Best parameter choice of Stochastic Resonance to enhance fault signature in bearings

Stochastic Resonance (SR) is a phenomenon studied and exploited for telecommunication, which permits the detection and amplification of weak signals by the assistance of noise. The first papers on this topic date back to the early 80s and were developed to explain some periodic natural phenomena. Other applications are in neuroscience, biology, medicine and, obviously, mechanics. Recently, a few researchers have tried to apply this technique for detecting faults in mechanical systems and also bearings. In this paper we discuss the best way to select the parameters to augment the performance of the algorithm. This is probably the main drawback of SR, since in system identification the procedure should be as blind as possible to be efficient and widely applicable. The classical bi-stable potential form is adopted in our study, with three parameters to be selected. Based on numerical tests, a characteristic trend of the amplification factor has been found with respect to the parameters variation, so that a general rule is consequently determined which gives the best performances in terms of detection and amplification. The SR algorithm is tested on both simulated and experimental data showing a good capacity of increasing the signal to noise ratio

Albert algebras over Z and other rings

Albert algebras, a specific kind of Jordan algebra, are naturally distinguished objects among commutative non-associative algebras and also arise naturally in the context of simple affine group schemes of type $F_4$, $E_6$, or $E_7$. We study these objects over an arbitrary base ring $R$, with particular attention to the case of the integers. We prove in this generality results previously in the literature in the special case where $R$ is a field of characteristic different from 2 and 3.Comment: v2: section 12 on number of generators is new, Theorem 13.5 now holds for semi-local rings (and even a somewhat wider class