Expected First Occurrence Time of Uncertain Future Events in One-Dimensional Linear Systems
Year: 2024
Type: conference-paper
Abstract: The rapid advancement of machine learning algorithms has significantly enhanced tools for monitoring system health, making data-driven approaches predominant in Prognostics and Health Management (PHM). In contrast, model-based approaches have seen modest progress, as they are often constrained by the need for prior knowledge of specific governing equations, limiting their applicability to a wide range of problems. Recently, rigorous theoretical foundations have been established to extend dynamical systems theory by incorporating prognosis of uncertain events. This article leverages this formal framework to introduce and demonstrate a fundamental mathematical result for one-dimensional linear dynamical systems. The presented theorem offers an exact expression for calculating the expected time at which an event will first occur in the future. Unlike typical thresholds, this event is triggered by a hazard zone, defined as an uncertain event likelihood function over the system's state space. Applications of this theorem can be found in implementing real-time prognostic frameworks, where it is crucial to quickly estimate the magnitude of impending failures. Emphasis is placed on minimizing computational burden to facilitate prognostic decision-making.
Institutions: Pontificia Universidad Católica de Chile, University of Chile
Language: English
Subfield: Safety, Risk, Reliability and Quality
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404125496