Detecting change in complex process systems with phase space methods
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.