# US 2025/0165673 A1 · Digital twinning method for monitoring operation state of tower of wind turbine generator system online

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- Number: US 2025/0165673 A1
- Document ID: US20250165673A1
- Status: Published application
- Kind: A1
- Application number: 18/736,512
- Filed: 2024-06-06
- Published: 2025-05-22
- Earliest claimed: 2023-11-22
- Assignees: Zhejiang University of Technology
- Applicants: Zhejiang University of Technology
- Inventors: Xiaohang JIN; Haoxuan YANG
- Web page: https://patentgrep.com/patent/US20250165673A1

## CPC

- G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM]
- G06F 30/17: Mechanical parametric or variational design
- G06F 2113/06: Wind turbines or wind farms
- G06F 2119/02: Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
- G06F 2119/14: Force analysis or force optimisation, e.g. static or dynamic forces
- Y02E 10/72: Wind turbines with rotation axis in wind direction
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- Y02E: REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION

## Abstract

Disclosed is a digital twinning method for monitoring an operation state of a tower of a wind turbine generator system online. The method includes: 1) constructing a simplified model of the tower of the wind turbine generator system, and discretizing the simplified model according to a finite element method to obtain a finite element model; 2) reducing an order of the finite element model of the tower according to proper orthogonal decomposition, analyzing precision of a reduced-order model under different orders, and selecting the reduced-order model having a smallest reduced order as a final reduced-order model on the premise that the precision satisfies actual engineering requirements; and 3) programming upper computer software in a computer, deploying the reduced-order model to the upper computer software, further building a physical entity of the tower, and monitoring a stress and a strain of the physical entity online through the reduced-order model.

## Claims

### Claim 1

A digital twinning method for monitoring an operation state of a tower of a wind turbine generator system online, comprising:
step 1, obtaining a simplified physical model of the tower of the wind turbine generator system according to geometrical characteristics of the tower of the wind turbine generator system, and analyzing an actual stress condition of the tower to construct a finite element model of the tower;
step 2, carrying out order reduction analysis on the finite element model constructed in step 1 according to proper orthogonal decomposition (POD), comparing precision of a reduced-order model under different orders, and determining a final reduced order, wherein the final reduced order satisfies engineering requirements of the reduced model under the order; and
step 3, designing and constructing upper computer software in a computer, and deploying the reduced-order model of the tower to the upper computer software; building a physical entity of the tower, installing a strain sensor and an inclination sensor, reading sensor data and uploading the data to an upper computer through a single chip microcomputer, so as to convert the data into a displacement boundary condition, and then inputting the displacement boundary condition into the reduced-order model for calculation; and determining accuracy of the digital twinning method for monitoring the operation state of the tower by calculating an error between a measured strain value of the strain sensor and a calculated strain value of the reduced-order model in the upper computer.

