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A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic CalculusThis work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.
Document ID
20190000066
Acquisition Source
Ames Research Center
Document Type
Conference Paper
Authors
Corbetta, Matteo
(SGT, Inc. Moffett Field, CA, United States)
Kulkarni, Chetan
(SGT, Inc. Moffett Field, CA, United States)
Date Acquired
January 14, 2019
Publication Date
January 7, 2019
Subject Category
Statistics And Probability
Report/Patent Number
ARC-E-DAA-TN61509
Meeting Information
Meeting: AIAA SciTech Forum 2019
Location: San Diego, CA
Country: United States
Start Date: January 7, 2019
End Date: January 11, 2019
Sponsors: American Inst. of Aeronautics and Astronautics
Funding Number(s)
CONTRACT_GRANT: NNA14AA60C
Distribution Limits
Public
Copyright
Public Use Permitted.
Keywords
stochastic calculus
Monte Carlo sampling
differential equations
prediction
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