Browsing by Subject "non-linear"

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    Open Access
    A Non-linear Visco-elastic Model for Dynamic Finite Element Simulation of Bovine Cortical Bone
    (2021) Blignaut, Caitlyn; Ismail, Ernesto; Cloete, Trevor
    Modelling and simulation of the human body during an impact situation such as a car accident, can lead to better designed safety features on vehicles. In order to achieve this, investigation into the material properties and the creation of a numerical model of cortical bone is needed. One approach to creating a material model of cortical bone suitable for these situations is to describe the material model as visco-elastic, as reported by Shim et al. [1], Bekker et al. [2] and Cloete et al. [3]. The work by Shim et al. and Bekker et al. developed three-dimensional models, but do not accurately capture the transition in behaviour in the intermediate strain rate region, while Cloete et al. developed a phenomenological model which captures the intermediate strain rate behaviour in one dimension. This work aims to verify and extend these models. The intermediate strain rate regime (1 s−1 to 100 s−1 ) is of particular interest because it is a key characteristic of the behaviour of cortical bone and several studies have been conducted to gather experimental data in this region [3, 4, 5, 6]. The behaviour can be captured using non-linear viscoelastic models. This dissertation focuses on the development and implementation of a material model of cortical bone based on non-linear visco-elastic models to capture the intermediate strain rate regime behaviour. The material model was developed using uni-axial test results from cortical bone. The model by Cloete et al. has been improved and extended, and issues of local and global strain rate with regards to the viscosity have been clarified. A hereditary integral approach was taken in the analysis and implementation of discrete models and was found to be consistent with mathematical models. The model developed was extended to three dimensions in a manner similar to that of Shim et al. and Bekker et al. for implementation in commercial finite element software (LS-Dyna and Abaqus).
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    Open Access
    Online Non-linear Prediction of Financial Time Series Patterns
    (2020) da Costa, Joel; Gebbie, Timothy
    We consider a mechanistic non-linear machine learning approach to learning signals in financial time series data. A modularised and decoupled algorithm framework is established and is proven on daily sampled closing time-series data for JSE equity markets. The input patterns are based on input data vectors of data windows preprocessed into a sequence of daily, weekly and monthly or quarterly sampled feature measurement changes (log feature fluctuations). The data processing is split into a batch processed step where features are learnt using a Stacked AutoEncoder (SAE) via unsupervised learning, and then both batch and online supervised learning are carried out on Feedforward Neural Networks (FNNs) using these features. The FNN output is a point prediction of measured time-series feature fluctuations (log differenced data) in the future (ex-post). Weight initializations for these networks are implemented with restricted Boltzmann machine pretraining, and variance based initializations. The validity of the FNN backtest results are shown under a rigorous assessment of backtest overfitting using both Combinatorially Symmetrical Cross Validation and Probabilistic and Deflated Sharpe Ratios. Results are further used to develop a view on the phenomenology of financial markets and the value of complex historical data under unstable dynamics.