Predicting Failure using Conditioning on Damage History: Demonstration on Percolation and Hierarchical Fiber Bundles

TL;DR

This paper demonstrates that conditioning failure predictions on damage history, such as crack size and location, significantly improves accuracy in models like percolation and fiber bundles, revealing heterogeneity and damage evolution.

Contribution

It introduces a probabilistic prediction framework that leverages damage history to enhance failure prediction accuracy in percolation and fiber bundle models.

Findings

Conditioning on damage history improves prediction accuracy.

Damage information extends the critical region in models.

The approach reveals heterogeneity and damage scenarios.

Abstract

We formulate the problem of probabilistic predictions of global failure in the simplest possible model based on site percolation and on one of the simplest model of time-dependent rupture, a hierarchical fiber bundle model. We show that conditioning the predictions on the knowledge of the current degree of damage (occupancy density $p$ or number and size of cracks) and on some information on the largest cluster improves significantly the prediction accuracy, in particular by allowing to identify those realizations which have anomalously low or large clusters (cracks). We quantify the prediction gains using two measures, the relative specific information gain (which is the variation of entropy obtained by adding new information) and the root-mean-square of the prediction errors over a large ensemble of realizations. The bulk of our simulations have been obtained with the two-dimensional site percolation model on a lattice of size $L \times L=20 \times 20$ and hold true for other lattice sizes. For the hierarchical fiber bundle model, conditioning the measures of damage on the information of the location and size of the largest crack extends significantly the critical region and the prediction skills. These examples illustrate how on-going damage can be used as a revelation of both the realization-dependent pre-existing heterogeneity and the damage scenario undertaken by each specific sample.