Classification of process dynamics with Monte Carlo singular spectrum analysis

Abstract

Metallurgical and other chemical process systems are often too complex to model from first principles. In such situations the alternative is to identify the systems from historic process data. Such identification can pose problems of its own and before attempting to identify the system, it may be important to determine whether a particular model structure is justified by the data before building the model. For example, the analyst may wish to distinguish between nonlinear (deterministic) processes and linear (stochastic) processes to justify the use of a particular methodology for dealing with the time series observations, or else it may be important to distinguish between different stochastic models. In this paper the use of a linear method called singular spectrum analysis (SSA) to classify time series data is discussed. The method is based on principal component analysis of an augmented data set consisting of the original time series data and lagged copies of the data. In addition, a nonlinear extension of SSA based on kernel-based eigenvalue decomposition is introduced. The usefulness of kernel SSA as a complementary tool in the search for evidence of nonlinearity in time series data or for testing other hypotheses about such data is illustrated by simulated and real-world case studies.