A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

[摘要] This 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.

[发布日期] 2019-01-07

[学科分类] 统计和概率

[关键词] MONTE CARLO METHOD;MATHEMATICAL MODELS;STOCHASTIC PROCESSES;CALCULUS;PROBABILITY DENSITY FUNCTIONS;PREDICTIONS;CASE HISTORIES;TEMPORAL DISTRIBUTION;CAPACITORS;LIFE (DURABILITY);LITHIUM;ELECTRIC BATTERIES;STRUCTURAL HEALTH MONITORING;DIFFERENTIAL EQUATIONS