# Diagnosing and Balancing Approaches of Bowed Rotating Systems: A Review
## 2 Materials and Methods
### Smart Inspection
#### 2.1.3 Time-Frequency Domain  
Using the frequency analysis also has its cons, too. Since time information is not available in this domain, it is impossible to determine the precise time point or time period at which a frequency component changed. The use of time-frequency-domain analysis has been increased to address this [58]. In both manual and automatic fault diagnosis, time-frequency-domain analysis, such as wavelet transformation, has become a powerful tool. This method is particularly effective at distinguishing nonlinear features, for instance, in revealing crack symptoms in rotor systems [59; 60].  
Several more researchers have also used the time-frequency-domain transformations to diagnose bowed rotor systems. In [61], [PERSON], [PERSON], and [PERSON] compared the effectiveness of the frequency-domain and time-frequency-domain (wavelet) transformations in the classification of unbalanced, bowed, and unbalanced-bowed rotor systems by means of the ANN. In the case of the frequency domain, amplitudes of frequency components of RMS (root mean square) of vibration velocity (mm/s) were selected as the input data to the ANN. On the other hand, the RMS of the detail coefficients of wavelet transformation were employed as the input data. In both cases, the achieved accuracy was above 99%, i.e., 99.81% and 99.9% in the cases of frequency and time-frequency domain, respectively.  
A combined approach consisting of continuous wavelet transform (CWT) and rough set theory was employed by [PERSON] et al. [62] in the classification of seven rotor systems, including a healthy induction motor, also with faulted bearings, stator fault, and voltage unbalance, as well as with a faulted shaft, i.e., bowed, broken, and unbalanced. The CWT spectrograms were used to extract statistical features such as mean, RMS, variance, standard deviation, crest, kurtosis, and entropy. Furthermore, the rough set procedure was used to select the most effective scales during the feature selection step, reducing the required computing time by 85%. The classification process was carried out using three supervised classifiers: multilayer perceptron (MLP), radial basis function (RBF), and support vector machine (SVM).  
[PERSON] and [PERSON] [63] decomposed the complex vibration signals of a bowed and unbalanced rotor system into a number of intrinsic mode functions using the empirical mode decomposition technique. The Hilbert spectrum was used to reveal the characteristics of these two damages following decomposition. The initial bow's impacts changed depending on its phase angle. Higher vibration amplitude and wider intra-wave frequency modulation band were observed when the phase angle of the residual bow was 0\({}^{\circ}\). In contrast, when the bow's phase angle was equal to 180\({}^{\circ}\), the vibration amplitude and frequency band were both diminished.  
[PERSON] et al. [64] used a deep convolutional neural network (DCNN) to classify rotor systems into four categories: healthy, bowed shaft, broken shaft, and unbalanced. Spectrograms of continuous wavelet transformations with Morlet as the mother function were introduced as input data. In addition, a layer-wise relevance propagation (LRP) post-training procedure was used to interpret the classification results.