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

Abstract

The invention belongs to the field of structures and relates to a method and a system for determining the weight and at least first coordinates of the centre of gravity of a structure such as a vehicle, in particular an aircraft.

Description

Technical Field

[0001] The present invention is in the field of structures and relates to a method and a system for determining the weight and the centre of gravity of a structure such as a vehicle, in particular an aircraft. Background Art

[0002] Accurately determining the weight and center of gravity of a structure is crucial to ensure the stability and correct performance of said structure. In the particular case of a vehicle, determining the weight and center of gravity of the vehicle is necessary to avoid critical movements that may compromise the stability of the vehicle when said vehicle is in operation.

[0003] According to current practice, aircraft and other vehicles are usually weighed inside a hangar on a scale or by lifting on a jack with a load cell. However, when the vehicle is outside the hangar, the weight of the cargo of the vehicle is usually obtained by estimating the weight of each pallet when the vehicle is loaded. After the weight is loaded in the vehicle, a calculation is performed to estimate the center of gravity (CG) based on the estimated weight and the estimated weight position. When the estimation of weight and center of gravity is inaccurate, the safety of the transportation performed by the vehicle may be compromised.

[0004] In order to provide a solution for autonomously determining the weight and centre of gravity of an aircraft in any situation on the ground, it has been proposed to obtain the weight and centre of gravity by positioning sensors inside the aircraft, in particular in the structure to which the landing gear is attached.

[0005] The landing gear is the landing device of an aircraft that supports the weight of the aircraft and is in principle the best location for instrumenting sensors. However, the landing gear structure has some disadvantages, since its geometry varies with the weight and also depends on the shock absorber behavior, which in turn depends greatly on temperature, internal friction, etc. In addition, during landing maneuvers, the sensors mounted on the landing gear support very heavy loads or even shock loads, which may destroy or damage the mounted sensors. Therefore, these behavior, characteristics and geometry changes must be taken into account by correcting the measurement results obtained by the sensors. This involves complex and time-consuming calculations to provide an estimate of the weight and the position of the center of gravity, the accuracy of which cannot be fully guaranteed.

[0006] US patent application US 5,548,517 A discloses an onboard system for measuring, calculating and displaying the gross weight and position / repositioning of the center of gravity of an aircraft. The system also incorporates a software calibration routine and accompanying hardware to correct and compensate for physical changes in the strut components due to temperature fluctuations, seal drag and hysteresis within the landing gear struts of modern "shock-absorbing" aircraft. However, the system implies: collecting data from multiple types of sensors to infer the landing gear movement and the geometry changes of the landing gear, i.e., collecting pressure sensor data to obtain telescopic strut movement, collecting rotation sensor data to obtain the articulation movement of the strut components, collecting strain gauge data to obtain shaft deflection, etc. From all this data, complex calculation methods must be performed to determine the weight and center of gravity of the aircraft. In addition, because there are many factors to be considered, the accuracy of the results may be affected.

[0007] Therefore, there is a need for a method for determining the weight and location of the center of gravity of a structure which avoids the above-mentioned problems and provides accurate measurements in a simple and reliable manner. Summary of the invention

[0008] The present invention provides a solution to the above-mentioned problem by a method for determining at least a first coordinate of the position of the weight and / or the center of gravity of a structure according to a first inventive aspect, a system according to a second inventive aspect, and a vehicle according to a third inventive aspect. In other inventive aspects, preferred embodiments of the present invention are defined.

