Fourier Transforms

The 21st century ushered in a new era of technology that has been reshaping everyday life, simplifying outdated processes, and even giving rise to entirely new business sectors. Today, contemporary users of products and services expect more and more personalized products and services that can meet their unique needs. In that sense, it is necessary to further develop existing methods, adapt them to new applications, or even discover new methods. This book provides a thorough review of some methods that have an increasing impact on humanity today and that can solve different types of problems even in specific industries. Upgrading with Fourier Transformation gives a different meaning to these methods that support the development of new technologies and have a good projected acceleration in the future

The dynamics of market efficiency: testing the adaptive market hypothesis in South Africa

A thesis submitted to the School of Economic and Business Sciences, Faculty of Commerce, Law and Management, University of the Witwatersrand in fulfilment of the requirements for the degree of Doctor of Philosophy (Ph/D). Johannesburg, South Africa June 2016In recent years, the debate on market efficiency has shifted to providing alternate forms of the hypothesis, some of which are testable and can be proven false. This thesis examines one such alternative, the Adaptive Market Hypothesis (AMH), with a focus on providing a framework for testing the dynamic (cyclical) notion of market efficiency using South African equity data (44 shares and six indices) over the period 1997 to 2014. By application of this framework, stylised facts emerged. First, the examination of market efficiency is dependent on the frequency of data. If one were to only use a single frequency of data, one might obtain conflicting conclusions. Second, by binning data into smaller sub-samples, one can obtain a pattern of whether the equity market is efficient or not. In other words, one might get a conclusion of, say, randomess, over the entire sample period of daily data, but there may be pockets of non-randomness with the daily data. Third, by running a variety of tests, one provides robustness to the results. This is a somewhat debateable issue as one could either run a variety of tests (each being an improvement over the other) or argue the theoretical merits of each test befoe selecting the more appropriate one. Fourth, analysis according to industries also adds to the result of efficiency, if markets have high concentration sectors (such as the JSE), one might be tempted to conclude that the entire JSE exhibits, say, randomness, where it could be driven by the resources sector as opposed to any other sector. Last, the use of neural networks as approximators is of benefit when examining data with less than ideal sample sizes. Examining five frequencies of data, 86% of the shares and indices exhibited a random walk under daily data, 78% under weekly data, 56% under monthly data, 22% under quarterly data and 24% under semi-annual data. The results over the entire sample period and non-overlapping sub-samples showed that this model's accuracy varied over time. Coupled with the results of the trading strategies, one can conclude that the nature of market efficiency in South Africa can be seen as time dependent, in line with the implication of the AMH.MT201

Recurrent neural network based approach for estimating the dynamic evolution of grinding process variables

170 p.El proceso de rectificado es ampliamente utilizado para la fabricación de componentes de precisión por arranque de viruta por sus buenos acabados y excelentes tolerancias. Así, el modelado y el control del proceso de rectificado es altamente importante para alcanzar los requisitos económicos y de precisión de los clientes. Sin embargo, los modelos analíticos desarrollados hasta ahora están lejos de poder ser implementados en la industria. Es por ello que varias investigaciones han propuesto la utilización de técnicas inteligentes para el modelado del proceso de rectificado. Sin embargo, estas propuestas a) no generalizan para nuevas muelas y b) no tienen en cuenta el desgaste de la muela, efecto esencial para un buen modelo del proceso de rectificado. Es por ello que se propone la utilización de las redes neuronales recurrentes para estimar variables del proceso de rectificado que a) sean capaces de generalizar para muelas nuevas y b) que tenga en cuenta el desgaste de la muela, es decir, que sea capaz de estimar variables del proceso de rectificado mientras la muela se va desgastando. Así, tomando como base la metodología general, se han desarrollado sensores virtuales para la medida del desgaste de la muela y la rugosidad de la pieza, dos variables esenciales del proceso de rectificado. Por otro lado, también se plantea la utilización la metodología general para estimar fuera de máquina la energía específica de rectificado que puede ayudar a seleccionar la muela y los parámetros de rectificado por adelantado. Sin embargo, una única red no es suficiente para abarcar todas las muelas y condiciones de rectificado existentes. Así, también se propone una metodología para generar redes ad-hoc seleccionando unos datos específicos de toda la base de datos. Para ello, se ha hecho uso de los algoritmos Fuzzy c-Means. Finalmente, hay que decir que los resultados obtenidos mejoran los existentes hasta ahora. Sin embargo, estos resultados no son suficientemente buenos para poder controlar el proceso. Así, se propone la utilización de las redes neuronales de impulsos. Al trabajar con impulsos, estas redes tienen inherentemente la capacidad de trabajar con datos temporales, lo que las hace adecuados para estimar valores que evolucionan con el tiempo. Sin embargo, estas redes solamente se usan para clasificación y no predicción de evoluciones temporales por la falta de métodos de codificación/decodificación de datos temporales. Así, en este trabajo se plantea una metodología para poder codificar en trenes de impulsos señales secuenciales y poder reconstruir señales secuenciales a partir de trenes de impulsos. Esto puede llevar a en un futuro poder utilizar las redes neuronales de impulsos para la predicción de secuenciales y/o temporales

