# US 11,029,191 B2 · Method and system for determining the weight and centre of gravity of a structure

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- Number: US 11,029,191 B2
- Document ID: US11029191B2
- Status: Granted
- Kind: B2
- Application number: 16/245,322
- Filed: 2019-01-11
- Published: 2019-07-18
- Granted: 2021-06-08
- Earliest claimed: 2018-01-17
- Assignees: Airbus Defence and Space, S.A.U.
- Applicants: Airbus Defence and Space, S.A.U.
- Inventors: Ángel Gago Tripero; Fernando Ibáñez Gruas
- Web page: https://patentgrep.com/patent/US11029191B2

## CPC

- G01G 19/07: for weighing aircraft
- G01G 23/01: Testing or calibrating of weighing apparatus
- G01L 1/225: {Measuring circuits therefor}
- G01L 25/00: Testing or calibrating of apparatus for measuring force, torque, work, mechanical power, or mechanical efficiency
- G01M 1/12: Static balancing; Determining position of centre of gravity (by determining imbalance G01M1/14)
- G01M 1/125: {of aircraft}
- G01M 5/0041: {by determining deflection or stress}
- G01G: WEIGHING (sorting by weighing B07C5/16)
- G01L: MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE (weighing G01G)
- G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR

## Abstract

A method and system for determining the weight and at least a first coordinate of the center of gravity of a structure such as a vehicle, in particular, an aircraft.

## Claims

### Claim 1

A method for determining a weight (W) and/or at least a first coordinate (X) of a position of a centre of gravity of a structure, the method comprising the following steps:
a) measuring responses (μ) of a first plurality of installed sensors located in sensitive load points of the structure, and
b) determining the weight (W) and/or the first coordinate (X) of the position of the centre of gravity of the structure based on the responses (μ), as:
W
=
C
w
+
∑
j
w
=
1
k
w
⁢
⁢
μ
j
w
·
β
j
w
X
=
C
x
+
∑
j
x
=
1
k
x
⁢
⁢
μ
j
x
·
γ
j
x
wherein W is the weight of the structure, X is the first coordinate of the position of the centre of gravity of the structure on a plane of projection, kW and kx, are natural numbers and μ are the responses (μ) measured by the first plurality of installed sensors, wherein a subscript in each of the responses (μ)denotes a corresponding sensor of the first plurality of the installed sensors which has performed the measurement,
wherein
for determining the weight (W) a first group of sensors is used which comprises a number of installed sensors kw,
for determining the first coordinate (X) of the centre of gravity a second group of sensors is used which comprises a number of installed sensors kx, and wherein
coefficients βjw, with jw=1, . . . kw, and γjx, with jx=1, . . . kx, and constants Cw, and cx are previously determined applying the following calibration steps:
i) locating a plurality of calibration sensors in sensitive load points of the structure, wherein the number of calibration sensors is m, m being a natural number,
ii) loading the structure with a probe weight (Wpi), obtaining a loading state (i), and measuring the first coordinate (Xi) of the position of the centre of gravity and the weight (Wi) of the structure in said loading state (i),
iii) measuring for each calibration sensor (r) the response (μr,i) associated to the loading state (i), with r=1, . . . m, being r a natural number,
iv) repeating steps ii) and iii) for a plurality of loading states (i), with i=1, s, being s the number of loading states, s being a natural number,
v) selecting groups of at least two calibration sensors and solving for each group an equation system with a number of equations (P) equal to or greater than Nw+1, being Nw the number of calibration sensors in the group, wherein the equation system is:
W
1
=
C
w
+
∑
n
=
1
N
w
⁢
⁢
μ
n
,
1
·
β
n
⋮
W
P
=
C
w
+
∑
n
=
1
N
w
⁢
⁢
μ
n
,
P
·
β
n
μn,q, with n=1, . . . , Nw, being the measured responses of the calibration sensors and Wq being the weight associated to the respective loading state q, q=1, P,
wherein the equation systems are solved by least squares method, obtaining as a result weight coefficients (βn) for n=1, . . . , Nw, and weight constant (Cw),
vi) determining for each group of calibration sensors an estimated weight (Wei) for each loading state (i) as
We
i
=
C
w
+
∑
n
=
1
N
w
⁢
⁢
μ
n
,
i
·
β
n
wherein μn,i are the responses of the calibration sensors of the group, associated to a loading state i,
vii) selecting a first group of calibration sensors which fulfils that a first probable error (PEw) is minimum, wherein PEw is:
PE
w
=
C
E
⁢
∑
i
=
1
s
⁢
⁢
(
We
i
-
W
i
)
2
s
-
(
N
w
+
1
)
s being the total number of loading states, Nw being the number of calibration sensors in said group of calibration sensors, and CE being a real positive number, viii) selecting groups of at least two calibration sensors and solving for each group an equation system with a number of equations (P) equal or greater than Nx+1, being Nx the number of calibration sensors in the group, wherein the equation systems is:
X
1
=
C
x
+
∑
n
=
1
N
x
⁢
⁢
μ
n
,
1
·
γ
n
⋮
X
P
=
C
x
+
∑
n
=
1
N
x
⁢
⁢
μ
n
,
P
·
γ
n
μn,q, with n=1, . . . , Nx, being the measured responses of the calibration sensors and Xq being the X-coordinate of the centre of gravity associated to the respective loading state q, q=1, . . . ,P,
wherein the equation systems are solved by least squares method, obtaining as a result X-coefficients (γn) for n=1, . . . , Nx, and X-constant (Cx),
ix) determining for each group of calibration sensors an estimated X-coordinate (Xei) of the centre of gravity for each loading state (i), as
Xe
i
=
C
x
+
∑
n
=
1
N
x
⁢
⁢
μ
n
,
i
·
γ
n
wherein μn,i are the responses of the calibration sensors of the group, associated to a loading state i,
x) selecting a second group of calibration sensors which fulfils that a second probable error (PEx) is minimum, wherein PEx is:
PE
X
=
C
E
⁢
∑
i
=
1
s
⁢
⁢
(
Xe
i
-
X
i
)
2
s
-
(
N
x
+
1
)
s being the total number of loading states, Nx, being the number of calibration sensors in said group of calibration sensors, and CE being a real positive number,
xi) selecting as the first plurality of installed sensors a plurality of calibration sensors including:
the first group of calibration sensors selected in step vii), and
the second group of calibration sensors selected in step x),
wherein kw is the number of sensors in the first group of calibration sensors and kx, is the number of sensors in the second group of calibration sensors.

