# Energy-Based Prognosis of the Remaining Useful Life of the Coating Segments in Hot Rolling Mill
## 2 Literature Review
### Methods for Assessing RUL
On the other hand, the methods of the second category aim to measure several parameters that are indirectly correlated to tool performance and use statistics or physics models to estimate tool wear Five methods were tested in [PERSON] et al. [30] for strip rolling mills, namely short-time Fourier transform (SHFT), continuous wavelet transforms (CWT), discrete wavelet transforms (DWT), Wigner-Ville distribution (WVD), and empirical mode decomposition (EMD), for detecting specific system fault states. The CWT, DWT, and EMD methods exhibited good applicability in non-stationary signals. From these three, CWT appeared to have the highest computational requirements, whereas DWT has the lowest, and EMD's computational load is considered as the medium. The EMD method has the highest resolution of these three methods. In [PERSON] et al. [31], cutting forces and acoustic emission (AE) signals are used for cutting-tool life estimation. Wear-state identification is based on a spectral exponent. The approach has shown effectiveness for timely warning when the tool is nearing the end of its life due to wear, as the spectral exponent becomes greater than 1. Other studies released, include Bayesian-filter-based [6] and Hidden Markov models [32]. In [PERSON] et al. [33], cyclostationarity was applied to vibration acceleration signals. This study aimed to extract efficient features for tool wear monitoring in a hot rolling mill. It was shown that the synchronous angular statistic (average and variance, Kurtosis, integrated Wigner-Ville spectrum) methods express cyclostationarity at first and second order. Moreover, parameters, namely kurtosis, power, spectral correlation function, and Wigner-Ville spectrum, are efficient for early diagnosis of faults in high-speed machining, compared with the traditional stationary methods. In [PERSON] et al. [34], vibration signals were decomposed through ensemble empirical mode decomposition (EEMD), and the intrinsic mode functions (IMFs), frequency spectrums of IMFs, and features related to amplitude changes of frequency were obtained. An algorithm was developed for real-time estimation of tool wear. The method proved to be very effective, with very low root mean square error. In [PERSON] et al. [35], third-degree regression models were used for vibration and electrical current signals. It was found that tool-wear estimation predictability is affected by the mean vibration signal energy, while electrical current signals provided clearer prediction results. A point at which ML outweighs model-based methods is the availability of predefined NNs, fuzzy-logic systems, and learning algorithms throughout the international literature. On the other hand, methods based in mathematics/physics models require one to build a model and develop the analysis process on his/her own, specialized for the case study. However, ML techniques face difficulties in dealing with production non-stationarities (e.g., processing parameter variations, production pauses), and most of the existing ML methods only carry out with constant working conditions. In contrast, model-based methods do better in that section. Managing production non-stationarity is a key aspect for generating a good prognosis, as adapting to condition changes is necessary for detecting changes in the increase rate of wear. The approach described in this study is classified in the second category of methods. Considering tool wear as a result of material fatigue due to thermomechanical load alternations, the method uses a novel feature to model tool wear and generates prognosis using a mathematical framework. The feature is constructed by performing energy analysis [36] on force and temperature data. In rolling mills, PdM techniques are nowadays implemented instead of traditional break-down or preventive maintenance strategies [37]. The majority of research studies concern fault detection in roller bearings, gearboxes and drivetrains, the tilting table, drivers, or the hydraulic systems [38; 39; 40; 41; 42; 43].