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Generalized q-Analysis of Log-Periodicity: Applications to Critical Ruptures

Wei-Xing Zhou·Didier Sornette
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Abstract

We introduce a generalization of the q-analysis, which provides a novel non-parametric tool for the description and detection of log-periodic structures associated with discrete scale invariance. We use this generalized q-analysis to construct a signature called the (H,q)-derivative of discrete scale invariance, which we use to detect the log-periodicity in the energy release rate and its cumulative preceding the rupture of five pressure tanks made of composite carbon-matrix material. We investigate the significance level of the spectral Lomb periodogram of the optimal (H,q)-derivative. We confirm and strengthen previous parametric results that the energy release rate and it cumulative exhibit log-periodicity before rupture. However, our tests to use this method as a scheme for the prediction of the critical value of the stress at rupture are not encouraging.

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Wei-Xing Zhou, Didier Sornette. 2002-01-25. Generalized q-Analysis of Log-Periodicity: Applications to Critical Ruptures. https://doi.org/10.1103/physreve.66.046111

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