### Claim 2 (depends on 1)

The digital twinning method for monitoring an operation state of a tower of a wind turbine generator system online according to claim 1, wherein
the step 1 further comprises: simplifying a flange connection structure between the tower of the wind turbine generator system, and simplifying the tower into a beam structure, so as to construct the simplified physical model of the tower;
a point of intersection of an axis of the tower before bending deformation and a lower end surface of the tower is an origin O of a coordinate system XYZ; and normal vectors of an end surface at a top end of the tower before bending deformation and after bending deformation are n0 and n1 respectively, and an included angle between the two vectors is an inclination angle θ of the end surface at the top end of the tower, and an expression of deflection w and the inclination angle θ of the end surface at the top end of the tower is as follows:
{
w
=
F
6
⁢
EI
⁢
L
3
-
FL
2
⁢
EI
⁢
L
2
θ
=
F
2
⁢
EI
⁢
L
2
-
FL
EI
⁢
L
⇒
w
=
2
3
⁢
L
⁢
θ
(
1
)
wherein F is a concentrated load applied at the top end of the tower, and has a unit of N; E is an elastic modulus of a tower material, and has a unit of Pa; I is cross sectional moment of inertia of the tower, and has a unit of m4; and L is a length of the tower, and has a unit of m;
the deflection w and an azimuth φ need to be determined to describe the bending deformation of the tower in a three-dimensional space, wherein the azimuth φ is configured to express a bending orientation of the tower; and therefore, the displacement boundary condition of the finite element model of the tower is determined by the two parameters of w and φ, and according to a principle of linear superposition and decomposition of force, the displacement boundary condition of the tower is determined to obtain:
q
b
=
w
x
⁢
q
bx
+
w
y
⁢
q
by
=
(
w
⁢
cos
⁢
φ
)
⁢
q
bx
+
(
w
⁢
sin
⁢
φ
)
⁢
q
by
(
2
)
wherein qbx=[1, 0, 1, 0, . . . , 1, 0]T, qby=[0, 1, 0, 1, . . . , 0, 1]T, and a vector length is determined by a specific displacement boundary condition; qb is a joint displacement vector determined by the displacement boundary condition of the tower, i.e. a joint displacement vector corresponding to a joint having a displacement constraint of the tower; wx is a component of total deflection in a direction X; and wy is a component of the total deflection in a direction Y; and
the deflection w at the top end of the tower is converted into the displacement boundary condition, the finite element model of the tower is constructed, and an equilibrium equation of the finite element model of the tower under the displacement boundary condition is shown in formula (3):
[
K
a
⁢
a
K
a
⁢
b
K
b
⁢
a
K
b
⁢
b
]
[
q
a
q
b
]
=
[
g
a
g
b
]
+
[
0
R
r
]
(
3
)
wherein Kaa is a stiffness matrix corresponding to a joint node having no displacement constraint of the tower; Kab and Kba are coupling matrices between the joint having the displacement constraint and the node having no displacement constraint of the tower; Kbb is a stiffness matrix corresponding to the joint having the displacement constraint of the tower; qa is a joint displacement vector of the joint having no displacement constraint of the tower; ga and gb are joint gravity load vectors corresponding to the joint having no displacement constraint and the joint having the displacement constraint of the tower respectively; and Rr is a joint support reaction force vector corresponding to the joint having the displacement constraint of the tower.

### Claim 3 (depends on 1)

The digital twinning method for monitoring an operation state of a tower of a wind turbine generator system online according to claim 1, wherein
the step 2 further comprises: constructing the reduced-order model of a displacement field of the tower by combining the POD with a finite element method as follows:
solving the finite element model of step 1 to obtain a displacement solution set of a joint, and selecting m samples from the set to form a matrix X=[q1, q2, . . . , qm], wherein qi=[u1, u2, . . . , uz]T is a displacement solution of the joint, and z is the number of degrees of freedom of the finite element model; {ζ1, ζ2, . . . , ζn} is set as a group of n orthonormal bases of X, and is written as a matrix form denoted as Φ; and for the finite element model of the tower, a joint displacement value qt at any moment is represented by {ζ1, ζ2, . . . , ζn}:
q
t
=
∑
i
-
1
n
b
ti
⁢
ζ
i
(
4
)
wherein bti=ζiTqt;
selecting first k orthonormal basis vectors from {ζ1, ζ2, . . . , ζn} to represent qt:
q
t
⁡
(
k
)
=
∑
i
=
1
k
b
ti
⁢
ζ
i
=
Φ
k
⁢
b
t
⁡
(
k
)
(
5
)
wherein Φk=[ζ1, ζ2, . . . , ζk]; k<n; and bt(k)=[bt1, bt1, . . . , btk]T;
establishing an error function as follows:
ε
2
=
∑
t
=
1
n

q
t
-
q
t
⁡
(
k
)

