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& A combination of embedding theorem and artificial intelligence along with residual analysis is used to analyze and forecast chaotic time series. Based on embedding theorem, the time series is reconstructed into proper phase space points and fed into a neural network whose weights and biases are improved using genetic algorithms. As the residuals of predicted time series demonstrated chaotic behavior, they are reconstructed as a new chaotic time series. A new neural network is trained to forecast future values of residual time series. The residual analysis is repeated several times. Finally, a neural network is trained to capture the relationship among the predicted value of the original time series, residuals, and the original time series. The method is applied to two chaotic time series, Mackey-Glass and Lorenz, for validation, and it is concluded that the proposed method can forecast the chaotic time series more effectively and accurately than existing methods.

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The finite element method has been applied in the area of the cervical spine since the 1970's. In the present research work, the finite element method was employed to model, validate and analyze a complete model of the human cervical spine from C1 to T1, including interconnecting intervertebral discs, ligaments and joints. The developed model of the cervical spine was validated by the experimental results presented in the literature. As the values obtained from the finite element analysis were mainly in the range of motion observed in the experiment; it was concluded that the finite element results were consistent with the reported data in the literature. Next, the validated model of the cervical spine was examined under physiological loading modes to locate the areas bearing maximum stress in the cervical spine. Finally, to study the effect of variations in the material properties on the output of the finite element analysis, a material property sensitivity study was conducted to the C3-T1 model of cervical spine. Changes in the material properties of the soft tissues affected the external and internal responses of both the hard and soft tissue components, while changes in those of the hard tissues only affected the internal response of hard tissues.

This dissertation aims to develop an effective and practical method to forecast chaotic time series. Chaotic behaviour has been observed in the areas of marketing, stock markets, supply chain management, foreign exchange rates, weather forecasting and many others. An effective forecasting model can reduce the potential risks and uncertainty and facilitate planning and decision making in chaotic systems. In this study, residual analysis using a combination of the embedding theorem and ensemble artificial neural networks is adopted to forecast chaotic time series. Based on the embedding theorem, the embedding parameters are determined and the time series is reconstructed into proper phase space points. The embedded phase space points are fed into the first neural network and trained. The weights and biases are kept to predict the future values of phase space points and accordingly to obtain future values of chaotic time series. The residual of the predicted time series is further analyzed; and, if a chaotic behaviour is observed, then the residuals are processed as a new chaotic time series and predicted. This iterative residual analysis can be repeated several times depending on the desired accuracy level and computational efficiency. Finally, the last neural network is trained using neural networks' result values of the time series and the residuals as input and the original time series as output. The initial weights and biases of the neural networks are improved using genetic algorithms. Taguchi's design of experiments is adopted to identify appropriate factor-level combinations to improve the result of the proposed forecasting method. A systematic approach is proposed to improve the combination of ensemble artificial neural networks and their parameters. The proposed methodology is applied to a number of benchmark and some real life chaotic time series. In addition, the proposed forecasting method has been applied to financial sector time series, namely, the stock markets and foreign exchange rates. The experimental results confirm that the proposed method can predict the chaotic time series more effectively in terms of error indices when compared with other forecasting methods in the literature.