ABSTRACT
In building a predictive chaotic model, the observed time series is reconstructed and embedded in sufficiently higher dimensional phase space with the time-delayed coordinates to unfold the attractor of surge dynamics. The predictive models can be constructed based on available data-driven techniques (i.e. ANN). Global and local models can be built. In global modeling, the whole dynamical behavior of the systems in phase space is described and predicted by one model. In contrast, the local modeling at each time step allows for characterizing the dynamical behavior locally and more flexible options of predictive local models can be utilized. However, this flexibility introduces a concern on selecting the good searching techniques for finding true dynamical neighbors and choosing the suitable number of dynamical neighbors used for building predictive local models. If compared to the earlier studies by Solomatine et al. (2000) and Velickov (2003; 2004) (see in Chapter 1), this research has introduced several improved techniques and innovations, including using recent techniques for nonlinear time series analysis (i.e. Cao’s method), considerable improvements in the algorithms for building predictive chaotic models (schemes to avoid false neighbors: utilizing multi-step prediction and trajectory based method, using ANN as a local model), possibility to build the chaotic model in case of incompleteness in the time series, reducing phase space dimension (an important issue for multivariate chaos), solving phase shift prediction error, optimizing predictive chaotic model using GA and ACCO, incorporating data assimilation using NARX neural network, and combining predictions from different types of chaotic models using dynamic averaging and dynamic neural network. Furthermore, the additional new data set is used in this work and the prediction performances of the predictive chaotic models are compared with other models, including ANN models. A number of enhancements in building a predictive chaotic model outlined in the objectives of this research have been implemented and tested. The main conclusions can be summarized as follows: Taking into account the presence of deterministic chaos in surge dynamics, a mixture of
multivariate predictive local models in the reconstructed phase-space of the dynamical system, which uses information from the real dynamical neighbors, has demonstrated a good capability for reliable short-term predictions. For the Hoek van Holland location, the overall 3 hours ahead surge prediction errors (RMSE) during storm condition for univariate CM, univariate ANN, multvariate CM and multivariate ANN are 12.91, 19.46, 11.99 and 16.78 cm, respectively.
