# US 2024/0201048 A1 · Generalized autocorrelation method for bearing fault feature extraction under variable rotational speed condition

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- Number: US 2024/0201048 A1
- Document ID: US20240201048A1
- Status: Published application
- Kind: A1
- Application number: 17/789,523
- Filed: 2022-02-10
- Published: 2024-06-20
- Earliest claimed: 2021-08-10
- Assignees: Jiangsu University
- Applicants: Jiangsu University
- Inventors: Wei FAN; Yingqi XU; Zhenqiang CHEN; Yujie SHEN; Long CHEN
- Web page: https://patentgrep.com/patent/US20240201048A1

## CPC

- G01M 13/045: Acoustic or vibration analysis
- G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR

## Abstract

A generalized autocorrelation method for bearing fault feature extraction under a variable rotational speed condition includes: resampling an original vibration signal in an order domain based on instantaneous phase information by using an order tracking processing method, to greatly weaken a frequency modulation phenomenon; further weakening background noise in consideration of a correlation between a plurality of adjacent fragments by using a generalized autocorrelation method; and controlling an accumulation of periodic disturbances by considering only a correlation between several adjacent signal fragments based on that conventional noise resistant correlation (NRC) methods consider a correlation between all signal fragments and cannot eliminate influence of accumulated periodic disturbances. Compared with the conventional methods, this method overcomes the difficulties caused by mutually restricting signal features, and achieves a better effect.

## Claims

### Claim 1

A generalized autocorrelation method for a bearing fault feature extraction under a variable rotational speed condition, comprising the following steps:
step S1, fusing an unknown fault signal (t) and a strong white Gaussian noise signal ε(t) to obtain a measured order tracking signal (t), wherein the measured order tracking signal (t)=(t)+ε(t). t represents an order domain, the strong white Gaussian noise signal ε(t)˜(0, σ2), a time series =[(1), (2), . . . , (L)]T represents an implementation of a cyclic signal (t), and L represents a total number of samples;
step S2, truncating the measured order tracking signal (t), and when L=mN, dividing into {1, 2, . . . m}, wherein i=[(i−1)N+1), . . . , (iN)]T, i=1, . . . , m, m represents a number of signal fragments, and N represents a length of each of the signal fragments and is an independent variable in a function;
step S3, proposing a generalized autocorrelation function based on an original autocorrelation function,
𝒴
(
N
)
=
1
m
-
n
+
1
⁢
∑
k
=
0
m
-
n
𝒴
k
(
N
)
,
wherein k(N) is a noise resistant correlation function:
𝒴
k
(
N
)
=
1
n
⁡
(
n
-
1
)
⁢
N
⁢
∑
1
≤
i
≠
j
≤
n
⁢
(
𝒴
k
+
i
k
)
T
⁢
𝒴
k
+
j
k
,
wherein n is selected manually, satisfies 2≤n≤m, and represents a number of block signals, and k+ik and k+jk represent discrete vector representations of a (k+i)th signal fragment and a (k+j)th signal fragment, respectively;
step S4, when L=Mn+N1 and N1>0, dividing into {1,1, 1,2, 2,1, 2,2 , . . . , m,1, m,2, m+1,1}, wherein i=1, . . . , m, N represents a length of each of the signal fragments and is an independent variable in the function,
{
𝒴
i
,
1
=
[
𝒴
(
(
i
-
1
)
⁢
N
+
1
,
…
,
𝒴
(
(
(
i
-
1
)
)
⁢
N
+
N
1
]
T
𝒴
i
,
2
=
[
𝒴
⁡
(
(
i
-
1
)
⁢
N
+
N
1
+
1
)
,
…
,
𝒴
⁡
(
iN
)
]
T
;
step S5, synthesizing {1,j, 2,j, . . . , mi,j)} to form a new signal j, wherein j=1,2, m1=m+1, m2=m, and
{
𝓇
1
=
[
𝒴
1
,
1
T
,
𝒴
2
,
1
T
,
…
⁢
𝒴
m
⁢
1
,
1
T
]
T
𝓇
2
=
[
𝒴
1
,
2
T
,
𝒴
2
,
2
T
,
…
,
𝒴
m
⁢
2
,
2
T
]
T
;
proposing a generalized autocorrelation function (N)=1(N1)+2(N2), wherein 1 and 2 are respectively weights of autocorrelation functions (N1) and (N2) of signals 1 and 2, and 1+2=1;
step S6, for the signal of the length L≥2N, if n=2, (N)=(N), the generalized autocorrelation function being an autocorrelation function, and
𝒜
⁡
(
N
)
=
𝒴
m
,
1
T
⁢
𝒴
m
+
1
,
1
+
∑
i
=
1
m
-
1
⁢
𝒴
i
T
⁢
𝒴
i
+
1
L
-
N
=
1
L
-
N
⁢
∑
i
=
1
L
-
N
⁢
𝒴
⁡
(
i
)
⁢
𝒴
⁡
(
i
+
N
)
=
ℛ
⁡
(
N
)
;
and
step S7, for the signal of the length L≥2N, an expectation of the generalized autocorrelation function being not greater than an average power of an original signal (t), i.e., E[(N)]≤,
𝒫
𝓍
=
1
n
⁡
(
L
-
(
N
-
1
)
⁢
N
)
⁢
∑
i
=
0
n
-
1
⁢
∑
j
=
1
L
-
(
N
-
1
)
⁢
N
⁢
x
⁡
(
iN
+
j
)
2
,
E
[
𝒜
⁡
(
N
)
]
=
E
[
𝓌
1
⁢
𝒜
𝓇
1
(
N
1
)
+
𝓌
2
⁢
𝒜
𝓇
2
(
N
2
)
]
≤
∑
i
=
1
n
⁢
(
∑
k
=
0
m
1
-
n
⁢
x
k
+
i
,
1
T
⁢
x
k
+
i
,
1
+
∑
k
=
0
m
2
-
n
⁢
x
k
+
i
,
2
T
⁢
x
k
+
i
,
2
)
n
⁡
(
m
1
-
n
+
1
)
⁢
N
1
+
n
⁡
(
m
2
-
n
+
1
)
⁢
N
2
=
1
n
⁡
(
L
-
(
N
-
1
)
⁢
N
)
⁢
∑
i
=
0
n
-
1
⁢
∑
j
=
1
L
-
(
N
-
1
)
⁢
N
⁢
x
⁡
(
iN
+
j
)
2
.

### Claim 2 (depends on 1)

The generalized autocorrelation method for the bearing fault feature extraction under the variable rotational speed condition according to claim 1, wherein the step of truncating the measured order tracking signal comprises:
when the original signal is exactly divisible into m fragments each with a length N and n. in a noise resistant correlation is determined manually, a length of the original signal being exactly a multiple of a period and N being exactly the period; if L is not exactly divisible by N, dividing the original signal into two sub-signals each comprising several signal fragments, constructing a series of noise resistant correlation functions based on the signal fragments, and using a weighted sum of the noise resistant correlation functions to suppress a strong background noise;
𝒜
⁡
(
N
)
=
{
𝒜
y
(
N
)
ℒ
=
mN
𝓌
1
⁢
𝒜
𝓇
1
(
N
1
)
+
𝓌
2
⁢
𝒜
𝓇
2
(
N
2
)
ℒ
≠
mN
⁢
𝓌
2
=
1
-
𝓌
1
⁢
𝓌
1
=
(
m
1
-
n
+
1
)
⁢
N
1
(
m
1
-
n
+
1
)
⁢
N
1
+
(
m
2
-
n
+
1
)
⁢
N
2
.