The S-statistic based on the comparison of two reconstructed attractors in the phase space was utilized to study whether two dependent time series (namely, evaluation and reference time series) were originated from the same mechanism or not. Evaluation time series were measured during the bed operation in a gas-solid bubbling fluidized bed and reference time series were generated according to phase randomized surrogate data series from the evaluation series. The results indicated that nonlinearity can be observed where the energy contribution of the macro-structures is more than that of the finer structures. It was found that a minimum in the energy of the finer structures with an increase in velocity corresponds to the transition between macro-structures and finer structures of the bubbling fluidization system. This conclusion can eventually help choose proper control systems and evaluation methods of signals in fluidized beds. (C) 2011 Elsevier Ltd. All rights reserved.