Functional Renormalization Prediction of Rupture

TL;DR

This paper introduces a theoretical method using functional renormalization to predict rupture times in systems exhibiting critical behavior, based on early observable data, and validates it with successful tests under various conditions.

Contribution

It presents a novel application of functional renormalization to predict rupture times from early data, improving understanding of critical failure processes.

Findings

Accurately predicts critical rupture time from early data.

Effective even with noisy measurements.

Works across different polynomial orders.

Abstract

We develop theoretical formulas for the prediction of the rupture of systems which are known to exhibit a critical behavior, based solely on the knowledge of the early time evolution of an observable, such as the acoustic emission rate as a function of time or of stress. From the parameterization of such early time evolution in terms of a low-order polynomial, we use the functional renormalization approach introduced by Yukalov and Gluzman to transform this polynomial into a function which is asymptotically a power law. The value of the critical time tc,conditioned on the assumption that tc exists, is thus determined from the knowledge of the coefficients of the polynomials. We test with success this prediction scheme with respect to the order of the polynomials and as a function of noise.