Discrete random sampling: Theory and practice in machine monitoring

Abstract

Abstract Random sampling was first introduced in the 1960’s (Beutler and Leneman, 1966 [1] ), and was then reused in the Compressive Sensing theory (published in 2006 (Donoho, 2006 [2])) for having two important advantages: anti-aliasing property and low sampling rate. These advantages decrease the demand of high speed acquisition and big data storage. In this paper, a brief review of the principal random sampling modes is presented: Additive Random Sampling (ARS) and Jittered Random Sampling (JRS) that both use probability distributions: uniform or Gaussian (Wojtiuk, 2000; Ben Romdhane, 2009; Luo, 2012; Lo and Purvis, 1997 [3–6]). In fact, the stationarity of the random point process is the essential criterion to guarantee the anti-aliasing property (Bilinksis and Mikelson, 1992 [7]). Accordingly, these modes of sampling are studied and used in simulation and hardware implementation. In addition, a study of the time quantization effect is done to explore the different aspects of discrete random sampling (Ben Romdhane, 2009; Luo, 2012 [4,5]). The performance of this sampling is approved by simulation and practice, using respectively Matlab and Arduino microcontroller, respectively, for acquiring signals at a randomly spaced clock. A database was created in order to observe the impact of statistical parameters such as the mean and the standard deviation for Gaussian distribution, and the interval endpoints of uniform distribution. In conclusion, the ARS with uniform distribution has been proved to have less limitations (Ben Romdhane, 2009 [4]), whereas the spectrum of sampled signal is free of alias and the sampling frequency is reduced (a much smaller than Nyquist-Shannon sampling rate). In order to take advantage of this mode, it is applied on vibration signals to enhance remoted machine monitoring.