## 1 Introduction
To improve the accuracy of HHT, some other advanced signal decomposition approaches, such as ensemble empirical mode decomposition (EEMD) [19], complementary ensemble empirical mode decomposition (CEEMD) [20], empirical wavelet transform [21], variable mode decomposition (VMD) [22], and adaptive local iterative filtering (ALIF) [23] have been employed to replace EMD to extract the sub-components of a signal. Despite these methods have a better performance over EMD in data decomposition, the premise of obtaining ideal results by using these methods is the good choice of parameters, the process of which is very complex. Singular spectrum decomposition (SSD) is a new adaptive data decomposition method [24], the basic principle of which is based on singular spectrum analysis (SSA). It could choose the parameters automatically and retrieve the construction components accurately. Moreover, the existence of non-meaningful components could be minimized to a large extend. However, the problem of end effects still has not been solved in the original SSD algorithm, which needs to be studied further. Some useful techniques such as extreme value point extension [25], data prediction [26] and waveform matching extension method [27] have been studied by scholars for restraining the end effect of EMD. However, these developed approaches have some drawbacks. For example, the extreme value point extension method only considers the information of several extreme value points near signal endpoint but does not take into account the internal law of the signal, so the effect of this method for complex non-stationary signals is not ideal. The data prediction method is on the base of the intelligent prediction techniques such as neural work [28] and support vector regression [29]. Its improvement effect depends largely on the parameter setting of the prediction tool itself, and the operation time is also long, which decreases the practicability of this method. The waveform matching extension method takes into account the internal laws and trends of signal and has high computation efficiency. However, how to choose the best matching waveformadaptively is a difficult problem. In view of the above problems, a novel adaptive waveform matching extension approach was introduced for solving the end effects and improving the decomposition accuracy of SSD. The improved SSD (ISSD) method was employed to replace EMD to extract the sub-component signals of the rotor vibration signal. Several sub-component signals called singular spectrum components (SSCs) can be extracted after the ISSD decomposition. Then an ISSD-HT TFS can be produced by using HT to demodulate every SSC. The ISSD-HT TFS is more accurate than the HHT TFS due to the advantages of ISSD over EMD. Considering that the main fault features of rotors locate in the former harmonics of rotary frequency of the TFS, a new index called characteristic frequency band energy entropy (CFBEE) was proposed in this paper to extract the local characteristics of the ISSD-HT TFS corresponding to different working conditions of rotors. After extracting the CFBEE as the feature vector, an outstanding machine-learning classifier called support vector machine (SVM) [30], which is especially suitable for the classification problem of small samples was used in this paper to achieve the fault identification of rotors. This organization of this paper is as follows: In Section 2, basic theory background of ISSD, characteristic frequency band energy entropy and SVM is introduced. Section 3 describes the framework of the proposed method. Simulation and experiment signals are analyzed in Sections 4 and 5, respectively. Besides, comparison is performed among the proposed method and three other methods to demonstrate the effectiveness and superiority of the proposed method. Conclusion is summarized in Section 6.