Non-monotonic precursory signals to multi-scale catastrophic failures

Identifying precursory trends in acoustic/seismic observations allows the forewarning/prediction of catastrophic events. However, rupturing across multiple scales leaves it unclear whether features of small events are applicable predictors of the larger ensemble final collapse. To resolve this issue, we present a multiscale heterogeneous model that straightforwardly characterizes the duration and mechanism of multiscale catastrophic failures. Our results identify four distinct classes of failure including random single breaks, small catastrophic failure (SCF) events, large catastrophic failure (LCF) events that consist of subordinate SCF and random break events, and a culminating macroscopic catastrophic failure (MCF) event resulting from the coalescence of subordinate LCF events. Only the local response quantities, recorded at their corresponding position, show an accelerating precursory trend to an SCF event. LCF events can appear in stages both before and after the maximum load in the system. Our findings highlight that although cumulative LCF event and deformation rates for the entire system always exhibit singular accelerating precursors as MCF is approached, this is not true at all individual event points. This may explain why no clearly accelerating precursor is observed before some catastrophic events. Thus, these results suggest a methodology for recognizing and distinguishing effective precursory information from monitoring signals across scales and in eliminating false predictions.