The issue of detecting abnormal vibrations from spectra is addressed in this article, when little is known both on the mechanical behavior of the system, and on the characteristic patterns of potential faults. With vibration measured from a bearing test rig and from an aircraft engine, we show that when only a small learning set is available, probabilistic approaches have several advantages, including modelling healthy vibrations, and thus ensuring fault detection. To do so, we compare two original algorithms: the first one relies on the statistics of the maximum of log-periodograms. The second one computes the probability density function (pdf) of the wavelet transform of log-periodograms, and a likelihood index when new periodograms are presented. A by-product of it is the ability to generate random log-periodograms according with respect to the learning dataset. Receiver Operator Characteristic (ROC) curves are built in several experimental settings, and show the superiority of one of our algorithms over state-of-the-art machine-learning-oriented fault detection methods; lastly we generate random samples of aircraft engine log-periodograms.