## 6 Conclusions  
A fault diagnosis method based on ensemble multiwavelet analysis is proposed for the condition identification of aero-engine rotor. Multiwavelet has been proven to be a powerful tool to describe the non-stationary vibration signal due to the property of multi-resolution analysis and the multiple wavelet basis functions. To overcome some mentioned limitations, ensemble multiwavelet basis function is constructed via a symmetric multiwavelet lifting scheme. Then, the ensemble multiwavelet transform is performed on the vibration signal of aero-engine rotors. The relative energy in each frequency band of the ensemble multiwavelet transform coefficients, which is equivalent to a percentage of the whole signal energy, is taken as the probability. Normalized information entropy is computed based on the relative energy to reflect and evaluate the state of aero-engine rotor. The proposed method is first applied to the fault detection of an experimental aero-engine rotor. Then the proposed method is used for an engineering application and the results shows that the proposed method performed excellently in this task. Finally, the robustness of the multiwavelet method against noise is also tested and verified by simulation and field experiments. Moreover, it must be said that although a similar multiwavelet method is also be used for equipment condition identification in reference [13], the severe shortcoming of low adaptivity on the developed multiwavelet basis greatly limits the ability of customized lifting multiwavelet on signal feature extraction. In addition, some findings need to be introduced based on the experimental results. First, fault feature identification and extraction is the fundamental and vital step in this method. Thus, the customized construction of the ensemble multiwavelet basis function is a very key step in this method, which greatly affects the performance of fault detection. Although the multiwavelet lifting scheme is a popular method, we are looking forward to developing some more novel and effective methods for construction. Next, evaluation index is another key factor for the fault detection of aero-engine rotors  
Figure 27: The multiwavelet information entropy values of all the of vibration signals on experimental planetary gearbox. as well as the construction of an ensemble multiwavelet basis function. The evaluation index must reflect the state information from the fault feature sensitively and effectively. A more useful index should be studied to reflect the state of the development of faults comprehensively in the future. All in all, ensemble multiwavelet analysis method can play a more important role in the detection of faults in aero-engine rotors in the future. In addition, the authors have attracted some interesting results and will carry out a related study in the future. First, the authors have checked the noise attenuation performance in simulation and experiments. However, it is also of significance to study the noise attenuation ability from the technical/methodological viewpoint by referring to the known model-based and signal-based methods [35]. Second, some interesting techniques, such as distributed sensor networks [36] and fault-tolerant techniques [37], are certainly useful for enhancing the ability of carrying out fault diagnosis of mechanical equipment. Thus, the above-mentioned techniques will be taken into consideration to study with the proposed method in future work. This research is supported financially by the Project of National Natural Science Foundation of China for Innovation Research Group (Grant No. 51421004), National Natural Science Foundation of China (Grant No. 51405379), China Postdoctoral Science Foundation (Grant No. 2014M562396, Grant No. 2015T81017), Fundamental Research Funds for the Central Universities of China (Grant No. XJJ2015106, Grant No. CXTD2014001) and Shaanxi Industrial Science and Technology Project (Grant No. 2015 GY121).