Investigation of Fan Blade off Events Using a Bayesian Framework

This paper illustrates a probabilistic method of studying Fan Blade Off (FBO) events which is based upon Bayesian inference. Investigating this case study is of great interest from the point of view of the engineering team responsible with the dynamic modelling of the fan. The reason is because subsequent to an FBO event, the fan loses its axisymmetry and as a result of that, severe impacting can occur between the blades and the inner casing of the engine. The mechanical modelling (which is not the scope of this paper) involves studying the oscillation modes of the fan at various release speeds (defined as the speed at which an FBO event occurs) and at various amounts of damage (defined as the percentage of blade which gets released during an FBO event). However, it is virtually infeasible to perform the vibrational analysis for all combinations of release speed and damage. Consequently, the Bayesian updating which forms the foundation of the framework presented in the paper is used to identify the most likely combinations prone to occur after an FBO event which are then going to be used further for the mechanical analysis. The Bayesian inference engine presented here makes use of expert judgements which are updated using in-service data (which for the purposes of this paper are fictitious). The resulting inputs are then passed through 1,000,000 Monte Carlo iterations (which from a physical standpoint represent the number of FBO events simulated) in order to check which are the most common combinations of release speed and blade damage so as to report back to the mechanical engineering team. Therefore, the scope of the project outlined in this paper is to create a flexible model which changes every time data becomes available in order to reflect both the original expert judgements it was based on as well as the real data itself. The features of interest of the posterior distributions which can be seen in the Results section are the peaks of the probability distributions. The reason for this has already been outlined: only the most likely FBO events (i.e.: the peaks of the distributions) are of interest for the purposes of the dynamics analysis. Even though it may be noticed that the differences between prior and posterior distributions are not pronounced, it should be recalled that this is due to the particular data set used for the update; using another data set or adding to the existing one will produce different distributions.