Application of the Instantaneous Rényi Entropy for Real-Time Damage Detection

Recently, Instantaneous Spectral Entropy (ISE) measurements have been proposed for real-time damage assessment purposes in nonstationary mechanical systems. These include Condition Monitoring (CM) in rotating machinery as well as Structural Health Monitoring (SHM) for civil structures. However, several distinct entropy definitions are available in the scientific literature, each with its advantages and limitations. In the present paper, the potential of the family of Rényi entropies is evaluated. The order α is varied between 0 (corresponding to the Hartley entropy, i.e., theMax-entropy) and+∞(Min-entropy), encompassing α → 1 (Shannon-entropy) and α = 2 (Collision entropy) as particular cases of special interest. The Wigner-Ville (WV), Smoothed Pseudo Wigner Ville (SPWV), Discrete Choi-Williams (DCW), and Continuous Wavelet (CWT) transforms are all tested for the time-frequency (TF) distribution of the target signal. In turn, this TF is used to compute the probability density function, fromwhich the ISE is estimated. A sensitivity analysis is run on all the parameters for each candidate TF transform, aiming at defining the best settings. All studies were performed on a well-known experimental dataset, the three-storey aluminium frame structure developed at the Los Alamos National Laboratories, considering the undamaged conditions as the normality model. The results show good potential for entropy-based real-time damage detection, especially for breathing cracks.