Noor Atinah Ahmad

Recent developments in phase-field models of solidification

In this paper we review the current state-of-the-art in the modeling of solidification by phase-field models. We briefly review the phase-field formulation of the solidification of a pure material and discuss how important physical effects, such as surface energy anisotropy, may be included. We go on to discuss numerical solutions of the phase-field equations, with particular reference to the computation of dendrites. Finally, we describe recent successful attempts to extend the phase-field methodology to alloys.

A Globally Convergent Stochastic Pairwise Conjugate Gradient-Based Algorithm for Adaptive Filtering

It is well known that, for the deterministic optimization problem, the method of conjugate gradient has superior convergence rates compared to ordinary gradient methods. For quadratic problems, the conjugate gradient method has finite termination property which makes it one of the most favorable iterative methods. However, the fast convergence and the finite termination property can easily break down when the function to be optimized is noisy since conjugacy among search directions can no longer be maintained over the course of the iterations. In this letter, a conjugation procedure is applied in an adaptive filtering algorithm, where, instead of producing a set of conjugate search directions, only pairwise conjugation of gradients is produced during each system update. Simulations show that the algorithm provides superior convergence compared to the stochastic gradient descent algorithm, and comparable to existing conjugate gradient-based adaptive filtering algorithms, but at a lower computational cost.

A Stochastic Total Least Squares Solution of Adaptive Filtering Problem

An efficient and computationally linear algorithm is derived for total least squares solution of adaptive filtering problem, when both input and output signals are contaminated by noise. The proposed total least mean squares (TLMS) algorithm is designed by recursively computing an optimal solution of adaptive TLS problem by minimizing instantaneous value of weighted cost function. Convergence analysis of the algorithm is given to show the global convergence of the proposed algorithm, provided that the stepsize parameter is appropriately chosen. The TLMS algorithm is computationally simpler than the other TLS algorithms and demonstrates a better performance as compared with the least mean square (LMS) and normalized least mean square (NLMS) algorithms. It provides minimum mean square deviation by exhibiting better convergence in misalignment for unknown system identification under noisy inputs.

Accelerated euclidean direction search algorithm and related relaxation schemes for solving adaptive filtering problem

The Euclidean direction search (EDS) method is a fairly recent algorithm for solving adaptive filtering problem. The method is a direction set based algorithm, where line searches are perform along Euclidean directions in a cyclic manner in order to search for the minimum of the cost function of the problem. In this paper, the EDS algorithm is described in terms of its relationship with relaxation schemes for solving linear system of equations such as the Gauss-Seidel and Jacobi iterative methods. An acceleration parameter, which is commonly used for such methods, are introduced here and its optimum value derived for uncorrelated input signals with mean 0. Verification of optimum acceleration parameter is demonstrated in the framework of an adaptive system modeling problem.

Adaptive total least squares based speech prediction

In this paper, an instantaneous total error based adaptive linear predictor is presented for linear predictive coding (LPC) of speech signals. In LPC, the speech signal is predicted by a linear combination of delayed input signals that are contaminated by noise. For this reason, total least mean squares (T-LMS) algorithm is used to decode the noisy input signals and to predict a speech signal. A compressed speech prediction is done when the mean squares total error is minimized, showing the efficiency of T-LMS based LPC model. Experimental results are recorded for different values of signal to noise ratio (SNR) of the input signals, and a comparative study is presented with instantaneous error squares based adaptive filter. These results show the preference of proposed predictor over the other.

Performance study of LMS based adaptive algorithms for unknown system identification

Adaptive filtering techniques have gained much popularity in the modeling of unknown system identification problem. These techniques can be classified as either iterative or direct. Iterative techniques include stochastic descent method and its improved versions in affine space. In this paper we present a comparative study of the least mean square (LMS) algorithm and some improved versions of LMS, more precisely the normalized LMS (NLMS), LMS-Newton, transform domain LMS (TDLMS) and affine projection algorithm (APA). The performance evaluation of these algorithms is carried out using adaptive system identification (ASI) model with random input signals, in which the unknown (measured) signal is assumed to be contaminated by output noise. Simulation results are recorded to compare the performance in terms of convergence speed, robustness, misalignment, and their sensitivity to the spectral properties of input signals. Main objective of this comparative study is to observe the effects of fast convergence rate of improved versions of LMS algorithms on their robustness and misalignment.

Existence and uniqueness of the solution of delay differential equations

In this paper, we will state and prove the existence and uniqueness theorems of solutions of the delay differential equations with variable time delay. The followed approach is based on constructing an equivalent sequence of approximate solutions related to the integral equation with time delay, then proving the uniform convergence of this sequence to the analytical solution related to the differential equation.

Stock market identification and estimation based on reduced fuzzy recursive least-squares approach

Stock market identification and forecasting are highly complex in terms of mathematical modeling due to the complexity of internal structure and external forces that contributes the nonlinear dynamics of its behaviors. In this paper, fuzzy system is used to identify the stock market and produce the parameters to estimate the closing price of the selected stock market. Due to the abilities of incorporating linguistic information, fuzzy system is proven to be a universal approximator at arbitrary accuracy. Here, fuzzy system with reduced fuzzy basis function is trained to be adaptive based on the recursive least-squares (RLS) approach. With the limitation of information available (black-box modeling), reduced fuzzy RLS approach is able to capture the nonlinear dynamics of the stock market and the simulation results are promising.

Modified variable gradient method for constructing the Lyapunov function using nonlinear programming method

In this paper, is used nonlinear programming method to modify the well-known variable gradient method for constructing the Lyapunov function of a system of ordinary differential equations. Thereafter the problem is formulated as a nonlinear optimization problem to evaluate the real symmetric matrix used in the definition of the quadratic form Lyapunov function by way of examples, we demonstrate the applicability of the method problem.

Robust DWT-SVD image watermarking with hybrid technique for embedding data in all frequencies

DWT-SVD digital watermarking scheme which is based on the combination of Discrete Wavelet Transform and Singular Value Decomposition is a recent digital watermarking technique and has become popular due to its robustness against various attacks. In this paper, we present an image watermarking scheme which combines previous DWT-SVD based methods which guarantees robustness without increasing algorithm complexity. In order to tackle the common drawback of existing DWT-SVD watermarking scheme, we also introduce a “reverse embedding’ technique and use scaled singular values. Because our proposed method combines the strength of previous methods, it is able to provide a comprehensive and much improved robustness against various kinds of attack and this is shown in the simulations. The reverse embedding technique also avoids negative film effect which is common in existing DWT-SVD image watermarking scheme.