As a novel time-frequency analysis method, adaptive local iterative filtering (ALIF) can decompose the time series into several stable components which contain the main fault information. In addition, the amplitude of singular value obtained by singular value decomposition (SVD) can reflect the energy distribution. Naturally, there are certain differences in the energy produced by different faults such as the broken tooth, wearing and normal. Thus, a novel method of mechanical fault

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... on method based on adaptive local iterative filtering and singular value decomposition is proposed in this paper. Firstly, ALIF method decomposed the original vibration signal into a number of stable components to establish an initial feature vector matrix. Then, the singular values energy corresponding to the feature matrix is employed as a criterion to identify various faults. Compared with the conventional EMD method by simulation experiments, ALIF method has obvious superiority in solving modal aliasing, which is more conducive to the advanced analysis. In this paper, the proposed method is employed to extract the fault information of rolling bearing fault signals from Case Western Reserve University Bearing Data Center. To further verify the effectiveness of the method, the case study is conducted at Drivetrain Diagnostics Simulator. To further illustrate the effectiveness of the method, the results obtained by this method are compared with EMD and EEMD. The results indicated the proposed method performs better in the classification of different mechanical faulty modes. method of beforehand noise reduction and reprocessing operation may lose some features and reduce the accuracy of signal reconstruction, resulting in false diagnosis conclusions. Due to the development of non-linear theory, many non-linear analysis methods have been proposed to deal with the problems of mechanical equipment fault diagnosis. For the processing of the non-linear and non-stationary signal, the current signal processing methods include Short-time Fourier Transform (STFT) [10, 11] , Wavelet Transform (WT) [12] [13] [14] [15] and Empirical Mode Decomposition (EMD) [16] [17] [18] etc. STFT is performed by selecting a window function, and assuming non-stationary signal to be stationary in the window. However, it requires that the analyzed signals in a short time interval. Essentially, it is still a smooth signal processing method, and the resolution is not high. WT is a multiscale signal analysis method based on STFT, which the width of the window function in the time axis translation process can be scalable. However, the selection of wavelet basis is hard to determine considering that the analyzed signals are presented with different characteristics. Moreover, after selecting the wavelet basis, the wavelet basis will remain unchanged during the processing, which lacks adaptability. Faced the above mentioned drawbacks, EMD has better performance. Huang et al. proposed a new signal analysis method to handle the non-linear and non-stationary problems, namely EMD. EMD can adaptively decompose a complex signal into a finite number of intrinsic mode functions (IMFs). Each IMF represents a set of characteristic scale signals. Furthermore, the energy which is extracted from each component can better reveal the inherent characteristics of fault information. However, this method can produce the problems of mode aliasing and uncertain order of the decomposition, which is harmful for feature extraction and different fault classification. To overcome the problem of mode mixing in EMD, Wu et al. [19, 20] proposed a noise assisted analysis method applied to the empirical mode decomposition namely ensemble empirical mode decomposition(EEMD), which can self-adaptively decompose a complicated signal into IMFs based on the local characteristic timescale of the signal. EEMD has two parameters to be set, which are the ensemble number m and the amplitude of the added white noise. However, this method produces more useless components. Cicone et al. [21, 22] presented a new adaptive time-frequency analysis method, namely adaptive local iterative filtering method(ALIF), which can be used to deal with nonlinear and non-stationary signals. ALIF is an adaptive decomposition method based on iterative filtering (IF). The difference between the two methods is that ALIF realizes adaptive decomposition of signals by choosing the length of the filters adaptively. ALIF can avoid the modal aliasing effectively and decompose the signals with same size and order. According to matrix analysis theory, the singular value is the inherent characteristic of the matrix, which has a good stability [23, 24] . When there is a small change in matrix element, the singular value of the matrix changes a little [25, 26] . Moreover, the singular value of the matrix has the scale and rotation invariance. Accordingly, the singular value of the matrix satisfies the requirements of the stability, rotation and scale invariance in feature extraction of pattern recognition, which can effectively describe the characteristics of the initial feature vector matrix. Since the influence of above non-linear factors and the complexity of the signal components, the faults of gear and rolling bearing parts are abnormal or different in the running process. The vibration signals obtained from the mechanical system will also change with the varied time, thus producing different energy signals. For gear and rolling bearing parts, different fault types always correspond to different degrees of vibration and complexity, which will lead to different energy values. Consequently, energy values can be used to classify different types of gear and rolling bearing faults. Thus, a novel fault classification method jointed adaptive local iterative filtering and singular value decomposition is proposed in this paper. Firstly, the vibration signal was decomposed into several components by ALIF, which was used to build an initial eigenvector matrix. Then, the singular value decomposition (SVD) was employed to decompose the initial feature vector to obtain the singular value, whose energy is selected as a criterion to identify various faults. This paper was organized as follows: the basic principle and characteristics of the proposed fault classification method based on the singular value energy spectrum and adaptive local