State assessment for bearing rotor static unbalance based on Welch-PSD and SAE

2.1. Feature extraction based on Welch-PSD

(1) Welch power spectral density estimate (Welch-PSD).

The Welch-PSD method is a power spectral density estimate method based on the revision of the Periodogram-PSD method and the Bartlett-PSD method. The Welch-PSD method allows the data segments to partially overlap, and the data window of each segment may not be rectangular, to improve the spectral distortion caused by rectangular window. Each segments power spectral density can be expressed as:

where $U=\frac{1}{M}\sum _{n=0}^{M-1}{d}_2^2\left(n\right)$ is a normalization factor, ensuring that the spectra is asymptotically unbiased estimates. $d_2\left(n\right)$ is a window function. By averaging the period graph of $L$ segment, we can obtain the power spectrum estimation of the whole signal $x_N\left(n\right)$:

(2) Feature extraction for bearing rotor static unbalance.

In the condition of unbalance fault of bearing rotor, the frequency spectrum of vibration signal is dominated by the bearing working frequency. Due to the nonlinear relationship, some harmonic components are involved. The unbalance vibration feature of the bearing rotor is the power value of the bearing rotating frequency in the vibration signal power spectrum, that is:

2.2. State assessment based on SAE

An auto-encoder neural network is an unsupervised learning algorithm, which includes an encoder and a decoder. As shown in Fig. 1, the input data is first encoded by $W_1$, the original $d$-dimensional input $x$ is mapped to the $k$-dimensional hidden layer $h$, and then $W_2$ is decoded to map $h$ back to the $d$ dimensional vector as close as possible to the original input of the encoder. Auto-encoder is a deep structure when the number of hidden layers of the auto-encoder is greater than 1. The output of the previous layer of the encoder (the middle hidden layer) is used as the input of the subsequent layer. Coding part overlay. That is, stacked automatic encoder.

In this paper, the SAE network is fine-tuned. The bearing rotor unbalance state label is added at the top of the neural network, and the unsupervised features are adjusted by a supervised method. The state assessment network is shown in Fig. 2. After the SAE model is trained, the model is fine-tuned using the unbalance state label to obtain the bearing vibration feature-rotor unbalance state neural network.

Fig. 1Basic structure of auto-encoder neural network

Fig. 2Basic Stacked structure of auto-encoder neural network

3.1. Data description

This paper uses data acquisition from the Machinery Fault Simulator (MFS) test-bed designed by Spectra Quest. In this experiment, 8 kinds of rotor unbalance failure experiments and a normal experiment were designed, and the fault injection position and bearing vibration signal collection position are shown in Fig. 3. Two fault injection holes are distributed on the rotor of the MFS test-bed at intervals of 20° to inject different degrees of unbalanced faults into the bearing rotor. This experiment changed the unbalance of the rotor by changing the angle position between the two counterweight screws. The fault injection position distribution and fault degree are shown in Table 1. The working frequency of the experimental bearing is 30 Hz, and the sampling frequency is 40000 Hz. Each state (8 fault states and 1 normal state) acquires a 4 s vibration signal.

Fig. 3Machinery fault simulator

3.2. Feature extraction of vibration signals

First of all, the original vibration signal is preprocessed, the noise in the original vibration signal is removed by wavelet packet to obtain bearing vibration information. Then, using the Welch-PSD method, the power spectrum density of the vibration signal can be obtained. The power value corresponding to the working frequency of the bearing is taken as the feature of the bearing vibration signal. The bearing vibration signal feature clustering of 9 states is shown in Fig. 4.

Table 1Rotor unbalance position and fault degree

Fault position
Unbalance (g·mm)	0	94.7	183.6	268.5	345.1
Fault position					–
Unbalance (g·mm)	411.3	465.0	504.5	528.7	–

3.3. State assessment based on SAE

The SAE neural network is trained to obtain the assessment model. The SAE neural network is first trained using normal state feature data and maximum fault degree state feature data. The health of normal working state is defined as 1. The maximum degree state of rotor unbalance is defined as the failure state, and the health is 0. The health is used as the training data label to fine tune the SAE neural network to obtain the rotor unbalance state assessment model. The SAE neural network training parameters are shown in Table 2.

The assessment model is used to assess the test data. The bearing vibration feature data are spliced from low to high according to rotor unbalance as the test data, which is composed to test the accuracy of the assessment model. The assessment results of the rotor unbalance using the assessment model for the test data are shown in Fig. 5. The experimental results show that the SAE neural network can accurately assess rotor unbalance faults in different degrees.

Fig. 4Clustering result of the fault features

Fig. 5Assessment result of the testing data