Burst statistics as a criterion for imminent failure

TL;DR

This paper investigates how the distribution of damage avalanche sizes changes near system failure, proposing that this shift can serve as an early warning signal for imminent failure.

Contribution

It analytically and numerically demonstrates a crossover in avalanche size distribution exponents near failure, suggesting a new criterion for predicting imminent catastrophic failure.

Findings

Power law exponent near failure is 3/2 for fiber bundles.

Exponent near failure is 2.0 for fuse networks.

Crossover in avalanche size distribution can signal imminent failure.

Abstract

The distribution of the magnitudes of damage avalanches during a failure process typically follows a power law. When these avalanches are recorded close to the point at which the system fails catastrophically, we find that the power law has an exponent which differs from the one characterizing the size distribution of all avalanches. We demonstrate this analytically for bundles of many fibers with statistically distributed breakdown thresholds for the individual fibers. In this case the magnitude distribution $D(\Delta)$ for the avalanche size $\Delta$ follows a power law $\Delta^{-\xi}$ with $\xi=3/2$ near complete failure, and $\xi=5/2$ elsewhere. We also study a network of electric fuses, and find numerically an exponent 2.0 near breakdown, and 3.0 elsewhere. We propose that this crossover in the size distribution may be used as a signal for imminent system failure.