About periodicity and signal to noise ratio - The strength of the autocorrelation function

In condition monitoring a part of the information necessary for decision-making comes from scrutinizing a time measure or a transform of this measure. Frequency domain is commonly exploited; lag domain is not, albeit advantages of the autocorrelation function have long been known. In this paper, we dwell on the autocorrelation function in order to extract some interesting properties of the measure. We propose two indicators in order to characterize the periodicity of a signal. First is based on the nonbiased autocorrelation function and indicates a fundamental periodicity rate. Second is based on the biased autocorrelation and gives a dominant-power periodicity rate. The study of the 2D-plane defined by these two indicators allows the definition of regions attached to one type of periodicity from periodic to aperiodic through almost-periodic and quasi-periodic. Combined with an estimation of the correlation support, a final decision about the periodicity of the signal is given. In case of a periodic signal, a way of estimating the global signal ratio is proposed. These new outputs are valuable for initializing more complex processing. All the algorithms proposed are fully automatic, one click use! Relevance of these indicators is shown on real-world signals, current and vibration measures mainly.