### Claim 2 (depends on 1)

The method according to claim 1, further comprising determining a second coordinate (Y) of the position of the centre of gravity of the structure, wherein the second coordinate (Y) of the position of the centre of gravity of the structure is determined based on the measured responses (μ) of the first plurality of installed sensors, as:
Y
=
C
y
+
∑
j
y
=
1
k
y
⁢
⁢
μ
j
y
·
τ
j
y
wherein Y is the second coordinate of the position of the centre of gravity of the structure on a plane of projection, ky is a natural number and μ are the responses measured by the first plurality of installed sensors, wherein the subscript in the response μ denotes the sensor which has performed the measurement,
wherein for determining the second coordinate (Y) of the position of the centre of gravity a third group of sensors is used which comprises a number of installed sensors ky, and wherein
Y-coefficients τjy, with jy=1, . . . ky, and Y-constant Cy are previously determined applying the following calibration steps at least after steps i)-iv), wherein the step ii) further comprises measuring the second coordinate (Yi) of the position of the centre of gravity of the structure in each loading state (i):
viii′) selecting groups of at least two calibration sensors and solving for each group an equation system with a number of equations (P) equal or greater than Ny+1, being Ny the number of calibration sensors in the group, wherein the equation systems is:
Y
1
=
C
y
+
∑
n
=
1
N
y
⁢
⁢
μ
n
,
1
·
τ
n
⋮
Y
P
=
C
y
+
∑
n
=
1
N
y
⁢
⁢
μ
n
,
P
·
τ
n
μn,q, with n=1, . . . , Ny, being the measured responses of the calibration sensors and Yq being the Y-coordinate of the centre of gravity associated to the respective loading state q, q=1, . . . , P,
wherein the equation systems are solved by least squares method, obtaining as a result Y-coefficients (τn) for n=1, . . . , Ny, and Y-constant (Cy),
ix′) determining for each group of calibration sensors an estimated Y-coordinate (Yei) of the centre of gravity for each loading state (i), as
Ye
i
=
C
y
+
∑
n
=
1
N
y
⁢
⁢
μ
n
,
i
·
τ
n
where μn,i are the responses of the calibration sensors of the group, associated to a loading state i, and
x′) selecting a third group of calibration sensors which fulfils that a third probable error (PEy) is minimum, wherein PEy is:
PE
Y
=
C
E
⁢
∑
i
=
1
s
⁢
⁢
(
Ye
i
-
Y
i
)
2
s
-
(
N
y
+
1
)
s being the total number of loading states, Ny being the number of calibration sensors in said group of calibration sensors, and CE being a real positive number,
wherein the first plurality of installed sensors further includes the third group of calibration sensors selected in step x′) and wherein ky is the number of sensors in the third group of calibration sensors.

