Fuzzy probabilistic assessment of aging aircraft structures subjected to multiple site fatigue damage

A strategy is developed for fuzzy probabilistic assessment of the fatigue resistance of aging aircraft structures due to multiple site fatigue damage (MSD). The residual strength of an aircraft structure may be significantly reduced by the existence of fatigue damage at multiple locations. Depending on the level of subjectivity and degree of knowledge, MSD-related parameters may be represented as either purely random variables or fuzzy random variables. The membership functions of probabilistic characteristics of fuzzy random variables, namely mean values and standard deviations, are developed. Mechanistic and probabilistic models used to evaluate multi-site fatigue damage are also presented. A probabilistic solution strategy, employing the first order reliability method (FORM), is combined with the response surface-based fuzzy modeling approach to develop possibility distributions of the probabilistic response quantities (namely reliability indices and failure probabilities) for components subjected to multiple site fatigue damage. Instead of providing the traditional single valued, purely probabilistic measure for reliability, the present formulation proves its merit in its ability to combine experimental data with expert knowledge to provide confidence bounds on the structural integrity of aging aircraft. Moreover, the predicted bounds are dependent on the level of knowledge regarding the fuzzy input parameters, with a higher degree of knowledge resulting in more narrow bounds. An example problem is used to demonstrate the advantages of the proposed methodology.