Crack Growth Prediction Based on Uncertain Parameters Using Ensemble Kalman Filter

Abstract

We are developing a method that will enable the estimation of crack shapes in such structures as power equipment and social infrastructure with greater precision as well as the prediction of crack growth life under conditions of uncertainty regarding crack perimeter structure and applied loads. Ascertaining the dimensions of cracks is complicated by the influences exerted by external loads on crack propagation as well as the geometry of crack perimeters. The prediction of crack propagation based on uncertain information is an overly conservative approach due to the lack of accuracy. This paper presents a Bayesian estimation of actual crack geometry based on predictions from a physical model of crack growth and measured crack geometry. The uncertainty in the load and the geometry of the crack perimeter are reflected in the crack propagation model. The range over which the uncertain parameters are estimated is updated simultaneously with estimations of the crack shape. Furthermore, we describe how optimal measurement intervals can be identified from the one-period-ahead prediction of crack growth based on a physical model. The application of properly spaced measurements and sequential Bayesian estimation can effectively mitigate the impact of measurement error and parameter uncertainty, thereby enhancing the precision of crack growth prediction. Sequential Bayesian estimation is an Ensemble Kalman Filter, and our physical model of crack propagation is a Paris measure based on fracture mechanics. The efficacy of the methodology presented in this paper is validated by the outcomes of the simulated observed data of a CT specimen.