### Claim 3 (depends on 2)

The method according to claim 2, further comprising the following steps:
c) measuring the responses (μ′) of a second plurality of installed sensors located in at least one lifting surface (h) of the structure, and
d) determining a corrected weight of the structure W (Wcorrected) and/or a corrected position (Xcorrected, Ycorrected) of the centre of gravity of the structure as:
W
corrected
=
W
-
∑
h
=
1
M
⁢
⁢
V
h
′
X
corrected
=
X
·
W
-
∑
h
=
1
M
⁢
⁢
(
X
h
′
·
V
h
′
)
W
-
∑
h
=
1
M
⁢
⁢
V
h
′
Y
corrected
=
Y
·
W
-
∑
h
=
1
M
⁢
⁢
(
Y
h
′
·
V
h
′
)
W
-
∑
h
=
1
M
⁢
⁢
V
h
′
wherein W is the calculated weight of the structure, (X, Y) is the calculated position of the centre of gravity of the structure,
wherein M is the number of lifting surfaces considered at step c),
wherein V′h is the vertical component of a resultant force applied on a lifting surface h of the structure,
wherein X′h and Y′h are the X-coordinate and Y-coordinate, respectively, through which the vertical component of the resultant force (V′h) passes, wherein V′h, X′h, and Y′h are determined based on the measured responses (μ′), for each lifting surface (h) as:
V
′
=
C
v
′
+
∑
j
v
=
1
L
v
⁢
⁢
μ
j
v
′
·
β
j
v
′
X
′
=
C
x
′
+
∑
j
x
=
1
L
x
⁢
⁢
μ
j
x
′
·
γ
j
x
′
Y
′
=
C
y
′
+
∑
j
y
=
1
L
y
⁢
⁢
μ
j
y
′
·
τ
j
y
′
wherein μ′ are the responses measured by the second plurality of installed sensors, the subscript in the response (μ′) denoting the sensor which has performed the measurement, being Lv, Lx, and Ly natural numbers,
wherein W, V′ and Wcorrected are expressed in the same axes system; X, X′ and Xcorrected are expressed according to the same coordinate system, and Y, Y′ and Ycorrected are expressed according to the same coordinate system,
and wherein:
for determining V′ a fourth group of sensors is used which comprises a number of installed sensors Lv,
for determining X′ a fifth group of sensors is used which comprises a number of installed sensors Lx,
for determining Y′ a sixth group of sensors is used which comprises a number of installed sensors Ly, and wherein
coefficients (βjv, with jv=1, . . . Lv γ′jx, with jx=1, . . . Lx, and τ′jy, with jy=1, . . . Ly, and constants C′v, C′x, C′y are previously determined applying the following calibration steps:
s-i) locating a plurality of calibration sensors in at least one lifting surface (h) of the structure, wherein the number of calibration sensors is m′, m′ being a natural number,
s-ii) applying a probe force to the at least one lifting surface (h) of the structure, obtaining a force state (ƒ), and measuring the vertical component of the resultant force (V′ƒ), the X-coordinate (X′ƒ) and the Y-coordinate (Y′ƒ) respectively through which the vertical component of the resultant force (V′ƒ) passes in said force state (ƒ),
s-iii) measuring for each calibration sensor (r) the response (μ′r,ƒ) associated to the force state (ƒ), with r=1, . . . m′, being r a natural number,
s-iv) repeating steps s-ii) and s-iii) for a plurality of force states (ƒ), with ƒ=1, . . . s′, being s′ the number of force states, wherein for each force state (ƒ) a different probe force is applied to the at least one lifting surface (h), s′ being a natural number,
s-v) selecting groups of at least two calibration sensors and solving for each group an equation system with a number of equations (P) greater than Nv+1, being Nv the number of calibration sensors in the group, wherein the equation system is:
V
1
′
=
C
v
′
+
∑
n
=
1
N
v
⁢
⁢
μ
n
,
1
′
·
β
n
′
⋮
V
P
′
=
C
v
′
+
∑
n
=
1
N
v
⁢
⁢
μ
n
,
P
′
·
β
n
′
with μ′n,q, with n=1, . . . , Nv, being the measured responses of the calibration sensors and V′q being the vertical component of the resultant force measured for the respective force state q, with q=1, . . . , P,
wherein the equation systems are solved by least squares method, obtaining as a result vertical force coefficients β′n for n=1, . . . , Nv and constant C′v,
s-vi) determining, for each group of calibration sensors an estimated vertical force (Ve′ƒ) for each force state (ƒ) as