2
2
=
∑
j
=
k
+
1
n
ζ
j
T
⁢
XX
T
⁢
ζ
j
(
6
)
in order to obtain an optimal solution of the error function under a constraint condition {ζ1, ζ2, . . . , ζn} of the orthogonal bases, introducing Lagrange factors uij (i, j=k+1, k+2, . . . , n) to construct a Lagrange function, so as to find the orthonormal bases corresponding to the optimal solution:
L
=
∑
j
=
k
+
1
n
ζ
j
T
⁢
XX
T
⁢
ζ
j
-
∑
i
=
k
+
1
n
∑
j
=
k
+
1
n
[
u
ij
(
ζ
i
T
⁢
ζ
j
-
δ
ij
)
]
(
7
)
wherein δij is a Kronecker function;
solving a partial derivative of ζj from two ends of formula (7) to obtain:
∂
L
∂
ζ
j
=
2
⁢
(
XX
T
⁢
ζ
j
-
∑
i
=
k
+
1
n
u
ij
⁢
ζ
j
)
=
2
⁢
⁢
XX
T
⁢
ζ
j
-
2
⁢
Φ
n
-
k
⁢
u
j
(
8
)
Φn−k=[ζk+1, ζk+2, . . . , ζn]T, and uj=[uk+1,j, uk+2,j, . . . , un,j]T;
writing the formula into a matrix form to obtain the following formula:
∂
L
∂
Φ
n
-
k
=
2
⁢
(
XX
T
⁢
Φ
n
-
k
-
Φ
n
-
k
⁢
U
n
-
k
)
(
9
)
wherein Un−k=[uk+1, uk+2, . . . , un]T;
in order to solve the optimal solution, making equation (9) equal to 0, and multiplying the equation left by Φn−kT, wherein internal vectors of a matrix Φn are orthonormal, and therefore Un−k=Φn−kTXXTΦn−k=(XTΦn−k)TXTΦn−k is obtained, and it is easy to know that Un−k is a positive semi-definite matrix, and therefore an orthogonal matrix P exists to diagonalize Un−k, so as to obtain PTΦn−kTXXTΦn−kP=PTUn−kP=Λ; and multiply two ends of the formula left by Φn−kP to obtain the following formula:
Φ
n
-
k
⁢
PP
T
⁢
Φ
n
-
k
T
⁢
XX
T
⁢
Φ
n
-
k
⁢
P
=
Φ
n
-
k
⁢
PP
T
⁢
U
n
-
k
⁢
P
=
Φ
n
-
k
⁢
P
⁢
Λ
⇓
(
10
)
XX
T
⁢
Φ
n
-
k
⁢
P
=
Φ
n
-
k
⁢
U
n
-
k
⁢
P
=
Φ
n
-
k
⁢
P
⁢
Λ
wherein Λ is a diagonal matrix of Un−k;
arranging diagonal elements of Λ in descending order, wherein it is seen from formula (10) that an i-th diagonal element of Λ is an eigenvalue λi of XXT, and an i-th column of a matrix Φn−kP is an eigenvector of XXT corresponding to λi; and
considering that the orthogonal matrix is norm-preserving under a Frobenius norm ∥•∥F2, formula (6) is rewritten as:
ε
2
=

X
T
⁢
Φ
n
-
k

F
2
=

X
T
⁢
Φ
n
-
k
⁢
P

F
2
=
trace
⁢
{
(
X
T
⁢
Φ
n
-
k
⁢
P
)
T
⁢
X
T
⁢
Φ
n
-
k
⁢
P
}
=
trace
⁢
{
Λ
}
(
11
)
forming a transformation matrix Φn from left singular value vectors corresponding to first n singular values of X, wherein Φn is an optimal solution of the error function under the condition that the constraint condition {ζ1, ζ2, . . . , ζn} is the orthonormal bases, and a minimum value of the error function is the sum of last n-k eigenvalues of the matrix XXT;
defining the following formula: ,
I
⁡
(
k
)
=
∑
i
=
1
k
λ
i
/
∑
i
=
1
n
λ
i
(
12
)
wherein λi is an eigenvalue of XXT arranged in descending order; and
retaining, by a k-dimensional base vector, d % of characteristic information of an original sample under the condition of I(k)≥d %; and constructing the reduced-order model under different orders, and calculating precision of the reduced-order model under different reduced orders separately to determine the appropriate reduced order and obtain the reduced-order model, wherein the finally determined reduced order satisfies actual engineering requirements of the reduced-order model under the order.

### Claim 4 (depends on 1)

The digital twinning method for monitoring an operation state of a tower of a wind turbine generator system online according to claim 1, wherein
in the step 3, the upper computer reads the sensor data uploaded by the single chip microcomputer, converts the data into the displacement boundary condition, and inputs the displacement boundary condition into the reduced-order model to achieve rapid calculation, so as to obtain calculated strain and stress values of the current physical entity of the tower and a displacement solution of a joint; after calculation of the reduced-order model is completed, a calculation result is processed in the upper computer, that is, deformation of the physical entity of the tower is rapidly quantified on the basis of the displacement solution of the joint and displayed in the upper computer; an error between a strain calculation result of the reduced-order model and an actual strain of the physical entity is obtained by means of a strain value calculated by the reduced-order model and a strain value measured by a sensor; and stress nephogram is visualized by combining the displacement solution of the joint with the calculated stress value to intuitively and clearly express stress distribution of the physical entity of the tower.