Semiparametric statistical analysis of the blade tip timing data for detection of turbine rotor speed instabilities.

In this paper, we propose an extension of an existing standard approach to the blade tip timing data when analyzing turbine rotor vibrations. Instabilities related to the non-constant trigonometric coefficients at prominent frequencies might not be noticed in the traditional analyses. Our methodology is based on time-varying coefficient statistical models, and hence it allows a full formalization of the estimation and other inferential tasks (uncertainty assessments, hypothesis tests etc.). First, we formulate a univariate generalized additive model that is useful for investigation of vibration behavior of individual blades. It can extract trajectories of the trigonometric coefficients. Using the trajectories, one can investigate time changes of power at a given frequency. In the second approach, we use a multivariate model for simultaneous assessment of all of the rotor blades. The model acknowledges similarity of the vibration behavior of closely located blades. It is formulated as a state-space model, and hence it allows for a wide range of prediction, smoothing, and filtering tasks. We illustrate the performance and practical usefulness of our models on real blade tip timing turbine monitoring data obtained from the Czech nuclear power plant Temelin.