Airframe integrity based on bayesian approach

Abstract

A Bayesian approach was initiated to estimate the crack size probability density function, pdf corresponding to the traditional conservative engineering end of service life limit, known as the 100% fatigue life expended (FLE) limit. The initial application of the Bayesian approach was based on fleet findings for a particular location on 25 inspected aircraft. The FLE values corresponding to the particular airframe location exceeded 100%. First a prior crack size probability density function, pdf, at FLE of 100% was estimated in line with underlying FLE presumptions and whatever information could be found in the literature. Second, for all the inspected aircraft at a FLE greater than 100%, the load histories were taken from the respective onboard structural data recording system (SDRS) datasets. The prior crack size pdf corresponding to the FLE values of each inspection was then simulated by a Monte Carlo technique starting with the prior pdf at 100% FLE. Since loads for the aircraft were known the only simulation uncertainty was in the material properties for crack growth, assuming no model uncertainty. Next the simulated prior crack size pdf at the inspected FLE and the corresponding observed cracks were combined via Bayesian updating to compute the posterior crack size pdf at the inspected FLE. The posterior crack size pdf at the inspected FLE was used to back-calculate the corresponding posterior crack size pdf that needed to be at the FLE of 100%. Simple (equal weights) averaging combined the resulting back-calculate the corresponding posterior crack size pdf functions at FLE of 100%. The computations resulted in an updated posterior crack size pdf at FLE equaling 100% representing the inventory population. In turn, the posterior pdf at FLE equaling 100% serves as the prior pdf for the next set of inspection results. Likewise, the PDF at FLE equaling 100% is used to project the current state of damage of any aircraft at some FLE greater than 100% that has not undergone inspection. In other words, the posterior pdf at FLE equal to 100% is used along with the known (measured) loads to estimate the current crack size pdf for an aircraft at FLE greater than 100%. Subsequently, the computed current crack size pdf is the basis for projection of the aircraft's crack size pdf corresponding to future usage