A Bayesian Approach to Airframe Reliability Management (PSAM-0183)


Aircraft aging has become an immense challenge for in terms of ensuring the safety of the fleet while controlling life cycle costs. One of the major concerns in aircraft structures is the development of fatigue cracks, for example in the fastener holes that connects the wing to the fuselage. Some methods have been proposed to manage this problem. Bayesian approach in which the current state of knowledge or degree of belief about an unknown quantity (for example a fatigue model parameter or crack size), as represented by a probability distribution, may change in light of new information and evidence. In this approach the Bayes' theorem is used to obtain the “updated” or posterior state of knowledge given the new information. This approach is promising since generic information about the fleet is available, but often information about a specific aircraft is limited. Implementation of this approach allows us to assess airframe integrity by updating generic data with airframe inspection data while such data are compiled. This paper discusses the methodology developed and employed for assessment of loss of airframe integrity and safety due to fatigue cracking in the fastener holes of aging aircrafts. The methodology requires a probability density function (pdf) of initial crack size. Subsequently, a crack growth regime begins. As the Bayesian analysis requires estimation of a prior initial crack size pdf such a pdf is subjectively assumed to be lognormally distributed. The prior distribution of crack size as crack grows is modeled through a combined Inverse Power Model (IPL) and lognormal relationships. The airframes are usually scheduled to undergo extensive structural integrity inspections at various intervals of time. The first set of inspections is used as the evidence for updating the crack size distribution at the various stages of aircraft life. Moreover, the materials used in the structural part of the aircrafts have variations in their properties due to their calibration errors, specimen geometry and testing machine alignment, and they also vary to some extent as to chemical composition, level of impurities and size and number of microscopic defects. Therefore, in order to manage airframe integrity in a more effective manner, the variability in the material properties must be also taken into account. In this case, one should explicitly address material properties scatter and crack growth model uncertainties in a probabilistic manner. A MatLab® routine is developed and used to calculate the crack growth using the proposed Bayesian approach. As the first step in this routine the material properties and the initial crack size are sampled (from their respective distributions). A standard Monte Carlo simulation is employed for this sampling process. At the corresponding aircraft age where inspections have been performed, the cracks observed, if any, have been used as the evidence to update (i.e., Bayesian updating) the crack size distribution and proceeded in time. After the updating, the estimation of the crack distribution is improved by taking into account the evidences observed, then it is possible to estimating the probability of structural failure as a function of flight hours for a given aircraft in the future. The results show very accurate and useful results about the reliability and integrity of airframes in aging aircrafts. The paper will explain the methodology used, the models employed, and some examples of applications.

  • Summary/Abstract
  • Introduction
  • Treatment of Loads
  • Crack Growth Model Used
  • Initial Crack Size Distribution
  • Estimation of the Prior Distribution of Crack Size as Crack Grows
  • Crack Observation (Evidence)
  • Bayesian Updating of Crack Size Distribution
  • Updating of the Prior Distributions at FLE = 100%
  • Forecasting Probability of Failure for a Specific FLEI
  • Discussion of Results
  • References

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