Dimensionality reduction by bayesian eigenvalue-analysis for state prediction in large sensor systems: with application in wind turbines

Abstract

The potential of the theory of random matrices are presented and evaluated as a statistical tool to represent the empirical correlations in a study of multivariate time series. A new sub space state prediction framework is proposed, consisting of the combination of a Bayesian state prediction algorithm and the eigenvalues of the empirical correlation matrix. In an industrial use-case of wind turbines, remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data, concerning the density of eigenvalues associated with the time series of different sensors, are found. Finally, the proposed framework outperforms the existing Bayesian state prediction algorithm and is computationally more feasible than feeding unprocessed data.