The Lethargy Coefficient Estimation of the Probabilistic Fatigue Life Model Using the Markov Chain Monte Carlo

Abstract

Recently, the researchers of prognostics and health management (PHM) have been developed to the field of engineering. In this study, probabilistic fatigue life which based on Zhurkov model is suggested using stochastically and statistically estimated lethargy coefficient. The fatigue life model was derived using Zhurkov life model and it was deterministically validated with the reference of fatigue life data. For this process, firstly, lethargy coefficient which is relative to the failure of materials has to be obtained with rupture time and stress from quasi-static tensile test. These experiments are performed using HS40R steel. However, lethargy coefficient has uncertainties due to inherent uncertainty and the variation of material properties in the experiments. Bayesian approach was employed for estimating the lethargy coefficient of the fatigue life model using Markov Chain Monte Carlo (MCMC) sampling method and considering its uncertainties. Once the samples are obtained, one can proceed to the posterior predictive inference on the fatigue life. This life model is reasonable through comparing with experimental fatigue life data. As a result, predicted fatigue life was observed that it was significantly decreased in accordance with increasing stress conditions relatively. This life model is reasonable through comparing with experimental fatigue life data.