Detecting change in complex process systems with phase space methods

摘要

Model predictive control has become a standard for most control strategies in modernprocess plants. It relies heavily on process models, which might not always befundamentally available, but can be obtained from time series analysis. The first stepin any control strategy is to identify or detect changes in the system, if present. Thedetection of such changes, known as dynamic changes, is the main objective of thisstudy. In the literature a wide range of change detection methods has been developedand 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 detectionmethods based on process history data assume a linear relationship between processvariables with some stochastic influence from the environment. These methods arewell developed, but fail when applied to nonlinear dynamic systems, which is focusedon in this study.A large number of the methods designed for nonlinear systems make use of statisticsdefined in phase space, which led to the method proposed in this study. Thecorrelation dimension is an invariant measure defined in phase space that is sensitiveto dynamic change in the system. The proposed method uses the correlationdimension as test statistic with and moving window approach to detect dynamicchanges in nonlinear systems.The proposed method together with two dynamic change detection methods withdifferent approaches was applied to simulated time series data. The first methodconsidered 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 theprediction error from a multilayer perceptron network. After the proposed method wasapplied to the data the three methods’ performance were evaluated.Time series data were obtained from simulating three systems with mathematicalequations and observing one real process, the electrochemical noise produced by acorroding system. The three simulated systems considered in this study are theBelousov-Zhabotinsky reaction, an autocatalytic process and a predatory-prey model.The time series obtained from observing a single variable was considered as the onlyinformation available from the systems. Before the change detection methods wereapplied to the time series data the phase spaces of the systems were reconstructed withtime delay embedding.All three the methods were able to do identify the change in dynamics of the timeseries data. The change-point detection algorithm did however produce a haphazard behaviour of its detection statistic, which led to multiple false alarms beingencountered. This behaviour was probably due to the distribution of the time seriesdata not being normal. The haphazard behaviour reduces the ability of the method todetect changes, which is aggravated by the presence of chaos and instrumental ormeasurement noise. Mutual cross prediction is a very successful method of detectingdynamic changes and is quite robust against measurement noise. It did howeverrequire the training of a multilayer perceptron network and additional calculations thatwere time consuming. The proposed algorithm using the correlation dimension as teststatistic 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 andreliable detection of dynamic changes, even in then presence of some instrumentalnoise.The proposed method with the correlation dimension as test statistic was the onlymethod applied to the real time series data. Here the method was successful indistinguishing between two different corrosion phenomena. The proposed methodwith the correlation dimension as test statistic appears to be a promising approach tothe detection of dynamic change in nonlinear systems.