[0009] In a first inventive aspect, the present invention provides a method for determining at least a first coordinate of a position of a weight and / or a center of gravity of a structure, the method comprising the following steps:

[0010] a) measuring the responses of a plurality of first mounted sensors located in sensitive load points of the structure; and

[0011] b) determining the first coordinates of the position of the weight and / or centre of gravity of the structure based on the measured response as:

[0012]

[0013]

[0014] Where W is the weight of the structure, X is the first coordinate of the position of the center of gravity of the structure on the projection plane, and k w and k x is a natural number, and μ is the response measured by the plurality of first installed sensors, wherein the subscript in the response indicates the sensor that has performed the measurement, wherein,

[0015] To determine the weight, use the number k w The first set of sensors installed is

[0016] To determine the first coordinates of the center of gravity, use the k-th order x The second set of sensors of the installed sensor, and wherein,

[0017] where j w =1,…k w The coefficient β jw , and where j x =1,…k x The coefficient γ jx , and the constant C w and C x is predetermined by applying the following calibration steps:

[0018] i) positioning a plurality of calibration sensors in sensitive load points of the structure, wherein the number of calibration sensors is m, where m is a natural number,

[0019] ii) loading the structure with a probe weight to obtain a loaded state, and measuring at least the weight and the first coordinate of the position of the center of gravity of the structure in said loaded state,

[0020] iii) for each calibrated sensor, measuring the response associated with the loading state,

[0021] iv) repeating steps ii) and iii) for multiple loading states i, where i=1, ...s, s is the number of loading states, and s is a natural number,

[0022] v) Selecting a calibration sensor group having at least two calibration sensors, and for each calibration sensor group, solving for a number P equal to or greater than N w +1 equation system, N w is the number of calibration sensors in the calibration sensor set, where the system of equations is:

[0023]

[0024] μ n,q is the measured response of the calibrated sensor, where n = 1, ..., N w , and W q is the weight associated with the corresponding loading state q, where q = 1, ..., P,

[0025] The system of equations is solved by the least squares method, thereby obtaining for n=1,...,N w The weight coefficient β n , and the weight constant Cw ,

[0026] vi) For each calibration sensor set, determine the estimated weight for each loading state as:

[0027]

[0028] Among them, μ n,i is the response of the calibration sensor in the calibration sensor set associated with loading state i,

[0029] vii) Select the first probability error PE w is the smallest first set of calibrated sensors, where PE w yes:

[0030]

[0031] s is the total number of loading states, N w is the number of calibration sensors in the calibration sensor set, C E is a positive real number, We i is the estimated weight for loading state i, and W i is the measured weight for loading state i,

[0032] viii) selecting a calibration sensor group having at least two calibration sensors, and for each calibration sensor group, solving for a number P equal to or greater than N x +1 equation system, N x is the number of calibration sensors in the calibration sensor set, where the system of equations is:

[0033]

[0034] μ n,q is the measured response of the calibrated sensor, and X q is the X coordinate of the center of gravity associated with the corresponding loading state q, where q=1,...,P,

[0035] The system of equations is solved by the least squares method, thereby obtaining for n=1,...,N x The X coefficient, and X constant,

[0036] ix) For each calibration sensor set, determine the estimated X coordinate of the center of gravity for each loading state as:

[0037]

[0038] Among them, μ n,iis the response of the calibration sensor in the calibration sensor set associated with loading state i,

[0039] x) Selecting a second set of calibration sensors that satisfies the second probability error is the smallest, where PE X yes:

[0040]

[0041] s is the total number of loading states, N x is the number of calibration sensors in the calibration sensor set, C E is a positive real number, Xe i is the estimated X coordinate for loading state i, and X i is the measured X coordinate for loading state i,

[0042] xi) selecting a plurality of calibration sensors as the plurality of first installed sensors, the plurality of calibration sensors comprising:

[0043] the first set of calibration sensors selected in step vii), and

[0044] the second set of calibration sensors selected in step x),

[0045] Among them, k w is the number of sensors in the first set of calibration sensors, and k x is the number of sensors in the second set of calibration sensors. k w and k x Less than or equal to m.

[0046] Therefore, before determining at least a first coordinate of the position of the weight and / or the center of gravity of the structure based on the measured responses of said plurality of first mounted sensors located in such structure, it is determined which sensors will be used. The selection of such plurality of first mounted sensors is performed by a calibration step.

