US 2024/0255380 A1Published application

Methods for determining the cyclostationnarity of a vibration signal relating to a mechanical system, for arranging vibration sensors for monitoring such a system, and for monitoring it

AssigneeAirbus Helicopters

InventorsHervé MOREL, Jérémy JOUVE, Anas HAD, Hugo ANDRE, Mohamed EL BADAOUI

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Abstract

A method for determining the cyclostationarity of a vibration signal transmitted by a vibration sensor arranged on a mechanical system and allowing a cyclostationarity indicator Iα to be calculated. The present disclosure also relates to a method for arranging vibration sensors, using the method for determining cyclostationarity applied to the signals transmitted by these vibration sensors at different positions and orientations. A position of a vibration sensor is validated as a function of this cyclostationarity indicator Iα. The present disclosure finally relates to a method for monitoring a mechanical system 10 using the method for determining cyclostationarity to determine the cyclostationarity of the vibration signals relating to the mechanical system before calculating the monitoring indicators of the mechanical system.

Claims16

Dependent claims

A method for determining the cyclostationarity of a vibration signal relating to a mechanical system, the mechanical system comprising at least one rotating member that rotates about a rotation axis, at least one vibration sensor transmitting the temporal vibration signal s(t), an angular sensor transmitting a temporal angular signal θ(t) that varies as a function of an angular position of the rotating member about the rotation axis, and a calculator,

the method comprising the following steps:
transforming the temporal vibration signal s(t) into an angular vibration signal s(θ), using the calculator, as a function of the temporal angular signal θ(t);
using the calculator to calculate a normalized cyclostationarity indicator Iα using a statistical hypothesis test and as a function of the angular vibration signal s(θ);
and
determining that the angular vibration signal s(θ) is cyclostationary when the cyclostationarity indicator Iα is greater than or equal to a predetermined cyclostationarity threshold, the predetermined cyclostationarity threshold being between 0 and 1,
for which the method is intended to determine cyclostationarity of order 1, and the statistical hypothesis test is a Student's test applied to an estimate {circumflex over (m)}(θ) of a synchronous mean of the angular vibration signal s(θ) in relation to a cyclic period Φ and the calculation of a cyclostationarity indicator Iα comprises an intermediate step of determining a statistical indicator ηα(θ) calculated according to the following relationship:
η
α
(
θ
)
=
t
α
K
-
1
.
σ
^
(
θ
)
K
,
wherein tαK-1 is half of a confidence interval associated with the Student's test with K−1 degrees of freedom with a risk 1α;
{circumflex over (σ)}(θ) is an estimate of the standard deviation of the angular vibration signal s(θ) corresponding to a normal distribution for an angle θ defined such that
σ
^
(
θ
)
=
(
θ
)
.
K
K
-
1
;
θ is the angular position of the rotating member about the rotation axis;
(θ) is an estimate of the synchronous variance of the angular vibration signal s(θ) in relation to the cyclic period Φ, such that
(
θ
)
=
1
K
⁢
∑
i
=
0
K
-
1
[
r
^
(
θ
+
i
.
Φ
)
]
2
;
{circumflex over (r)}(θ) is an estimate of a residual of the angular vibration signal s(θ) such that {circumflex over (r)}(θ)=s(θ)−{circumflex over (m)}(θ);
{circumflex over (m)}(θ) is the estimate of the synchronous mean in relation to the cyclic period Φ such that
m
^
(
θ
)
=
1
K
⁢
∑
i
=
0
K
-
1
⁢
s
⁡
(
θ
+
i
.
Φ
)
;
√{square root over ( )} is the square root function;
Σ is the sum function;
Φ is the cyclic period of the angular vibration signal s(θ);
K is a number of cycles such that
K
=
N
Φ
;
N is a number of sampling points forming the angular vibration signal s(θ);
and
i is an integer varying from 0 to (K−1).

109 more elements

The method for determining the cyclostationarity of a vibration signal relating to a mechanical system, the mechanical system comprising at least one rotating member that rotates about a rotation axis, at least one vibration sensor transmitting the temporal vibration signal s(t), an angular sensor transmitting a temporal angular signal θ(t) that varies as a function of an angular position of the rotating member about the rotation axis, and a calculator,

the method comprising the following steps:
transforming the temporal vibration signal s(t) into an angular vibration signal s(θ), using the calculator, as a function of the temporal angular signal θ(t);
using the calculator to calculate a normalized cyclostationarity indicator Iα using a statistical hypothesis test and as a function of the angular vibration signal s(θ);
and
determining that the angular vibration signal s(θ) is cyclostationary when the cyclostationarity indicator Iα is greater than or equal to a predetermined cyclostationarity threshold, the predetermined cyclostationarity threshold being between 0 and 1,
for which the method is intended to determine cyclostationarity of order 2 and the statistical hypothesis test is Bartlett's test applied to an estimate of a synchronous variance of the angular vibration signal s(θ) in relation to a cyclic period Φ and the cyclostationarity indicator Iα is calculated according to the following relationship:
I
α
=
exp
⁢
(
-
x
α
2
ψ
)
,
wherein exp is the exponential mathematical function;
ψ is a scalar determined as a function of the estimate of the synchronous variance such that:
ψ
=
3
⁢
N
.
(
K
-
1
)
.
[
ln
⁡
(
∑
n
=
1
N
(
θ
n
)
/
N
)
-
∑
n
=
1
N
⁢
ln
(
(
θ
n
)
)
/
N
]
3
⁢
N
.
(
K
-
1
)
+
N
+
1
;
(θ) is the estimate of the synchronous variance in relation to the cyclic period Φ, such that
(
θ
)
=
1
K
⁢
∑
i
=
0
K
-
1
[
r
^
(
θ
+
i
.
Φ
)
]
2
;
{circumflex over (r)}(θ) is an estimate of a residual of the angular vibration signal s(θ) such that {circumflex over (r)}(θ)=s(θ)−{circumflex over (m)}(θ);
{circumflex over (m)}(θ) is an estimate of the synchronous mean of the angular vibration signal s(θ) in relation to the cyclic period Φ, such that
m
^
(
θ
)
=
1
K
⁢
∑
i
=
0
K
-
1
⁢
s
⁡
(
θ
+
i
.
Φ
)
;
Σ is the sum function;
θ is the angular position of the rotating member about the rotation axis;
Φ is the cyclic period of the angular vibration signal s(θ);
K is a number of cycles such that
K
=
N
Φ
;
N is a number of sampling points forming the angular vibration signal s(θ);
i is an integer varying from 0 to (K−1);
ln is the natural logarithm function;
and
α2 is a confidence interval associated with a chi-squared distribution with (N−1) degrees of freedom with a risk 1−α.

148 more elements

Dependencies are inferred from the claim text.

Facts

Application: 18/399,847Filed 29 Dec 2023
Priority: FR 230083930 Jan 2023
Published: 1 Aug 2024
Term ends: Not estimatedThe source records don’t support an estimate.

Classification5 codes

G01H 1/003
Measuring characteristics of vibrations in solids by using direct conduction to the detector: of rotating machines
G01M 13/028
Gearings; Transmission mechanisms: acoustic or vibration analysis
G01H 1/12
Measuring characteristics of vibrations in solids by using direct conduction to the detector: of longitudinal or not specified vibrations
G01H
Measurement of mechanical vibrations or ultrasonic, sonic or infrasonic waves