Detecting Nonlinearity in Pressure Data Inside the Draft Tube of a Real Francis Turbine

Abstract

A general method for testing nonlinearity in time series is described and applied to measurements of different pressure data inside the draft tube surge of a real Francis turbine. Comparing the current original time series to an ensemble of surrogates time series, suitably constructed to mimic the linear properties of the original one, we was able to distinguish a linear stochastic from a nonlinear deterministic behaviour and, moreover, to quantify the degree of nonlinearity present in the related dynamics. The problem of detecting nonlinear structure in real data is quite complicated by the influence of various contaminations, like broadband noise and/or long coherence times. These difficulties have been overcame using the combination of a suitable nonlinear filtering technique and a qualitative redundancy statistic analysis. The above investigations allow a quantitative characterization of different dynamical regimes of motion of gas cavities inside real turbines and, moreover, allow to support the reliability of some related mathematical modelizations.