Browsing by Author "Acuña Ureta, David Esteban"

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    Computation of time probability distributions for the occurrence of uncertain future events
    (2021) Acuña Ureta, David Esteban; Orchard, M. E.; Wheeler, P.
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    Expected First Occurrence Time of Uncertain Future Events in One-Dimensional Linear Systems
    (Prognostics and Health Management Society, 2024) Acuña Ureta, David Esteban; Fuentealba Secul, Diego Ignacio; Orchard, Marcos E.
    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 analytical expression for approximating 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.
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    Near-instantaneous battery End-of-Discharge prognosis via uncertain event likelihood functions
    (2023) Acuña Ureta, David Esteban; Marcos E. Orchard
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    Underlying Probability Measure Approximated by Monte Carlo Simulations in Event Prognostics
    (2023) Acuña Ureta, David Esteban; Marcos Orchard
    The prognostic of events, and particularly of failures, is a key step towards allowing preventive decision-making, as in the case of predictive maintenance in Industry 4.0, for example. However, the occurrence time of a future event is subject to uncertainty, so it is natural to think of it as a random variable. In this regard, the default procedure (benchmark) to compute its probability distribution is empirical, through Monte Carlo simulations. Nonetheless, the analytic expression for the probability distribution of the occurrence time of any future event was presented and demonstrated in a recent publication. In this article it is established a direct relationship between these empirical and analytical procedures. It is shown that Monte Carlo simulations numerically approximate the analytically known probability measure when the future event is triggered by the crossing of a threshold.