Divergence-Based Segmentation Algorithm for Heavy-Tailed Acoustic Signals with Time-Varying Characteristics

Abstract

Many real-world systems change their parameters during the operation. Thus, before the analysis of the data, there is a need to divide the raw signal into parts that can be considered as homogeneous segments. In this paper, we propose a segmentation procedure that can be applied for the signal with time-varying characteristics. Moreover, we assume that the examined signal exhibits impulsive behavior, thus it corresponds to the so-called heavy-tailed class of distributions. Due to the specific behavior of the data, classical algorithms known from the literature cannot be used directly in the segmentation procedure. In the considered case, the transition between parts corresponding to homogeneous segments is smooth and non-linear. This causes that the segmentation algorithm is more complex than in the classical case. We propose to apply the divergence measures that are based on the distance between the probability density functions for the two examined distributions. The novel segmentation algorithm is applied to real acoustic signals acquired during coffee grinding. Justification of the methodology has been performed experimentally and using Monte-Carlo simulations for data from the model with heavy-tailed distribution (here the stable distribution) with time-varying parameters. Although the methodology is demonstrated for a specific case, it can be extended to any process with time-changing characteristics.

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“…One may say that regime A is smoothly transforming to regime B. This issue was investigated by Grzesiek et al [41]. It is also the case here, especially as there is "no jump" from good condition to warning state, that the machine in good condition slowly starts the degradation process.…”

“…Simulation of degradation data in the presence of Gaussian noise is shown in Figure 5. For a non-Gaussian case, the symmetric α-stable distribution is selected as an example of heavy-tailed, non-Gaussian distribution [41,[69][70][71][72].…”

Robust switching Kalman filter for diagnostics of long-term condition monitoring data in the presence of non-Gaussian noise

“…Using the long-term condition monitoring data is a crucial element in both diagnostics and prognostics. Many methods published in recent years for CBM can be categorized into four main groups [1]: stochastic-based [2,3,4,5,6,7,8], machine learning-based [9,10,11,12], physics or model-based [13,14], and hybrid methods [15,16]. Both machine learning and stochastic approaches such as neural networks [12,17,18,19,20,21,22,23] and hidden Markov models (HMM) [24,25,26,27,28,29] have strong potential to be used for diagnostics and prognostics areas.…”