  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.
