Classification of process dynamics with Monte Carlo singular spectrum analysis
Identification of non-linear systems can be a daunting task and in the process industries the problem is complicated considerably by the presence of noise from various sources, non-stationarity of the data and intermittence, such as observed in particulate flows. Traditional methods, such as frequency analysis and linear modelling do not handle these systems well. Similar problems arise with the application of non-linear theory developed over the last few decades, where much of the analysis depends on embedding of the data in a phase space or pseudophase space, since these methods were not originally designed to deal with noisy systems. In contrast, singular spectrum analysis is a method which can be used to identify structure and distinguish noise from important information in multivariate data, such as the trajectory matrices of time series measurements. It provides an orthogonal basis onto which the data can be transformed, so that components of the time series can be investigated individually. With Monte Carlo methods, the components can be compared with those from linear surrogate data in order to identify possibly non-linearities in the data. In this paper, this versatile technique is briefly explained and illustrated by means of case studies.