English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We formulate the problem of probabilistic predictions of global failure inthe simplest possible model based on site percolation and on one of thesimplest model of time-dependent rupture, a hierarchical fiber bundle model. Weshow that conditioning the predictions on the knowledge of the current degreeof damage (occupancy density $p$ or number and size of cracks) and on someinformation on the largest cluster improves significantly the predictionaccuracy, in particular by allowing to identify those realizations which haveanomalously low or large clusters (cracks). We quantify the prediction gainsusing two measures, the relative specific information gain (which is thevariation of entropy obtained by adding new information) and theroot-mean-square of the prediction errors over a large ensemble ofrealizations. The bulk of our simulations have been obtained with thetwo-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 fiberbundle model, conditioning the measures of damage on the information of thelocation and size of the largest crack extends significantly the criticalregion and the prediction skills. These examples illustrate how on-going damagecan be used as a revelation of both the realization-dependent pre-existingheterogeneity and the damage scenario undertaken by each specific sample.Comment: 7 pages + 11 figure

Predicting failure using conditioning on damage history: Demonstration on percolation and hierarchical fiber bundles