Pseudoprospective forecasting of failure time

Abstract

Power-law precursory acceleration of observable quantities has been accepted as an effective way to predict time to failure in both materials and structures. However, the form of the power-law exponent is seldom known a priori and is a key challenge in blind prediction. We report a linear relation with respect to time t of the estimated failure times t_{*} that are calculated step by step using the most recent updates of the monitored quantity. Our findings indicate that the monitored quantity can be defined as any power of the inverse rate. All projections of t_{*} for any exponent universally intersect with the straight line of t=t_{*}, with the intersection uniquely defining the failure time. The method is validated against synthetic data, laboratory experiments (materials failure), and volcanic eruption data (structural failure). Our work provides the basis for a significant improvement in time to failure forecasting where the controlling power-law exponent is not known in advance.