Effects of Structural Tests on Aircraft Safety

This paper presents a methodology to investigate the effects of structural tests on aircraft safety. In particular, the paper focuses on the effect of the number of coupon tests and structural element tests on the final distribution of failure stress. The mean failure stress is assumed to be predicted by a failure criterion (e.g.. Tsai-Wu), and the initial distribution of this mean failure stress reflects the uncertainty in the analysis procedure that uses coupon test data to predict structural failure. In addition to the uncertainty in the mean failure stress, there is also uncertainty in its variability due to the finite number of coupon tests. Bayesian updating is used to update the failure stress distribution based on results of the element tests. A Monte Carlo simulation of a large number of uncertainties and the possible test results are used to obtain the probability of structural failure in a certification test or in actual flight. Incorporating the Bayesian updating into the Monte Carlo simulation loop is computationally prohibitive; therefore, a surrogate procedure is devised to overcome the computational challenge. A structural design following the Federal Aviation Administration regulations is considered, and the tradeoffs between the number of tests and the weight and probability of failure in the certification test and in service are explored. To make this tradeoff analysis computationally affordable, response surface approximations are used to relate the knockdown factor to the probability of failure in service and in the certification test. It is found that it is possible to do a simultaneously probabilistic design and satisfy the Federal Aviation Administration regulations for deterministic design.