Time series prediction and forecasting using Deep learning Architectures

Nature brings time series data everyday and everywhere, for example, weather data, physiological signals and biomedical signals, financial and business recordings. Predicting the future observations of a collected sequence of historical observations is called time series forecasting. Forecasts are essential, considering the fact that they guide decisions in many areas of scientific, industrial and economic activity such as in meteorology, telecommunication, finance, sales and stock exchange rates. A massive amount of research has already been carried out by researchers over many years for the development of models to improve the time series forecasting accuracy. The major aim of time series modelling is to scrupulously examine the past observation of time series and to develop an appropriate model which elucidate the inherent behaviour and pattern existing in time series. The behaviour and pattern related to various time series may possess different conventions and infact requires specific countermeasures for modelling. Consequently, retaining the neural networks to predict a set of time series of mysterious domain remains particularly challenging. Time series forecasting remains an arduous problem despite the fact that there is substantial improvement in machine learning approaches. This usually happens due to some factors like, different time series may have different flattering behaviour. In real world time series data, the discriminative patterns residing in the time series are often distorted by random noise and affected by high-frequency perturbations. The major aim of this thesis is to contribute to the study and expansion of time series prediction and multistep ahead forecasting method based on deep learning algorithms. Time series forecasting using deep learning models is still in infancy as compared to other research areas for time series forecasting.Variety of time series data has been considered in this research. We explored several deep learning architectures on the sequential data, such as Deep Belief Networks (DBNs), Stacked AutoEncoders (SAEs), Recurrent Neural Networks (RNNs) and Convolutional Neural Networks (CNNs). Moreover, we also proposed two different new methods based on muli-step ahead forecasting for time series data. The comparison with state of the art methods is also exhibited. The research work conducted in this thesis makes theoretical, methodological and empirical contributions to time series prediction and multi-step ahead forecasting by using Deep Learning Architectures

Estimation of real traffic radiated emissions from electric vehicles in terms of the driving profile using neural networks

The increment of the use of electric vehicles leads to a worry about measuring its principal source of environmental pollution: electromagnetic emissions. Given the complexity of directly measuring vehicular radiated emissions in real traffic, the main contribution of this PhD thesis is to propose an indirect solution to estimate such type of vehicular emissions. Relating the on-road vehicular radiated emissions with the driving profile is a complicated task. This is because it is not possible to directly measure the vehicular radiated interferences in real traffic due to potential interferences from another electromagnetic wave sources. This thesis presents a microscopic artificial intelligence model based on neural networks to estimate real traffic radiated emissions of electric vehicles in terms of the driving dynamics. Instantaneous values of measured speed and calculated acceleration have been used to characterize the driving profile. Experimental electromagnetic interference tests have been carried out with a Vectrix electric motorcycle as well as Twizy electric cars in semi-anechoic chambers. Both the motorcycle and the car have been subjected to different urban and interurban driving profiles. Time Domain measurement methodology of electromagnetic radiated emissions has been adopted in this work to save the overall measurement time. The relationship between the magnetic radiated emissions of the Twizy and the corresponding speed has been very noticeable. Maximum magnetic field levels have been observed during high speed cruising in extra-urban driving and acceleration in urban environments. A comparative study of the prediction performance between various static and dynamic neural models has been introduced. The Multilayer Perceptron feedforward neural network trained with Extreme Learning Machines has achieved the best estimation results of magnetic radiated disturbances as function of instantaneous speed and acceleration. In this way, on-road magnetic radiated interferences from an electric vehicle equipped with a Global Positioning System can be estimated. This research line will allow quantify the pollutant electromagnetic emissions of electric vehicles and study new policies to preserve the environment