[0047] As a result of the calibration step, the plurality of first installed sensors are selected and the j w =1,…k w The coefficient of and among them x =1,…k x The coefficient γ jx , and the constant C w and C x In the present invention, the constant C w and C xBased on the calculated coefficients and constants, the weight of the structure and / or the first coordinates of the centre of gravity can be determined at any time from the measured responses of said first plurality of installed sensors using the equations defined in step b) of the method of the invention.

[0048] The method allows determining at least one coordinate of the position of the center of gravity. In a specific embodiment, the position of the center of gravity of the structure is defined by two coordinates. These two coordinates represent the position of the center of gravity on the plane (ground) of the structure, that is, the position of the center of gravity projected on the plane of the structure, or on the plane or surface on which the structure is supported. Therefore, throughout this entire document, the plane of projection will be understood as the plane of the structure or the plane or surface on which the structure is supported. In addition, throughout this entire document, the first coordinate can be any of the two coordinates of the position of the center of gravity. The position of the center of gravity is defined relative to a coordinate system, the origin of which is a predefined point. In an embodiment in which the structure is an aircraft, the X axis is preferably selected as the projection on the horizontal plane along the longitudinal direction of the fuselage (roll axis), and the Y axis is preferably selected as the projection on the horizontal plane in the lateral direction (pitch axis). In a preferred embodiment, the origin of the axis is located at a specific distance in front of the nose of the aircraft.

[0049] In the calibration step i) of the method, a plurality of calibration sensors are installed in sensitive load points of the structure.

[0050] In the context of this specification, a sensitive load point of a structure is understood to be a point of the structure that is subject to substantially linear stress and / or strain in response to the weight of the structure. Substantially linear stress and / or strain in said sensitive load point means that the structural changes in said sensitive load point are only due to the weight loaded in the structure and the weight of the structure itself.

[0051] Once a plurality of calibration sensors are installed in the structure, first, the structure is loaded with different detection weights, wherein, according to each detection weight, a loading state is obtained. For each loading state, the first coordinate of the position of the center of gravity of the structure and / or the weight is measured. The measurement of the weight and the first coordinate of the position of the center of gravity can be performed in a conventional manner. In an embodiment, a plurality of weighing scales are used to determine the weight and the position of the center of gravity. In this embodiment, the structure is placed on a weighing scale, and the weight of the structure is determined as the sum of the weights measured by the weighing scales. The position of the center of gravity is determined based on the known position of each weighing scale and the weight measured by each weighing scale. Since the first coordinate of the position of the center of gravity can be any one of the two coordinates of the center of gravity, any one of these coordinates can be determined as described above.

[0052] In addition, for each loading state, the measured response of each calibration sensor is recorded. Once the responses of the calibration sensors and the weight and the first coordinates of the position of the center of gravity are obtained and recorded for each loading state, the coefficients and constants of the weight of the structure and the coefficients and constants of the first coordinates of the position of the center of gravity of the structure are determined, respectively.

[0053] The plurality of loading conditions in the calibration step may be obtained by modifying the weight and / or the position of the probe weight loaded on the structure.

[0054] To determine these coefficients and constants, a calibration sensor set having at least two calibration sensors is selected and, for each calibration sensor set, a system of equations as defined in step v) and step viii) is solved by the least squares method. In the system of equations, each equation corresponds to a loading state and the number of equations is equal to or greater than the number of calibration sensors in the calibration sensor set plus one.

[0055] To determine which of the calibration sensors will be the installed sensors for determining the first coordinates of the position of the weight and / or center of gravity of the structure, select:

[0056] A first set of calibration sensors satisfying a first probability error is minimized; and

[0057] A second set of calibration sensors satisfying a minimum second probability error;

[0058] Therein, these probability errors are defined in step vii) and step x) of the method, respectively.

[0059] The constant C used to calculate the first probability error E The value of may be equal to or different from the constant C used to calculate the second probability error E The value of the constant C E is a positive real number. In a preferred embodiment, in order to calculate the first probability error and the second probability error, the constant C E It is 0.6745.