Ve
f
′
=
C
v
′
+
∑
n
=
1
N
v
⁢
⁢
μ
n
,
f
′
·
β
n
′
where μ′n,ƒ are the responses of the calibration sensors of the group, associated to a force state ƒ,
s-vii) selecting a fourth group of calibration sensors which fulfils that fourth probable error (PE′v) is minimum, wherein PE′v is:
PE
v
′
=
C
E
⁢
∑
f
=
1
s
⁢
⁢
′
⁢
⁢
(
Ve
f
′
-
V
f
′
)
2
s
′
-
(
N
v
+
1
)
s′ being the total number of force states, Nv being the number of calibration sensors in said group of calibration sensors, and CE being a real positive number,
s-viii) selecting groups of at least two calibration sensors and solving for each group an equation system with a number of equations (P) equal to or greater than Nx+1, being Nx the number of calibration sensors in the group, wherein the equation systems is:
X
1
′
=
C
x
′
+
∑
n
=
1
N
x
⁢
⁢
μ
n
,
1
′
·
γ
n
′
⋮
X
P
′
=
C
x
′
+
∑
n
=
1
N
x
⁢
⁢
μ
n
,
P
′
·
γ
n
′
μ′n,q, with n=1, . . . , Nx, being the measured responses of the calibration sensors and X′q being the X-coordinate through which the measured vertical component of the resultant force (V′q) passes, associated to the respective force state q, q=1, . . . , P
wherein the equation systems are solved by least squares method, obtaining as a result X-coefficients γ′n for n=1, . . . , Nx, and X-constant C′x,
s-ix) determining for each group of calibration sensors an estimated X-coordinate (Xe′ƒ) through which the vertical component of the resultant force (V′ƒ) passes for each force state (ƒ), as
Xe
f
′
=
C
x
′
+
∑
n
=
1
N
x
⁢
⁢
μ
n
,
f
′
·
γ
n
′
where μ′n,ƒ are the responses of the calibration sensors of the selected group associated to a force state (ƒ),
s-x) selecting a fifth group of calibration sensors which fulfils that a fifth probable error (PE′x) is minimum, wherein PE′x is:
PE
X
′
=
C
E
⁢
∑
f
=
1
s
⁢
⁢
′
⁢
⁢
(
Xe
f
′
-
X
f
′
)
2
s
′
-
(
N
x
+
1
)
s′ being the total number of force states, Nx being the number of calibration sensors in said group of calibration sensors, and CE being a real positive number,
s-xi) selecting groups of at least two calibration sensors and solving for each group an equation system with a number of equations P equal or greater than Ny+1, being Ny the number of calibration sensors in the group, wherein the equation systems is:
Y
1
′
=
C
y
′
+
∑
n
=
1
N
y
⁢
⁢
μ
n
,
1
′
·
τ
n
′
⋮
Y
P
′
=
C
y
′
+
∑
n
=
1
N
y
⁢
⁢
μ
n
,
P
′
·
τ
n
′
μ′n,q, with n=1, . . . , Ny, being the measured responses of the calibration sensors and Y′q being the Y-coordinate through which the measured vertical component of the resultant force (V′q) passes associated to the respective force state (q), q=1, . . . ,P
wherein the equation systems are solved by least squares method, obtaining as a result Y-coefficients τ′n for n=1, . . . , Ny and Y-constant C′y,
s-xii) determining for each group of calibration sensors an estimated Y- coordinate (Ye′ƒ) through which the vertical component of the resultant force (V′ƒ) passes for each force state (ƒ), as
Ye
f
′
=
C
y
′
+
∑
n
=
1
N
y
⁢
⁢
μ
n
,
f
′
·
τ
n
′
where μ′n,ƒ are the responses of the calibration sensors of the selected group associated to a force state ƒ,
s-xiii) selecting a sixth group of calibration sensors which fulfils that a sixth probable error (PE′y) is minimum, wherein PE′y is:
PE
Y
′
=
C
E
⁢
∑
f
=
1
s
⁢
⁢
′
⁢
⁢
(
Ye
f
′
-
Y
f
′
)
2
s
′
-
(
N
y
+
1
)
s′ being the total number of force states, Ny being the number of calibration sensors in said group of calibration sensors, and CE being a real positive number,
s-xiv) selecting as the second plurality of installed sensors a plurality of calibration sensors including:
the fourth group of calibration sensors selected in step s-vii),
the fifth group of calibration sensors selected in step s-x), and
the sixth group of calibration sensors selected in step s-xiii),
wherein Lv is the number of sensors in the fourth group of calibration sensors, Lx is the number of sensors in the fifth group of calibration sensors and Ly is the number of sensors in the sixth group of calibration sensors.

