A Probabilistic Estimation Approach for the Failure Forecast Method Using Bayesian Inference

Abstract Positive-feedback mechanisms such as fatigue induce a self-accelerating behavior, captured by models displaying infinite limit-state asymptotics, collectively known as the failure forecast method (FFM). This paper presents a Bayesian model parameter estimation approach to the fully nonlinear FFM implementation and compares the results to the classic linear regression formulation, including a regression uncertainty model. This process is demonstrated in a cyclic loading fatigue crack propagation application, both on a synthetic data set and on a full fatigue experiment. A novel ”switch point” parameter is included in the Bayesian formulation to account for nonstationary changes in the growth parameter.