## 1 Introduction
Iterative signal extraction method was utilized to reduce the noise interference in modal parameters identification by [PERSON] et al. [30]. Changes in resonant and anti-resonant frequencies were used by [PERSON] et al. [31] to detect crack locations in a two-crack torsional shaft. [PERSON] et al. [32] utilized the changes in phase angle of frequency response function to identify the location and depth of an open crack in a rotor. [PERSON] et al. [33] proposed a method for open crack localization of a shaft by comparing the map of the modal constants of the reverse directional frequency response functions with the reference map of the un-cracked model. The support vector machine (SVM) is a common pattern recognition-based method with many applications [34], and was used to realize crack identification with features extracted by wavelet transform in [10]. A notch in a stationery rotor was identified by the first four natural frequencies using artificial neural network (ANN) by [PERSON] et al. [35]. As a summary for the literature review, there are more crack detection methods than crack identification methods for rotors, and among the crack detection methods, signal based methods are in the majority. These signal based methods can realize crack detection conveniently, while they are difficult in crack parameters identification. For modal parameters based methods, the crack will definitely affect the modal parameters, but the modal parameters are not sensitive to shallow cracks. And for the pattern recognition-based methods, a large amount of crack samples are required to train the models, which limits the application of such kind of methods. For model based methods, they could perform well in crack identification, only if the models were accurate enough. Therefore, the accuracy of a modelling method and efficiency of an identification approach should be the focuses. Based on the above short review, there is a trend to transform the crack identification problem into an optimization problem, and through updating iterations to find the crack parameters minimizing the difference between measured features and calculated features, which can be classified as model updating method [36]. The model updating method has been widely used in structural damage identification [37; 38; 39; 40], and what matters the most are the model construction and identification efficiency. For the static beam or plate, an accurate model is far more easily to obtain, which will be not the case for rotating rotors, especially when a breathing crack is there. Therefore, how to establish an efficient and reasonable updating model is quite important for crack identification in rotors. Super-harmonic features are good indicators of a crack in a rotor, which emerge since the presence of a crack leads to asymmetric behaviour and a breathing crack introduces nonlinearity. Although super-harmonic features can also be caused by other faults, such as coupling misalignment which also induces super-harmonics in vibration response of a rotor [41], it is much easier to identify and correct [42]. So in this work only the crack is considered. Energy variation of the 3\(\times\) component (where X represents the frequency corresponding to the rotating speed) extracted based on Wavelet Packet Transform [43; 44; 45] was used to quantify the crack depth of a crack with known crack location in a rotor by [PERSON] et al. [46], and the analytical Jeffcott rotor model and the corresponding experimental rotor with a saw-cut crack were studied to validate the method. EMD method [47; 48; 49] was applied to steady-state responses generated from a Jeffcott rotor to extract the 3\(\times\) and 2\(\times\) components in the neighborhood of 1/3 and 1/2 of the critical rotating speed by [PERSON] et al. [50], results showed that the variation of averaged amplitudes of super-harmonic components provided clear and robust signatures of early cracks in rotating rotors.