### Claim 4 (depends on 1)

The method according to claim 1, comprising, after steps vii), x) and/or x′), verifying for at least one loading state i that
the first group of calibration sensors fulfills that a weight residual value (εWi) is lower than a first predefined threshold,
ɛ
⁢
⁢
w
i
=
100
·
(
We
i
-
W
i
)
W
i
,
wherein and/or
the second group of calibration sensors fulfills that a X-coordinate residual value (εXi) is lower than a second predefined threshold,
ɛ
⁢
⁢
x
i
=
100
·
(
Xe
i
-
X
i
)
X
i
,
wherein and/or
the third group of calibration sensors fulfills that a Y-coordinate residual value (Eyi) is lower than a third predefined threshold,
wherein
ɛ
⁢
⁢
y
i
=
100
·
(
Ye
i
-
Y
i
)
Y
i
.

### Claim 5 (depends on 1)

The method according to claim 1, wherein at each iteration of step ii) the structure is loaded with the probe weights Wpi in steps of a predetermined percentage of a maximum admissible weight of the structure.

### Claim 6 (depends on 1)

The method according to claim 1, wherein the structure is an on ground vehicle.

### Claim 7 (depends on 6)

The method according to claim 6, wherein at least one sensitive load point is located in at least one bulkhead of the vehicle.

### Claim 8 (depends on 6)

The method according to claim 6, wherein the on ground vehicle is an aircraft.

### Claim 9 (depends on 8)

The method according to claim 8, wherein at least one sensitive load point is located in at least one landing gear bulkhead.

### Claim 10 (depends on 8)

The method according to claim 8, wherein at least one sensitive load point is located in the nose landing gear pin.

### Claim 11 (depends on 8)

The method according to claim 8, wherein at least one sensitive load point is located in the main landing gear pin.

### Claim 12 (depends on 1)

The method according to claim 1, wherein the first coordinate (Xi) of the position of the centre of gravity and/or the weight (Wi) is measured in calibration step ii) using scales and/or jacks with load cells, preferably, using three hydraulic jacks.

### Claim 13 (depends on 1)

The method according to claim 1, wherein
at step vii) a plurality of first groups of calibration sensors are selected, which fulfil that the first probable error is minimum, and/or wherein
at step x) a plurality of second groups of calibration sensors are selected, which fulfil that the second probable error is minimum, and/or wherein
at step x′) a plurality of third groups of calibration sensors are selected, which fulfil that the third probable error is minimum.

