The feature extraction of wheelset-bearing fault is important for the safety service of high-speed train. In recent years, sparse representation is gradually applied to the fault diagnosis of wheelset-bearing. However, it is difficult for traditional sparse representation to extract fault features ideally when some strong interference components are imposed on the signal. Therefore, this paper proposes a novel feature extraction method of wheelset-bearing fault based on the wavelet sparse representation with adaptive local iterative filtering. In this method, the adaptive local iterative filtering reduces the impact of interference components effectively and contributes to the extraction of sparse impulses. The wavelet sparse representation, which adopts L1-regularized optimization for a globally optimal solution in sparse coding, extracts intrinsic features of fault in the wavelet domain. To validate the effectiveness of this proposed method, both simulated signals and experimental signals are analyzed. The results show that the fault features of wheelset-bearing are sufficiently extracted by the proposed method.

As the core system of high-speed trains, the bogie frame plays an extremely crucial role in the operation process. Among the components of the bogie frame, wheelset-bearing is the core component for the connection between the wheelset and the frame. When a high-speed train operates on a rail, the wheelset-bearing plays an important role in the power transmission. Compared with the other common bearings on the static mechanical equipment, the service conditions of the wheelset-bearing are quite different. The wheelset-bearing bears not only the static pressure of high-speed train but also the unstable dynamic load caused by the radial acceleration during operating time. A higher speed naturally causes a greater vibration and dynamic force to the wheelset-bearing. In addition, the wheelset-bearing will bear a large axial force when the train passes through a curve.

When a high-speed train operates on a rail, various operation characteristics could cause the wheelset-bearing fault. Since the distance between adjacent stations is usually not long for high-speed train, the acceleration and the braking of high-speed train occur frequently. This causes the dynamic load range of the wheelset-bearing to change greatly and frequently. In addition, due to the effect of overwhelming impact from track-vehicle system, which is caused by the polygonal wear of wheels, track irregularities, and irregular turnout, various faults (such as peeling, flaw) might appear on the wheelset-bearing. Once these faults appear under the condition of high-speed rotation, the service conditions of wheelset-bearing will deteriorate rapidly, which will eventually affect the safety of high-speed train. Therefore, it is of great significance to detect wheelset-bearing fault [

In general, when the bearing fault occurs, the periodical impulses are generated. Therefore, the vibration signals are collected to determine whether the fault exists on the bearing. During the operation of high-speed train, the defect inevitably appears on the wheel-tread. Compared with the traditional bearing, the energy of the rotation frequency for wheelset, generated by the defect on the wheel-tread, is larger because of the interaction between wheel-tread and rail. Therefore, the vibration information of both rotation frequency and harmonics for wheelset is also evidently contained in the collected vibration signals, which makes the frequency components contained in the vibration signals more complex [

As for the fault detection in a general bearing, many fault diagnosis methods, including empirical model decomposition and its variants [

In the traditional sparse representation, the power levels of different features will affect the results extracted by the sparse representation [

When sparse representation is solely applied in time domain, it will lead to the inadequate feature extraction. This indicates that the acquired fault features cannot be extracted thoroughly. The wavelet domain is another scale representation of signal [

To diagnose wheelset-bearing fault more effectively, a novel feature extraction method, namely, ALIF-SBAKW, based on the wavelet sparse representation (Split Bregman for sparse coding and approximate K-SVD for dictionary learning) with the adaptive local iterative filtering (ALIF), is proposed in this paper. The paper is organized as follows. Section

According to the sparsity of fault impulses, the observed signals can be represented sparsely by combining the dictionary with the sparse coefficient, as shown in

It can be observed that (

To solve this kind of optimization problem, a penalty factor

In fact, the length of signal, i.e.,

The signal is segmented into a series of truncated-signals with a certain overlap.

To solve the objective optimization problem in (

In order to better extract the intrinsic features of signals, the wavelet decomposition can be adopted in sparse representation. As for a one-dimensional signal, there are mainly two forms of coefficients after wavelet decomposition: approximation coefficients (CAs) and detail coefficients (CDs). The CAs contain the main information of the original signal. On the contrary, the CDs contain the subordinate components of the original signal. The wavelet decomposition of the signal is given in Figure

The wavelet decomposition of signal.

