# US 12,222,259 B1 · Rolling bearing fault diagnosis method based on fast fourier transform coding and lightweight convolutional neural network

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- Number: US 12,222,259 B1
- Document ID: US12222259B1
- Status: Granted
- Kind: B1
- Application number: 18/898,744
- Filed: 2024-09-27
- Granted: 2025-02-11
- Earliest claimed: 2023-11-10
- Assignees: Guangdong University of Petrochemical Technology
- Applicants: Guangdong University of Petrochemical Technology
- Inventors: Mei Liu; Kun Cui; Huizi Han; Shijie Liu
- Web page: https://patentgrep.com/patent/US12222259B1

## CPC

- G01M 13/045: Acoustic or vibration analysis
- G06N 3/045: Combinations of networks
- G06N 3/0464: Convolutional networks [CNN, ConvNet]
- Y02T 90/00: Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
- G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- Y02T: CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION

## Abstract

Provided is a rolling bearing fault diagnosis method based on FFT coding and L-CNN, including: obtaining original bearing fault vibration data, extracting intrinsic mode components of different frequency bands in the original bearing fault vibration data, calculating a permutation entropy value corresponding to each of the intrinsic mode components, and performing wavelet threshold denoising according to the permutation entropy value to obtain a denoised reconstructed time domain signal; performing fast Fourier transform to the denoised reconstructed time domain signal to obtain a frequency domain signal and a phase angle corresponding to the time domain signal, reconstructing the frequency domain signal according to a preset rule, retaining frequency domain data of features of the phase angle, and drawing FFT-x heat maps of different fault type data according to an amplitude range; and constructing an model L-CNN, and inputting coded data into the L-CNN model, and obtaining fault diagnosis results.

## Claims

### Claim 1

A rolling bearing fault diagnosis method based on FFT coding and L-CNN, comprising:
obtaining original bearing fault vibration data, extracting intrinsic mode components of different frequency bands in the original bearing fault vibration data, calculating a permutation entropy value corresponding to each of the intrinsic mode components, and performing wavelet threshold denoising according to the permutation entropy value to obtain a denoised reconstructed time domain signal;
performing fast Fourier transform to the denoised reconstructed time domain signal to obtain a frequency domain signal and a phase angle corresponding to the time domain signal, reconstructing the frequency domain signal according to a preset rule, retaining frequency domain data of features of the phase angle, and drawing FFT-x heat maps of different fault type data according to an amplitude range; wherein
the drawing FFT-x heat maps of different fault type data comprises:
decomposing the denoised reconstructed time domain signal into several single harmonic components by fast Fourier transform, and obtaining a relationship between amplitude, phase, power and frequency domain of each harmonic of the signal; and
when the phase angle is in a first quadrant and a second quadrant, a frequency domain value is positive, and when the phase angle is in a third quadrant and a fourth quadrant, a frequency domain value is negative; and according to this characteristic, reconstructing the frequency domain signal, and according to an amplitude characteristic of a reconstructed frequency domain signal, setting a boundary to (−150, 150) for heat map coding; and
constructing an improved lightweight convolutional neural network model L-CNN, and inputting coded data in the FFT-x heat maps into the L-CNN model for processing and diagnosis, and obtaining fault diagnosis results;
the inputting coded data in the FFT-x heat maps into the L-CNN model for processing and diagnosis, comprising:
capturing different levels of features of the coded data in the FFT-x from different scales by using convolution kernels with different sizes, and weighting captured features for importance of each channel by structures of global average pooling, one-dimensional convolution, channel multiplication and spatial replication through an ECA attention mechanism; and
processing a channel dimension and a spatial dimension of a color feature of an input FFT-x coded map by depth separable convolution to obtain a feature map; exchanging a channel sequence of the feature map between different depths and different groups by using a ChannelSplit module and a Channelshuffle module, and changing a channel arrangement mode; further extracting data features based on the residual and depth separable convolution; and finally, outputting the fault diagnosis results through average pooling and two fully connected layers.

### Claim 2 (depends on 1)

The rolling bearing fault diagnosis method based on FFT coding and L-CNN according to claim 1, wherein the extracting intrinsic mode components of different frequency bands in the original bearing fault vibration data comprises:
S1.1, adding Gaussian white noises with normal distribution to the original bearing fault vibration data to obtain an i-th signal yi(t), and decomposing the i-th signal yi(t) by EMD to obtain a first intrinsic mode function IMF1(t) and a residual component r1(t) of yi(t);
S1.2, using the residual component r1(t) as original data to decompose reconstructed r1(t)+β1E1(ωi(t) to obtain an intrinsic mode function IMF2(t) and a residual component r2(t), wherein E1 is EMD decomposition, β1 is a standard deviation of the Gaussian white noises, and ωi(t) is a Gaussian white noise; and
S1.3, repeating the S1.2 to obtain a (k+1)-th intrinsic mode function IMFk+1(t) and a k-th residual component rk(t).

### Claim 3 (depends on 2)

The rolling bearing fault diagnosis method based on FFT coding and L-CNN according to claim 2, wherein performing wavelet threshold denoising according to the permutation entropy value comprises:
judging a noisy level of the each of the intrinsic mode components according to the permutation entropy value, and dividing the each of the intrinsic mode components into an effective IMF and a noisy IMF according to the noisy level;
based on data features of the noisy IMF, selecting wavelet bases and decomposition layers to decompose noisy bearing fault vibration data, and calculating wavelet coefficients and selecting a Sqtwolog threshold to calculate a threshold corresponding to each of the wavelet coefficients, and quantizing the wavelet coefficients; and
performing inverse wavelet transform to quantized wavelet coefficients to obtain a denoised IMF, and then reconstructing a bearing vibration signal from the effective IMF and the denoised IMF to obtain the denoised reconstructed signal.

### Claim 4 (depends on 3)

The rolling bearing fault diagnosis method based on FFT coding and L-CNN according to claim 3, wherein a method for calculating the wavelet coefficients is:
I
CWT
(
a
,
b
)
=
1
a
⁢
∫
x
⁡
(
t
)
⁢
ϕ
⁡
(
t
-
b
a
)
⁢
dt
wherein ICWT is a wavelet coefficient, a is a scale function, b is a position function, and t is a delay time;
a method for calculating a threshold corresponding to each of the wavelet coefficients is:
th
=
mid
0.6745
⁢
2
⁢
ln
⁢
N
wherein th is the threshold corresponding to the each of the wavelet coefficients, mid is a middle value of each decomposed band coefficient, and N is a length of the wavelet coefficient.

### Claim 5 (depends on 1)

The rolling bearing fault diagnosis method based on FFT coding and L-CNN according to claim 1, wherein an expression of the reconstructed frequency domain signal is:
F
⁡
(
x
)
=
{
f
⁡
(
x
)
θ
>
0
-
f
⁡
(
x
)
θ
<
0
wherein F(x) is the reconstructed frequency domain signal, f(x) is an original bearing frequency domain signal, and θ is the phase angle.

### Claim 6 (depends on 1)

The rolling bearing fault diagnosis method based on FFT coding and L-CNN according to claim 1, wherein an objective function of the improved lightweight convolutional neural network model is evaluated as a cross entropy loss function:
Loss
=
-
∑
i
=
1
output
size
y
i
·
log
⁢
y
^
i
wherein Loss is a model loss value, yi is a model fault classification prediction value, and ŷi is a model classification true value.