Uncertainty of Thermodynamic-Entropy-Based Reliability and Remaining Useful Life Predictions Under Variable Amplitude Fatigue

Abstract Traditionally, engineers have used empirical relationships such as the modified Goodman relation and the Basquin equation to design for fatigue and Miner’s Rule to calculate reliability and to predict the remaining useful life (RUL) of structures subjected to fatigue. Research has shown the viability of using thermodynamic entropy as an alternative to traditional empirical relationships for fatigue-related design, reliability estimation, and RUL prediction. This entropy-based approach relies upon fatigue fracture entropy, a material property shown empirically to be connected with an entropy-based Miner’s Rule. Practical application of any approach, however, demands an accounting for uncertainty; otherwise, any predictions inherently carry a higher level of risk. Entropy-based formulations observed in the literature provide no such accounting. This work provides an analytically derived formulation for uncertainty in both entropy-centered and empirically based physics-of-failure-centered (PoF-centered) approaches to estimating reliability. For both the PoF- and entropy-centered approaches, Monte Carlo simulation data of an AISI 304 stainless steel rod subjected to variable amplitude fatigue produced estimates of both cycle-based and time-based reliability using both entropy-centered and PoF-centered formulations. This procedure includes non-parametric as well as parametric approaches. The entropy-based calculations compare well with their traditional counterparts above 80% reliability. More investigation to improve the simulation as well as comparing against empirical fatigue tests are recommended.