The fault features of bearing are mainly hidden in the CAs after the wavelet decomposition of signal. Accordingly, they can be called impulse wavelet coefficients (IWCs). In addition, the CDs mainly contain the noise component of signal. According to the performance of wavelet decomposition, the sparse representation can be accomplished by the obtained IWCs. The objective function can be transformed into

At the beginning of wavelet sparse representation,

Split Bregman (SB) iteration is one of the effective methods of L1-regularized optimization. Due to its ability to solve a very wide class of L1-regularized problems by using alternating iteration, SB has been widely used in the field of image processing [

In (

When solving (

In addition,

After the sparse coefficient matrix

This problem can be solved directly by SVD decomposition (i.e.,

Based on the K-SVD, approximate K-SVD (AK-SVD) is introduced to improve the dictionary by iteration and reduce the computational burden simultaneously [

In order to reduce the impact of the nonstationary and the wheelset’s rotation frequency components, adaptive local iterative filtering (ALIF) is used to process signals. ALIF is a novel time-frequency analysis algorithm, which is inspired by EMD [

The algorithm of ALIF.

In this algorithm, the operator

The ALIF performs much better when processing the separation of the aforementioned two components. ALIF follows the iterative framework of the EMD algorithm. The moving average in ALIF is the convolution between the signal and the low pass filter. The low pass filter, constructed by the solution of FP equation, is compactly supported and is tending to zero smoothly at both ends, which ensures the nonexistence of artificial oscillations. In addition, the length

As presented in Section

A novel feature extraction method of wheelset-bearing fault, ALIF-SBAKW, is proposed in this paper. The flowchart of ALIF-SBAKW is shown in Figure

Step 1: the collected vibration signal is decomposed into a series of IMFs by ALIF. The impulse-IMF containing the impulses with noise can be selected from the IMFs.

Step 2: the IWCs can be obtained by the wavelet decomposition of impulse-IMF. Generally, the number of decomposed levels can be set to 1 or 2 for the signal with a short length. The noise level

Step 3: sparse representation can be applied to the given

Step 4: in order to achieve the purposes of strengthening the IWCs and enhancing the impulse response in the original signal, the convolution between the IWCs and a typical impulse is applied. The extracted impulses of the vibration signal can be reconstructed by the wavelet reconstruction with convolutional IWCs and zero-setting CDs.

The flowchart of ALIF-SBAKW.

In order to illustrate and verify the effect of the proposed ALIF-SBAKW, a simulation validation is designed in this section. As the analysis in Section

Parameters of signal

4 | 46 | 800 | 1800 |

The simulated signal: (a) impulse components

The simulated

When the sampling frequency and sampling time are set to 10000 Hz and 1 s, respectively, a simulated signal

In order to obtain a good performance of fault extraction in ALIF-SBAKW, the selection of suitable adjusted gain

It should be noted that, except the adjusted gain

According to the flowchart of ALIF-SBAKW, a series of crucial calculated parameters are given. The threshold

The decomposed IMFs using the ALIF: (a–e) IMF1–IMF5.

The simulated results using the ALIF-SBAKW method: (a) extracted signal and (b) Hilbert envelope spectrum of signal in (a).

In order to further illustrate the advancement of proposed method, two comparative methods are applied to analyze the same simulated signal. Firstly, wavelet sparse representation, i.e., SBAKW, is used to process the simulated signal directly. The adjusted gain

The simulated results using the SBAKW: (a) extracted signal and (b) Hilbert envelope spectrum of signal in (a).

The simulated results using ALIF-OMPK with target sparsity: (a) extracted signal and (b) Hilbert envelope spectrum of signal in (a).

The simulated results using ALIF-OMPK with error goal: (a) extracted signal and (b) Hilbert envelope spectrum of signal in (a).

Making a comparison between SBAKW and ALIF-SBAKW, features of interferences are extracted by using SBAKW in Figure

The results extracted by ALIF-OMPK under two different iteration stopping criteria can also identify the information of fault characteristic, as shown in Figures

In order to further validate the effect of the proposed ALIF-SBAKW, the experimental data of wheelset-bearing fault has been obtained through the testing rig shown in Figure

Experimental device: (a) testing rig, (b) accelerometer, (c) outer-race fault, and (d) roller fault.

Parameters of testing bearing.

26.9 | 180 | 19 | 0.1571 |

In this section, the proposed ALIF-SBAKW method is used to analyze the collected vibration signal. In order to further validate the effect of proposed ALIF-SBAKW and highlight its superiority, four different comparative methods, namely, SBAKW, ALIF-OMPK (using target sparsity), EWT, and fast kurtogram [

In the experiment of outer-race fault, the collected signal is shown in Figure

The collected outer-race fault signal and its Hilbert envelope spectrum: (a) time-domain waveform and (b) Hilbert envelope spectrum of signal in (a).

