on an optimal control theory in which a performance function
of the fluid force is introduced. The performance function should be
minimized satisfying the state equation. This problem can be transformed
into the minimization problem without constraint conditions
by using the adjoint equation with adjoint variables corresponding to
the state equation. The performance function is defined by the drag
and lift forces acting on the body. The weighted gradient method
is applied as a minimization technique, the Galerkin finite element
method is used as a spatial discretization and the four-step explicit
scheme is used as a temporal discretization to solve the state equation
and the adjoint equation. As the interpolation, the orthogonal basis
bubble function for velocity and the linear function for pressure
are employed. In case that the orthogonal basis bubble function is
used, the mass matrix can be diagonalized without any artificial
centralization. The shape optimization is performed by the presented
method.
Abstract: An inverse geometry problem is solved to predict an
unknown irregular boundary profile. The aim is to minimize the
objective function, which is the difference between real and
computed temperatures, using three different versions of Conjugate
Gradient Method. The gradient of the objective function, considered
necessary in this method, obtained as a result of solving the adjoint
equation. The abilities of three versions of Conjugate Gradient
Method in predicting the boundary profile are compared using a
numerical algorithm based on the method. The predicted shapes show
that due to its convergence rate and accuracy of predicted values, the
Powell-Beale version of the method is more effective than the
Fletcher-Reeves and Polak –Ribiere versions.
Abstract: The solution algorithm, based on Lagrangian relaxation, a sub-gradient method and a heuristic to find the upper bound of the solution, is proposed to solve the coordinated fleet routing and flight scheduling problems. Numerical tests are performed to evaluate the proposed algorithm using real operating data from two Taiwan airlines. The test results indicate that the solution algorithm is a significant improvement over those obtained with CPLEX, consequently they could be useful for allied airlines to solve coordinated fleet routing and flight scheduling problems.
Abstract: We investigated statistical performance of Bayesian inference using maximum entropy and MAP estimation for several models which approximated wave-fronts in remote sensing using SAR interferometry. Using Monte Carlo simulation for a set of wave-fronts generated by assumed true prior, we found that the method of maximum entropy realized the optimal performance around the Bayes-optimal conditions by using model of the true prior and the likelihood representing optical measurement due to the interferometer. Also, we found that the MAP estimation regarded as a deterministic limit of maximum entropy almost achieved the same performance as the Bayes-optimal solution for the set of wave-fronts. Then, we clarified that the MAP estimation perfectly carried out phase unwrapping without using prior information, and also that the MAP estimation realized accurate phase unwrapping using conjugate gradient (CG) method, if we assumed the model of the true prior appropriately.
Abstract: This article is based on the technique which is called
Discrete Parameter Tracking (DPT). First introduced by A. A. Azab
[8] which is applicable for less order reference model. The order of
the reference model is (n-l) and n is the number of the adjustable
parameters in the physical plant.
The technique utilizes a modified gradient method [9] where the
knowledge of the exact order of the nonadaptive system is not
required, so, as to eliminate the identification problem. The
applicability of the mentioned technique (DPT) was examined
through the solution of several problems.
This article introduces the solution of a third order system with
three adjustable parameters, controlled according to second order
reference model. The adjustable parameters have great initial error
which represent condition.
Computer simulations for the solution and analysis are provided
to demonstrate the simplicity and feasibility of the technique.
Abstract: This paper focuses on a technique for identifying the geological boundary of the ground strata in front of a tunnel excavation site using the first order adjoint method based on the optimal control theory. The geological boundary is defined as the boundary which is different layers of elastic modulus. At tunnel excavations, it is important to presume the ground situation ahead of the cutting face beforehand. Excavating into weak strata or fault fracture zones may cause extension of the construction work and human suffering. A theory for determining the geological boundary of the ground in a numerical manner is investigated, employing excavating blasts and its vibration waves as the observation references. According to the optimal control theory, the performance function described by the square sum of the residuals between computed and observed velocities is minimized. The boundary layer is determined by minimizing the performance function. The elastic analysis governed by the Navier equation is carried out, assuming the ground as an elastic body with linear viscous damping. To identify the boundary, the gradient of the performance function with respect to the geological boundary can be calculated using the adjoint equation. The weighed gradient method is effectively applied to the minimization algorithm. To solve the governing and adjoint equations, the Galerkin finite element method and the average acceleration method are employed for the spatial and temporal discretizations, respectively. Based on the method presented in this paper, the different boundary of three strata can be identified. For the numerical studies, the Suemune tunnel excavation site is employed. At first, the blasting force is identified in order to perform the accuracy improvement of analysis. We identify the geological boundary after the estimation of blasting force. With this identification procedure, the numerical analysis results which almost correspond with the observation data were provided.
Abstract: The conjugate gradient optimization algorithm
usually used for nonlinear least squares is presented and is
combined with the modified back propagation algorithm yielding
a new fast training multilayer perceptron (MLP) algorithm
(CGFR/AG). The approaches presented in the paper consist of
three steps: (1) Modification on standard back propagation
algorithm by introducing gain variation term of the activation
function, (2) Calculating the gradient descent on error with
respect to the weights and gains values and (3) the determination
of the new search direction by exploiting the information
calculated by gradient descent in step (2) as well as the previous
search direction. The proposed method improved the training
efficiency of back propagation algorithm by adaptively modifying
the initial search direction. Performance of the proposed method
is demonstrated by comparing to the conjugate gradient algorithm
from neural network toolbox for the chosen benchmark. The
results show that the number of iterations required by the
proposed method to converge is less than 20% of what is required
by the standard conjugate gradient and neural network toolbox
algorithm.