Statistical analysis of the extreme values of stress time series from the Portevin-Le Châtelier effect

In an effort to understand the deterministic vs stochastic character of the Portevin-Le Châtelier (PLC) phenomenon, we investigate the structure of the underlying mechanism that generates the stick-slip patterns of stress over time. The stress time series is reduced to a series of successive pairs of minimum and maximum values representing the stick-slip patterns and a statistical analysis by means of hypothesis testing is applied to it. The null hypothesis of least deterministic structure is that the time series of extreme values is a bounded random walk of alternating direction (BRWAD); that is, besides the constraint of succession of minima to maxima bounded at a predefined range there are no other correlations in the data. To implement the test we use surrogate data generated by a model consistent with a BRWAD type process, which also uses the statistics of the original data to best mimic them. The proposed hypothesis testing is found to perform properly on simulated data from stochastic and deterministic systems. For the PLC time series, the null hypothesis is rejected at a high level of confidence giving evidence for some deterministic structure in the succession of the extreme stress values. This result allows for further statistical analysis including also the time aspect of the stick-slip patterns.