# Probabilistic Model-Based Prognostics Using Meshfree Modeling

## Abstract

Improved system reliability and reduced maintenance cost are guaranteed if the prediction of remaining useful life (RUL) is deemed to be accurate. Energy systems, like wind turbines, are the primary beneficiaries of this achievement as they tend to suffer from an unexpected early life failure of components that resulted in the loss of revenue and high maintenance costs. The issue of uncertainty in the prediction of a future state is yet a prevailing issue in prognostics and due attention is paramount. Hence, there is a need for establishing a comprehensive framework to quantify uncertainty in prognostics and this research addresses this issue by considering a research question that reads ‘can uncertainty considerations improve the prediction of RUL?’ The following specific aims were developed to answer the research question: (1) develop a meshfree cantilever beam with uncertainty in loading conditions, and (2) predict remaining useful life reliably. A probabilistic framework was developed that efficiently predicts remaining useful life of a component using a combination of meshfree model and degradation model. To account for prediction uncertainty, modeling and loading uncertainties are quantified and incorporated into the framework. As an example, the problem of a cantilever beam subjected to a fatigue loading was considered and local radial point interpolation method was used to find the stresses. The cyclic stresses and the damage model, constructed using the *S*-*N* equation, are implemented in the prognostics framework to predict the RUL. Uncertainties in the RUL were quantified in terms of probability density functions, cumulative distribution functions, and 98% confidence limit. The prognostics framework is flexible and can be used as a starting point for RUL prediction of other physical phenomena such as crack propagation, by incorporating more sources of uncertainties in order to make it comprehensive.

### Keywords

Uncertainties Prognostics and health management Remaining useful life Probabilistic Meshfree modeling### References

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