State of the Art and Development Trend - Computational Intelligence in Time Series Forecasting - page 339

breakage, based on measurements of spindle and feed motor currents. For
decomposition of power inputs to the spindle and to the feed motor servos, both
continuous and discrete wavelet transforms were used, and for detection of tool
wear state a fuzzy classification method was developed relying on mathematical
models of relationships between the current signals and the cutting parameters in
the various tool wear states.
Recently, the results of wavelet application in time series forecasting and
prediction have been published. Zhang et al . (2001) used wavelet decomposition
for multi-resolution forecasting of financial time series. For this purpose, the time
series was decomposed into an invariant scale-related representation and the
individual wavelet series modelled by a separate multilayer perceptron. In order to
build the overall time series forecast, the individual forecasts are recombined by a
linear reconstruction property of the inverse transform with the chosen
autocorrelation shell representation. Also, for time series preprocessing, a
combined Bayesian and wavelet-based approach was used. Wavelet decomposition
was also used by Soltani (2002) for nonlinear time series prediction. To produce
improved prediction values, he used a combination of wavelet decomposition (as a
filtering step) and neural networks. The most difficult problems to be solved here
are the selection of an appropriate model order and the determination of optimal
estimator complexity. Chen et al . (1999), again, used the multiresolution learning
capability of a feedforward wavelet neural network described above for single- and
multi-step predictions of chaotic time series and for systems modelling. Finally, in
his Ph.D. thesis, Lotric (2000) used wavelet-based smoothing in time series
prediction with neural networks and applied it to process quality control.
10.4 Fractally Configured Neural Networks
Engineering, information science, and mathematics have learnt much from biology
and physiology. Examples are the creation of genetic and evolutionary searches,
the discovery of Hebbian learning, reinforcement learning, associative memories,
etc . From the complexity points of view, all arts of learning are categorized as
elementary learning processes used for recognition and classification of patterns
from given data. With the progress of time, the attention was shifted towards
higher level learning processes or cognitive functions , which are based on a set of
elementary learning processes. As a tool for solving problems involved in higher
level processes that, for instance, conventional neural networks cannot solve,
fractally configured neural networks (or simply fractal networks ) have been
proposed. The primary reason for this was because the higher cognitive functions,
such as consciousness , are basically hierarchically organized complex systems that
cannot be modelled by a simple neural network, but rather they need several sub-
networks (Takeshi and Akifumi, 1999).
In general systems theory , various concepts have been elaborated for modelling
of hierarchically organized modular systems , among them the concept of partially
bounded open systems , in which the system itself and it's modules interact with
their environment through their inputs and outputs. In the same way, the modules
interact with each other at each hierarchical level as well as with the modules at a