Estimation of real traffic radiated emissions from electric vehicles in terms of the driving profile using neural networks

The increment of the use of electric vehicles leads to a worry about measuring its principal source of environmental pollution: electromagnetic emissions. Given the complexity of directly measuring vehicular radiated emissions in real traffic, the main contribution of this PhD thesis is to propose an indirect solution to estimate such type of vehicular emissions. Relating the on-road vehicular radiated emissions with the driving profile is a complicated task. This is because it is not possible to directly measure the vehicular radiated interferences in real traffic due to potential interferences from another electromagnetic wave sources. This thesis presents a microscopic artificial intelligence model based on neural networks to estimate real traffic radiated emissions of electric vehicles in terms of the driving dynamics. Instantaneous values of measured speed and calculated acceleration have been used to characterize the driving profile. Experimental electromagnetic interference tests have been carried out with a Vectrix electric motorcycle as well as Twizy electric cars in semi-anechoic chambers. Both the motorcycle and the car have been subjected to different urban and interurban driving profiles. Time Domain measurement methodology of electromagnetic radiated emissions has been adopted in this work to save the overall measurement time. The relationship between the magnetic radiated emissions of the Twizy and the corresponding speed has been very noticeable. Maximum magnetic field levels have been observed during high speed cruising in extra-urban driving and acceleration in urban environments. A comparative study of the prediction performance between various static and dynamic neural models has been introduced. The Multilayer Perceptron feedforward neural network trained with Extreme Learning Machines has achieved the best estimation results of magnetic radiated disturbances as function of instantaneous speed and acceleration. In this way, on-road magnetic radiated interferences from an electric vehicle equipped with a Global Positioning System can be estimated. This research line will allow quantify the pollutant electromagnetic emissions of electric vehicles and study new policies to preserve the environment

Recurrent neural network based approach for estimating the dynamic evolution of grinding process variables

170 p.El proceso de rectificado es ampliamente utilizado para la fabricación de componentes de precisión por arranque de viruta por sus buenos acabados y excelentes tolerancias. Así, el modelado y el control del proceso de rectificado es altamente importante para alcanzar los requisitos económicos y de precisión de los clientes. Sin embargo, los modelos analíticos desarrollados hasta ahora están lejos de poder ser implementados en la industria. Es por ello que varias investigaciones han propuesto la utilización de técnicas inteligentes para el modelado del proceso de rectificado. Sin embargo, estas propuestas a) no generalizan para nuevas muelas y b) no tienen en cuenta el desgaste de la muela, efecto esencial para un buen modelo del proceso de rectificado. Es por ello que se propone la utilización de las redes neuronales recurrentes para estimar variables del proceso de rectificado que a) sean capaces de generalizar para muelas nuevas y b) que tenga en cuenta el desgaste de la muela, es decir, que sea capaz de estimar variables del proceso de rectificado mientras la muela se va desgastando. Así, tomando como base la metodología general, se han desarrollado sensores virtuales para la medida del desgaste de la muela y la rugosidad de la pieza, dos variables esenciales del proceso de rectificado. Por otro lado, también se plantea la utilización la metodología general para estimar fuera de máquina la energía específica de rectificado que puede ayudar a seleccionar la muela y los parámetros de rectificado por adelantado. Sin embargo, una única red no es suficiente para abarcar todas las muelas y condiciones de rectificado existentes. Así, también se propone una metodología para generar redes ad-hoc seleccionando unos datos específicos de toda la base de datos. Para ello, se ha hecho uso de los algoritmos Fuzzy c-Means. Finalmente, hay que decir que los resultados obtenidos mejoran los existentes hasta ahora. Sin embargo, estos resultados no son suficientemente buenos para poder controlar el proceso. Así, se propone la utilización de las redes neuronales de impulsos. Al trabajar con impulsos, estas redes tienen inherentemente la capacidad de trabajar con datos temporales, lo que las hace adecuados para estimar valores que evolucionan con el tiempo. Sin embargo, estas redes solamente se usan para clasificación y no predicción de evoluciones temporales por la falta de métodos de codificación/decodificación de datos temporales. Así, en este trabajo se plantea una metodología para poder codificar en trenes de impulsos señales secuenciales y poder reconstruir señales secuenciales a partir de trenes de impulsos. Esto puede llevar a en un futuro poder utilizar las redes neuronales de impulsos para la predicción de secuenciales y/o temporales