The proposed ALIF-SBAKW method is used to analyze the collected signal in Figure

Results obtained by the proposed ALIF-SBAKW: (a–d) IMF1-IMF4, (e) extracted signal, and (f) Hilbert envelope spectrum of signal in (e).

In order to further validate the effect of proposed ALIF-SBAKW, four comparative methods are conducted. In SBAKW, the adjusted gain

Results obtained by SBAKW: (a) extracted signal and (b) Hilbert envelope spectrum of signal in (a).

Results obtained by ALIF-OMPK: (a) extracted signal and (b) Hilbert envelope spectrum of signal in (a).

Results obtained by EWT: (a) detected boundaries of Fourier spectrum, (b) the 13th subband signal, and (c) Hilbert envelope spectrum of signal in (b).

Results obtained by fast kurtogram: (a) kurtogram, (b) extracted signal, and (c) Hilbert envelope spectrum of signal in (b).

Making comparison between SBAKW and ALIF-SBAKW, although some kinds of vibration features can be extracted by using SBAKW, they mainly derive from the energy of power-line interference. The characteristic frequency of power-line interference

In the roller fault experiment, the collected signal is shown in Figure

The collected roller fault signal and its Hilbert envelope spectrum: (a) time-domain waveform and (b) Hilbert envelope spectrum of signal in (a).

The collected signal is firstly processed by the proposed ALIF-SBAKW method. Similarly, the adjusted gain

Results obtained by the proposed ALIF-SBAKW: (a–d) IMF1-IMF4, (e) extracted impulses, and (f) Hilbert envelope spectrum of signal in (e).

Similarly, four comparative methods are used to process the collected signal. In SBAKW, the adjusted gain

Results obtained by SBAKW: (a) extracted signal and (b) Hilbert envelope spectrum of signal in (a).

Results obtained by ALIF-OMPK: (a) extracted signal and (b) Hilbert envelope spectrum of signal in (a).

Results obtained by EWT: (a) detected boundaries of Fourier spectrum, (b) the 17th subband signal, and (c) Hilbert envelope spectrum of signal in (b).

Results obtained by fast kurtogram: (a) kurtogram, (b) extracted signal, and (c) Hilbert envelope spectrum of signal in (b).

The reason why the double fault characteristic frequency

According to the comparison in Hilbert envelope spectrum, it can be observed from Figures

Comparison among the three methods.

Indicator | Method | ||
---|---|---|---|

ALIF-SBAKW | ALIF-OMPK | Fast kurtogram | |

Number of harmonics | 8 | 5 | |

CF | 11.08 | 5.62 | |

IF | 17.29 | 7.58 | |

Kurtosis | 20.44 | 5.57 | |

ESK | 20.00 | 19.88 |

Theoretically, when the values of CF, IF, and kurtosis are higher, the features of impulses extracted in time domain are relatively stronger. In addition, the ESK mainly reflects the richness of fault information in Hilbert envelope spectrum. As shown in Table

The fault diagnosis of wheelset-bearing has great significance to the safety of high-speed train. Sparse representation is an advanced method for bearing fault extraction. However, it is hard for the traditional sparse representation to conduct fault extraction under severe service conditions, especially under the complicated track-vehicle system. If the energy of interference is stronger than the energy of fault features, the interference component, instead of the fault features, will be detected and extracted. Therefore, the ALIF-SBAKW is proposed in this paper. There are two reasons why this new method can solve this problem. On the one hand, the ALIF can effectively reduce or eliminate the nonstationary and the wheelset’s rotation frequency components (caused by severe service conditions of the high-speed train), which is conducive to realizing fault extraction. On the other hand, the wavelet sparse representation can deeply find the intrinsic features of signal and extract the wheelset-bearing fault. The ALIF-SBAKW method is validated by simulated and experimental signals. The results show that the ALIF-SBAKW method is extraordinarily suitable for the fault feature extraction of wheelset-bearing signals, especially compared with SBAKW, ALIF-OMPK, EWT, and fast kurtogram in experimental validation. To some extent, this novel method can effectively complete the fault diagnosis of wheelset-bearing.

Finally, although the ALIF-SBAKW method can effectively extract the fault feature, this method cannot be effectively applied to the separation of multiple faults now. Therefore, further research should be made to solve the considered problems. In addition, the fault extraction method, proposed by Qin et al. in [

The derivation process of simplification from (

Then, both of the above equations can be replaced by

The experimental data are based on the CRRC project and are confidential.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (no. 51905453) and the China Postdoctoral Science Foundation (no. 2019M663899XB).