A General Framework for Uncertainty Propagation Based on Point Estimate Methods

A general framework to approach the challenge of uncertainty propagation in model based prognostics is presented in this work. It is shown how the so-called Point Estimate Methods (PEMs) are ideally suited for this purpose because of the following reasons: 1) A credible propagation and representation of Gaussian (normally distributed) uncertainty can be done with a minimum of computational effort for non-linear applications. 2) Also non-Gaussian uncertainties can be propagated by evaluating suitable transfer functions inherently. 3) Confidence intervals of simulation results can be derived which do not have to be symmetrically distributed around the mean value by applying PEM in conjunction with the Cornish-Fisher expansion. 4) Moreover, the entire probability function of simulation results can be reconstructed efficiently by the proposed framework. The joint evaluation of PEM with the Polynomial Chaos expansion methodology is likely to provide good approximation results. Thus, non-Gaussian probability density functions can be derived as well. 5) The presented framework of uncertainty propagation is derivativefree, i.e. even non-smooth (non-differentiable) propagation problems can be tackled in principle. 6) Although the PEM is sample-based the overall method is deterministic. Computational results are reproducible which might be important to safety critical applications. Consequently, the proposed approach may play an essential part in contributing to render the prognostics and health management into a more credible process. A given study of a generic uncertainty propagation problem supports this issue illustratively. This work includes unpublished elements of the Ph.D.-Thesis (Schenkendorf, 2014).