Designing stable neural identifier based on Lyapunov method

The stability of learning rate in neural network identifiers and controllers is one of the challenging issues which attracts great interest from researchers of neural networks. This paper suggests adaptive gradient descent algorithm with stable learning laws for modified dynamic neural network (MDNN) and studies the stability of this algorithm. Also, stable learning algorithm for parameters of MDNN is proposed. By proposed method, some constraints are obtained for learning rate. Lyapunov stability theory is applied to study the stability of the proposed algorithm. The Lyapunov stability theory is guaranteed the stability of the learning algorithm. In the proposed method, the learning rate can be calculated online and will provide an adaptive learning rare for the MDNN structure. Simulation results are given to validate the results

Complex-valued Adaptive Digital Signal Enhancement For Applications In Wireless Communication Systems

In recent decades, the wireless communication industry has attracted a great deal of research efforts to satisfy rigorous performance requirements and preserve high spectral efficiency. Along with this trend, I/Q modulation is frequently applied in modern wireless communications to develop high performance and high data rate systems. This has necessitated the need for applying efficient complex-valued signal processing techniques to highly-integrated, multi-standard receiver devices. In this dissertation, novel techniques for complex-valued digital signal enhancement are presented and analyzed for various applications in wireless communications. The first technique is a unified block processing approach to generate the complex-valued conjugate gradient Least Mean Square (LMS) techniques with optimal adaptations. The proposed algorithms exploit the concept of the complex conjugate gradients to find the orthogonal directions for updating the adaptive filter coefficients at each iteration. Along each orthogonal direction, the presented algorithms employ the complex Taylor series expansion to calculate time-varying convergence factors tailored for the adaptive filter coefficients. The performance of the developed technique is tested in the applications of channel estimation, channel equalization, and adaptive array beamforming. Comparing with the state of the art methods, the proposed techniques demonstrate improved performance and exhibit desirable characteristics for practical use. The second complex-valued signal processing technique is a novel Optimal Block Adaptive algorithm based on Circularity, OBA-C. The proposed OBA-C method compensates for a complex imbalanced signal by restoring its circularity. In addition, by utilizing the complex iv Taylor series expansion, the OBA-C method optimally updates the adaptive filter coefficients at each iteration. This algorithm can be applied to mitigate the frequency-dependent I/Q mismatch effects in analog front-end. Simulation results indicate that comparing with the existing methods, OBA-C exhibits superior convergence speed while maintaining excellent accuracy. The third technique is regarding interference rejection in communication systems. The research on both LMS and Independent Component Analysis (ICA) based techniques continues to receive significant attention in the area of interference cancellation. The performance of the LMS and ICA based approaches is studied for signals with different probabilistic distributions. Our research indicates that the ICA-based approach works better for super-Gaussian signals, while the LMS-based method is preferable for sub-Gaussian signals. Therefore, an appropriate choice of interference suppression algorithms can be made to satisfy the ever-increasing demand for better performance in modern receiver design

Ab Initio Molecular Dynamics (Aimd)- a New Approach for Development of Accurate Potentials

In this study a new approach is presented for the development of accurate potential-energy hypersurfaces based on ab initio calculations that can be utilized to conduct molecular dynamics and Monte Carlo simulations to study chemical and mechanical properties at the atomistic level. The method integrates ab initio electronic structure calculations with the interpolation capability of multilayer neural networks. A sampling technique based on novelty detection is also developed to ensure that the neural network fitting for the potential energy spans the entire configuration space involved during the simulation. The procedure can be initiated using an empirical potential or direct dynamics simulation. The procedure is applied for developing the potential energy hypersurface for five-atom clusters within a silicon workpiece. Ab initio calculations were performed using Gaussian 98 electronic structure program. Results for five-atom silicon clusters representing the bulk and the surface structure are presented.Mechanical & Aerospace Engineerin

Detection of early warning signs of currency crises in South Africa

In a world characterised by globalisation, particularly increased financial integration and capital mobility, international economic theory stipulates that countries rather maintain a floating exchange rate system than a fixed exchange rate system in order to have less susceptibility to currency crises (Glick & Hutchison, 2011). South Africa, the economic powerhouse of Africa, is an interesting case to examine. It has a floating exchange rate and should thus be more resistant to currency crises due to market adjustment expectations that limit the build-up of pressure in its foreign exchange markets. South Africa’s foreign exchange market is characterised as volatile with recurring turbulent periods with currency crises observed in 1996, 1998, 2001 and 2008, of which the 2007/2008 global financial crisis was the worst the world had experienced since the Great Depression of the 1930s and it had a significant, negative impact on the South African economy and certainly exposed the country’s vulnerably (South African Reserve Bank, 2012). Having experienced these periods of currency crisis in South Africa and with no specific tool adequately tested and developed for the South African economy to accurately detect such an event before its occurrence, this research was an attempt to fill this gap within the economics discipline. The purpose of this thesis was to examine and make use of Early Warning System (EWS) models to ascertain which one best identifies potential early warning signs of a currency crisis in South Africa. To achieve this, the study tested two standard and commonly used EWS models, namely the Signals and probit models. Added to these approaches, two newer EWS models, namely the Markov regime switching model and the artificial neural networks model were tested. To date only two studies on EWS models for currency crises have been conducted in South Africa. Knedlik (2006) used the signals approach and Knedlik and Scheufele (2007) used the signals, probit/logit and Markov regime switching approaches. Both studies recommended that further research was needed. With this in mind, this thesis built on these studies by extending the sample period under observation from 1993/02 to 2017/03 to fully capture the probability of the global financial crisis of 2007/2008. This study separated the sample period into two parts, a first period (1993/02 – 2004/12) catering for the July 1998 and December 2001 crises and a second period (2005/01 – 2017/03) catering for the October 2008 crisis. This was done to separately observe how well the models detected early warning signs of the October 2008 crisis due to its global nature. By exploring the potential of artificial intelligence by employing the non-parametric approach of artificial neural networks, which has not yet been applied in the South African context for the probability prediction of currency crises, and comparing its prediction performance to the signals, the probit and the Markov regime switching EWS models, this thesis fills an existing information gap. This study found that of these four EWS models for predicting the probabilities of currency crises within the 24-month crisis window, the signals model performed better than the other models for the period 1993/02 – 2004/12. However, the final-outcome of the best model in probability prediction of South African currency crises is not straightforward for this period, as the artificial neural network model and Markov regime switching model performed almost as well as the signals model. During the period 2005/01 – 2017/03, the artificial neural networks model outperformed the other three models in capturing the global financial crisis of 2007/2008, specifically with regard to the evaluations of the percentage of pre-crisis periods called correctly and the percentage of tranquil periods called correctly. As the cut-off probability increases, the artificial neural networks model is the superior model and is not closely followed by the other models. The artificial neural network model also indicated a stable / tranquil economy during the period following the global financial crisis (from about 2009 – 2017), which is a true reflection of that period. The findings of this study suggest that the artificial neural network model is a powerful tool in the probability prediction of early warning signs of currency crises in South Africa