Development of simple estimation method for the influence of parameter uncertainty of probability distributions against evaluation result of probabilistic fracture mechanics

Abstract

Probabilistic fracture mechanics (PFM) analysis is an evaluation method for the structural integrity of components containing a crack, with considering the random variability of the input physical parameters, such as crack growth rate. The characteristics of the variability are described in the form of probability distribution, which is defined by probabilistic parameters such as mean and variance. Without sufficient information about the random variability, the parameter of the probability distribution may contain uncertainty, so that evaluated failure probability also contains uncertainty. Therefore, as the output of PFM analyses, not only the failure probability but also their uncertainty derived from the parameter uncertainty should be evaluated. In this paper, we describe the parameter uncertainty in the form of the interval of the parameter. We propose the simple estimation method for upper and lower bound of the interval of the PFM result derived from the above parameter interval. Additionally, we propose the uncertainty index that denotes the interval of the result derived from the interval of each parameter. These proposals are based on the first order reliability method (FORM). The proposed estimation method and the uncertainty index are validated through the evaluations, whose conditions are based on past evaluation study. At the first stage, accuracy of the evaluated result by FORM is validated through comparison between FORM and the directional simulation method. And then, the proposed methods are validated through the comparison with the result by FORM.

Keywords

• failure probability
• uncertainty
• probabilistic fracture mechanics
• directional simulation
• first order reliability method