Identifying the existence of nonlinear structures in a time series acquired from real world systems, is necessary to distinguish chaos from correlated noise. Measures that detect temporal correlations in a time series might be insufficient to extract deterministic features from an experimental data that is contaminated with noise. Here, we employ surrogate methods to analyze experimental data obtained from an engineering system, a turbulent combustor, with Hurst exponent and translational error as discriminating measures. We conclude from the analysis that the noise level in the data could be sufficiently large to suppress the nonlinearities in the time series. Thus, the null hypothesis that the data is generated from a stochastic process cannot be rejected with sufficient confidence on a statistical basis. However, a high dimensional Mackey-Glass system also shows similar features in the presence of additive noise. Thus, we make a conjuncture that the experimental time series acquired during the stable operation in the turbulent combustor is generated from a high dimensional chaotic system contaminated with noise.
E. A. Gopalakrishnan, Tony, J., Sreelekha, E., and Sujith, R. I., “Hurst exponent and translation error as discriminating measures to identify the chaotic nature of an experimental time series”, Conference on Nonlinear Systems and Dynamics, Mar. 13-15, 2015, Mohali, India. 2015.