Method and system for determining the weight and centre of gravity of a structure

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.