Bayesian inference for outlier detection in vibration spectra with small learning dataset

The issue of detecting an abnormal vibration spectrum of aircraft engine is addressed in this article.We show that Bayesian inference has many advantages in order to compute a novelty index, and thus ensure fault detection, when only a mall learning set is available. Fault detection in aircraft engine is often a matter of setting threshold for specific frequency values.To do so, $N$ vibratory log-spectra are usually used to estimate confidence intervals under a standard noise probability law. This point of view has a drawback: if the fault signature appears outside of the set of monitored frequencies, it will not be detected. On the opposite, in this article we consider the spectra as a curve, and look for outliers whose global shape differs. We consider Bayesian linear regression with a spline basis in order to reduce dimension, then set some priors for the regressor and the noise. This allows us to compute a novelty index when a new spectrum is presented, thanks to marginal likelihood computation. The Bayesian point of view is chosen for two reasons : first because it is well-known to deal more easily than maximum likelihood estimators with small data set, which is the situation we have to cope with.Then, because it avoids the need to set a threshold a priori, as in the frequentist case.We compare this setting with standard fault detection methods such as neural networks or confidence intervals under an additive noise and show it performs better when the learning set is small.