# Review of Recent Advances in the Application of the Wavelet Transform to Diagnose Cracked Rotors
###### Abstract  
Wavelet transform (WT) has been used in the diagnosis of cracked rotors since the 1990s. At present, WT is one of the most commonly used tools to treat signals in several fields. Understandably, this has been an area of extensive scientific research, which is why this paper aims to summarize briefly the major advances in the field since 2008. The present review considers advances in the use and application of WT, the selection of the parameters used, and the key achievements in using WT for crack diagnosis. c pacs: 97.10.  
in [10]. The most commonly used model in this field is the simple Jeffcott rotor model, detailed in [11; 12]. The Finite Elements Approach (FEA) has attracted researchers as an investigative tool for the study of crack breathing phenomena. However, traditional FEA has some limitations, such as low efficiency and accuracy, slow convergence, and strong nonlinearity. Wavelet spaces have also been employed, and from this wavelet finite element methods (WFEM) have been developed [13]. When comparing numerical results obtained using this model with experimental data, it is not only possible to detect the crack, but also the location and depth of that crack. These models have been applied to experimental results in works as demonstrated by [14], where it was combined with Genetic Algorithms (GA). Other examples of the WFEM model have been presented in [15; 16]. Signals obtained from studying rotating machinery have complex structures and are comprised of a large amount of information. The aim of condition monitoring is to select the proper processing to extract the optimal features of a signal for fault detection. The features must fit two main requirements: they must be easy to handle with a low computational cost, and they must contain valuable information about the fault to be predicted. Within vibration methods, there is a large range of different signal processing methods that can be applied for this purpose. Short Time Fourier Transform (STFT) and Hilbert transform (HT) have traditionally been used to observe changes in response or in eigenfrequencies when a crack forms and propagates [17; 18]. In 2004, [PERSON] _et al._[19] affirmed that, for cracks, 1x and 2x frequency components using Fast Fourier Transform (FFT) and HT experiment very important changes at the steady state when a crack forms. However, in practice, these changes are very difficult to detect due to the presence of noise and other interfering factors. In recent years, new techniques classified by [PERSON] _et al._[19], which they termed 'non-traditional methods', have appeared. The non-traditional techniques that have emerged work in both the time and frequency domains. Specifically, the Hilbert-Huang Transform (HHT), based on the Empirical Mode Decomposition (EMD) for obtaining the Intrinsic Mode Functions (IMFs), has been used effectively in the diagnosis of cracked rotors. This approach was detailed in [20; 21]. However, due to its effectiveness in treating non-stationary signals, the most widely used technique in crack diagnosis in rotors is the Wavelet Transform (WT). Nowadays, WT is the most common technique used to treat signals [22]. WT theory has also been applied to acoustic emission (AE) signals to detect crack growth, as demonstrated in [23]. Recently, AE signals have been widely used in order to monitor the condition of rotating machinery. When the sensor is close to the source, AE is capable of detecting crack growth [24]. Typical frequencies associated with activity of AE range from 20 kHz to 1 MHz. A review of the use of WT in the diagnosis of faults in machinery was presented by [PERSON] and [PERSON] [25] in 2004. They stated that the use of WT had not yet achieved precedent. The main reason for this is that the wavelet application is not a straightforward issue due to the requirement to select the wavelet function and the range scale, and also due to the fact that there are no standardized or generalized methods to carry out these requirements.