### Claim 14

A system configured for determining a weight (W) and/or at least a first coordinate of a position of s centre of gravity of a structure, comprising:
a plurality of installed sensors located on the structure,
a data acquisition module configured to register data from the plurality of installed sensors located on the structure, and
a data processor configured to:
determine the weight (W) and/or the first coordinate (X) of the position of the centre of gravity of the structure based on measured responses (μ), as:
W
=
C
w
+
∑
j
w
=
1
k
w
⁢
⁢
μ
j
w
·
β
j
w
X
=
C
x
+
∑
j
x
=
1
k
x
⁢
⁢
μ
j
x
·
γ
j
x
wherein W is the weight of the structure, X is the first coordinate of the position of the centre of gravity of the structure on a plane of projection, kw and kx are natural numbers and μ are the responses measured by the first plurality of installed sensors, wherein a subscript in each of the measured responses (μ) denotes a sensor which has performed a corresponding one of the measurement responses (μ),
wherein
for determining the weight (W) a first group of sensors is used which comprises a number of installed sensors kw,
for determining the first coordinate (X) of the centre of gravity a second group of sensors is used which comprises a number of installed sensors kx, and wherein
coefficients βjw, with jw=1, . . . kw, and γjx, with jx=1, . . . kx, and constants Cw and Cx are previously determined applying the following calibration steps:
i) locating a plurality of calibration sensors in sensitive load points of the structure, wherein the number of calibration sensors is m, m being a natural number,
ii) loading the structure with a probe weight (Wpi), obtaining a loading state (i), and measuring the first coordinate (Xi) of the position of the centre of gravity and the weight (Wi) of the structure in said loading state (i),
iii) measuring for each calibration sensor (r) the response (μr,i) associated to the loading state (i), with r=1, . . . m, being r a natural number,
iv) repeating steps ii) and iii) for a plurality of loading states (i), with i=1, . . . s, being s the number of loading states, s being a natural number,
v) selecting groups of at least two calibration sensors and solving for each group an equation system with a number of equations (P) equal to or greater than Nw+1, being Nw the number of calibration sensors in the group, wherein the equation system is:
W
1
=
C
w
+
∑
n
=
1
N
w
⁢
⁢
μ
n
,
1
·
β
n
⋮
W
P
=
C
w
+
∑
n
=
1
N
w
⁢
⁢
μ
n
,
P
·
β
n
μn,q, with n=1, . . . , Nw, being the measured responses of the calibration sensors and Wq being the weight associated to the respective loading state q, q=1, . . . , P,
wherein the equation systems are solved by least squares method, obtaining as a result weight coefficients (βn) for n=1, . . . , Nw and weight constant (Cw),
vi) determining for each group of calibration sensors an estimated weight (Wei) for each loading state (i) as
We
i
=
C
w
+
∑
n
=
1
N
w
⁢
⁢
μ
n
,
i
·
β
n
wherein μn,i are the responses of the calibration sensors of the group, associated to a loading state i,
vii) selecting a first group of calibration sensors which fulfils that a first probable error (PEw) is minimum, wherein PEw is:
PE
w
=
C
E
⁢
∑
i
=
1
s
⁢
⁢
(
We
i
-
W
i
)
2
s
-
(
N
w
+
1
)
s being the total number of loading states, Nw being the number of calibration sensors in said group of calibration sensors, and CE being a real positive number,
viii) selecting groups of at least two calibration sensors and solving for each group an equation system with a number of equations (P) equal or greater than Nx+1, being Nx the number of calibration sensors in the group, wherein the equation systems is:
X
1
=
C
x
+
∑
n
=
1
N
x
⁢
⁢
μ
n
,
1
·
γ
n
⋮
X
P
=
C
x
+
∑
n
=
1
N
x
⁢
⁢
μ
n
,
P
·
γ
n
μn,q, with n=1, . . . , Nx, being the measured responses of the calibration sensors and Xq being the X-coordinate of the centre of gravity associated to the respective loading state q, q=1, . . . ,P,
wherein the equation systems are solved by least squares method, obtaining as a result X-coefficients (γn) for n=1, . . . , Nx, and X-constant (Cx),
ix) determining for each group of calibration sensors an estimated X-coordinate (Xei) of the centre of gravity for each loading state (i), as
Xe
i
=
C
x
+
∑
n
=
1
N
x
⁢
⁢
μ
n
,
i
·
γ
n
wherein μn,1 are the responses of the calibration sensors of the group, associated to a loading state i,
x) selecting a second group of calibration sensors which fulfils that a second probable error (PEx) is minimum, wherein PEx is:
PE
X
=
C
E
⁢
∑
i
=
1
s
⁢
⁢
(
Xe
i
-
X
i
)
2
s
-
(
N
x
+
1
)
s being the total number of loading states, Nx being the number of calibration sensors in said group of calibration sensors, and CE being a real positive number,
xi) selecting as the first plurality of installed sensors a plurality of calibration sensors including:
the first group of calibration sensors selected in step vii), and
the second group of calibration sensors selected in step x),
wherein kw is the number of sensors in the first group of calibration sensors and kx is the number of sensors in the second group of calibration sensors.

### Claim 15 (depends on 14)

A vehicle comprising the system according to claim 14.