Research of multi-concurrent fault diagnosis of rotating machinery based on VMD and KICA

2.1. The proposed method

In this paper, a fault diagnosis method of rotating machinery based on VMD-based KICA is proposed. The procedure of the proposed method has been summarized in Fig. 1. The detailed procedure is described as follows:

Step 1: The collected single-channel signal $\mathbf{X}\left(t\right)$ is decomposed with VMD and each VM can be obtained.

Step 2: Calculate the correlation coefficient of each VM to $\mathbf{X}\left(t\right)$. Then, choose high correlation VMs to form a new observation signal.

Step 3: Use KICA to extract the fault signals from the new observation signal.

Fig. 1The summarized procedure of the proposed method

2.2. Evaluation index $\mathbf{\rho }$

The fault signal extracted from the real signal generally contains some noise. In the power spectrum of the extracted fault signal, the power of the fault frequency is usually the highest, and other frequencies can be considered as noise. If the power of the noise is very close to or even higher than the power of the fault frequency, the fault type cannot be accurately determined. Therefore, in order to compare the extraction effect of each fault diagnosis method, this paper proposes an evaluation index $\rho$:

where $P_f$ is the power of fault frequency, $P_s$ is the power of secondary high frequency. Therefore, the bigger the value of $\rho$, the better the effect of the extraction.

3.1. Fault of inner ring and outer ring of rolling bearing mixed

The experimental device is shown in Fig. 2. The whole device is driven by a 550 W (220 V-50 Hz) AC motor and drives the shaft system with couplings. The shaft section between two bearing seats is equipped with a belt wheel, and the belt drives the active gear shaft of gear box. There are two rolling bearings on the shaft system. The inner and outer rings of the rolling bearing are respectively machined with tiny pitting pits of 0.3 mm in depth and 0.5 mm in diameter to simulate the fault of inner ring and outer ring. One acceleration transducer is installed vertically on the shell near the rolling bearing. The sampling frequency $f_s=$ 8192 Hz and sampling point number is 8192. The motor speed is 850 rpm, that is, the rotation frequency $f_r=$ 14.2 Hz.

The equation of fault frequency of inner ring is:

The equation of fault frequency of outer ring is:

where $N$ is the number of roller, $d$ is the diameter of roller, $D$ is the pitch diameter of bearing, and $\alpha$ is bearing contact angle. According to Eq. (2) and Eq. (3), $f_{ic}=$ 106 Hz and $f_{oc}=$ 70 Hz.

Fig. 2The experimental device

3.1.1. EEMD + FastICA

In this method, the mixed signal $x$ is decomposed by EEMD first and each intrinsic mode function (IMF) can be obtained. Then, calculate the correlation coefficient of each IMF to $x$. IMFs with high correlation coefficient were selected to reconstruct the new observation signal. Finally, the fault signals can be extracted by FastICA. The power spectrum of the extracted fault signals is shown in Fig. 3.

Fig. 3The power spectrum of the extracted fault signals based on EEMD + FastICA

a)

b)

The frequency of 70 Hz can be seen in Fig. 3(a), and the frequency of 106 Hz can be seen in Fig. 3(b). According to Eq. (1), ${\rho }_{oc}=$ 0.426, ${\rho }_{ic}=$ 0.112. However, in Fig. 3(b), the amplitude of the frequency of 70 Hz is very large. Mode mixing has a great impact on fault diagnosis.

3.1.2. The proposed method

In this method, the mixed signal $x$ is decomposed by VMD first and each VM can be obtained. Then, calculate the correlation coefficient of each VM to $x$. VMs with high correlation coefficient were selected to reconstruct the new observed signal. Finally, the fault signals can be extracted by KICA. The power spectrum of the extracted fault signals is shown in Fig. 4.

The frequency of 70 Hz can be seen in Fig. 4(a), and the frequency of 106 Hz can be seen in Fig. 4(b). According to Eq. (1), ${\rho }_{oc}=$ 0.922, ${\rho }_{ic}=$ 1.319.

Fig. 4The power spectrum of the extracted fault signals based on VMD+KICA

The evaluation index of two methods are in Table 1. The $\rho$ of the proposed method is much bigger than EEMD + FastICA. Therefore, the proposed method has a better effect of extraction. The result proves that the proposed method is efficient to extract the features of single-channel signal with multi-concurrent faults.

Table 1Evaluation index statistics

	${\rho }_{oc}$	${\rho }_{ic}$
EEMD + FastICA	0.426	0.112
The proposed method	0.922	1.319

3.2. Fault of outer ring of rolling bearing and gear breaking mixed

In order to verify the effectiveness of fault diagnosis with two components of rotating machinery, the fault of outer ring of rolling bearing and gear breaking are applied here. The sampling frequency $f_s=$ 8192 Hz and sampling point number is 8192. The motor speed is 850 rpm, that is, the rotation frequency $f_r=$ 14.2 Hz. The number of gear teeth $Z=$ 20. The number of the broken tooth $Z_b=$ 1. According to $f_c=Z\times f_r$, the gear mesh frequency $f_c=$ 283.3 Hz. When the gear is affected by broken tooth fault, the rotation frequency $f_r$ and its frequency multiplication will be the main features in frequency-domain, and the frequency $f_z=Z_b\times f_c$ will also exist.

Fig. 5The power spectrum of the extracted fault signals based on VMD + KICA

a)

b)

In the proposed method, the mixed signal $x$ is decomposed by VMD first and each VM can be obtained. Then, calculate the correlation coefficient of each VM to $x$. VMs with high correlation coefficient were selected to reconstruct the new observed signal. Finally, the fault signals can be extracted by KICA. The power spectrum of the extracted fault signals is shown in Fig. 5.

As can be seen from Fig. 5, Fig. 5(a) is the fault signal of outer ring of rolling bearing. Fig. 5(b) is the fault signal of gear breaking. Furthermore, the fault features are significantly obvious. It demonstrates that the proposed method has a good performance of fault diagnosis with the fault of outer ring of rolling bearing and gear breaking mixed.