Xiao-Sheng Si, Wenbin Wang, Chang-Hua Hu, Dong-Hua Zhou and Michael G. Pechta
a CALCE Electronic Products and Systems, University of Maryland, College Park, MD 20742, USA
Abstract:
Remaining useful life estimation is central to the
prognostics and health management of systems, particularly for
safety-critical systems, and systems that are very expensive. We
present a non-linear model to estimate the remaining useful life
of a system based on monitored degradation signals. A diffusion
process with a non-linear drift coefficient with a constant threshold
was transformed to a linear model with a variable threshold to
characterize the dynamics and non-linearity of the degradation
process. This new diffusion process contrasts sharply with existing
models that use a linear drift, and also with models that use
a linear drift based on transformed data that were originally
non-linear. Both existing models are based on a constant threshold.
To estimate the remaining useful life, an analytical approximation
to the distribution of the first hitting time of the diffusion
process crossing a threshold level is obtained in a closed form
by a time-space transformation under a mild assumption. The
unknown parameters in the established model are estimated using
the maximum likelihood estimation approach, and goodness of
fit measures are applied. The usefulness of the proposed model
is demonstrated by several real-world examples. The results
reveal that considering non-linearity in the degradation process
can significantly improve the accuracy of remaining useful life
estimation.
Keywords : Brownian motion, degradation, diffusion process,first hitting time, maximum likelihood, non-linear drift, remaining useful life
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