| Summary: | Model predictive control has become a standard for most control strategies in modern
process plants. It relies heavily on process models, which might not always be
fundamentally available, but can be obtained from time series analysis. The first step
in any control strategy is to identify or detect changes in the system, if present. The
detection of such changes, known as dynamic changes, is the main objective of this
study. In the literature a wide range of change detection methods has been developed
and documented. Most of these methods assume some prior knowledge of the system,
which is not the case in this study. Furthermore a large number of change detection
methods based on process history data assume a linear relationship between process
variables with some stochastic influence from the environment. These methods are
well developed, but fail when applied to nonlinear dynamic systems, which is focused
on in this study.
A large number of the methods designed for nonlinear systems make use of statistics
defined in phase space, which led to the method proposed in this study. The
correlation dimension is an invariant measure defined in phase space that is sensitive
to dynamic change in the system. The proposed method uses the correlation
dimension as test statistic with and moving window approach to detect dynamic
changes in nonlinear systems.
The proposed method together with two dynamic change detection methods with
different approaches was applied to simulated time series data. The first method
considered was a change-point algorithm that is based on singular spectrum analysis.
The second method applied to the data was mutual cross prediction, which utilises the
prediction error from a multilayer perceptron network. After the proposed method was
applied to the data the three methods’ performance were evaluated.
Time series data were obtained from simulating three systems with mathematical
equations and observing one real process, the electrochemical noise produced by a
corroding system. The three simulated systems considered in this study are the
Belousov-Zhabotinsky reaction, an autocatalytic process and a predatory-prey model.
The time series obtained from observing a single variable was considered as the only
information available from the systems. Before the change detection methods were
applied to the time series data the phase spaces of the systems were reconstructed with
time delay embedding.
All three the methods were able to do identify the change in dynamics of the time
series data. The change-point detection algorithm did however produce a haphazard behaviour of its detection statistic, which led to multiple false alarms being
encountered. This behaviour was probably due to the distribution of the time series
data not being normal. The haphazard behaviour reduces the ability of the method to
detect changes, which is aggravated by the presence of chaos and instrumental or
measurement noise. Mutual cross prediction is a very successful method of detecting
dynamic changes and is quite robust against measurement noise. It did however
require the training of a multilayer perceptron network and additional calculations that
were time consuming. The proposed algorithm using the correlation dimension as test
statistic with a moving window approach is very useful in detecting dynamic changes.
It produced the best results on the systems considered in this study with quick and
reliable detection of dynamic changes, even in then presence of some instrumental
noise.
The proposed method with the correlation dimension as test statistic was the only
method applied to the real time series data. Here the method was successful in
distinguishing between two different corrosion phenomena. The proposed method
with the correlation dimension as test statistic appears to be a promising approach to
the detection of dynamic change in nonlinear systems.
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