[0060] Thus, for determining the weight, a first set of sensors is used, and for determining the first coordinates of the position of the center of gravity, a second set of sensors is used. These sensor sets are predetermined in a calibration step and define the plurality of first mounted sensors, which are positioned in sensitive load points of the structure and which are used to determine at least one of the first coordinates of the center of gravity and the weight. One or more of the mounted sensors included in one of the sensor sets may also be included in the other sensor set.

[0061] Advantageously, since the invention allows determining at least the first coordinates of the position of the centre of gravity and the weight based on measurements obtained by sensors located in at least one sensitive load point, the method improves the accuracy and reliability of determining the weight and the centre of gravity.

[0062] In certain embodiments, the method further comprises: determining a second coordinate of the location of the center of gravity of the structure, wherein the second coordinate of the location of the center of gravity of the structure is determined based on the measured responses of the plurality of first mounted sensors as:

[0063]

[0064] where Y is the second coordinate of the position of the center of gravity of the structure on the projection plane, k y is a natural number, and μ is a response measured by the plurality of first installed sensors, wherein the subscript in the response μ indicates the sensor that has performed the measurement,

[0065] In order to determine the second coordinate of the position of the center of gravity, a number k of y The third set of sensors of the installed sensors, and wherein, at least after steps i) to iv), the Y coefficient is predetermined by applying the following calibration steps and Y constant C y , where j y =1,…k y , wherein step ii) further comprises measuring a second coordinate of the position of the center of gravity of the structure in each loading state:

[0066] viii') Select a calibration sensor group having at least two calibration sensors, and for each calibration sensor group, solve the problem of having a number of sensors equal to or greater than N y +1 equation system, N y is the number of calibration sensors in the calibration sensor set, where the system of equations is:

[0067]

[0068] μ n,q is the measured response of the calibrated sensor, and Y q is the Y coordinate of the center of gravity associated with the corresponding loading state q, where q = 1, ..., P,

[0069] The system of equations is solved by the least squares method, thereby obtaining for n=1,...,N y Y coefficient τ n , and the Y constant C y ,

[0070] ix') For each calibration sensor set, determine the estimated Y coordinate of the center of gravity for each loading state as:

[0071]

[0072] Among them, μ n,i is the response of the calibration sensor in the calibration sensor set associated with loading state i, and

[0073] x') selects the third probability error PE Y is the smallest third group of calibrated sensors, where PE Y yes:

[0074]

[0075] s is the total number of loading states, N y is the number of calibration sensors in the calibration sensor set, C E is a positive real number, Ye i is the estimated Y coordinate for loading state i, and Y i is the measured Y coordinate for loading state i,

[0076] wherein the plurality of first installed sensors further comprises a third set of calibration sensors selected in step x′), and wherein k y is the number of sensors in the third set of calibration sensors. k y Less than or equal to m.

[0077] The constant C used to calculate the third probability error E The value of may be equal to or different from the constant C used to calculate the first probability error and / or the second probability error. E The value of the constant C E is a positive real number. In a preferred embodiment, in order to calculate the first probability error, the second probability error and the third probability error, the constant C E It is 0.6745.

[0078] Before determining the second coordinates of the location of the center of gravity of such a structure based on the measured responses of the plurality of first mounted sensors located in the structure, it is necessary to determine which sensors are to be used.

[0079] Therefore, due to the calibration step, a third set of installed sensors is also selected and the coefficient τ is calculated jy and Y constant C y , where j y =1,…k y In the present invention, the constant C yBased on the calculated coefficients and constants, a second coordinate of the center of gravity of the structure can also be determined at any time from the measured responses of the plurality of first mounted sensors.

[0080] According to this embodiment, the calibration further comprises steps viii') to x'). Once a plurality of calibration sensors are installed in the structure and the structure is loaded with different probe weights to obtain a plurality of loading states, for each loading state, the second coordinate of the position of the center of gravity is also measured. The measurement of the second coordinate of the position of the center of gravity can be performed in a conventional manner, such as using a plurality of weighing scales. The second coordinate of the position of the center of gravity is determined based on the known position of each weighing scale and the weight measured by each weighing scale.

[0081] Once the response of the calibration sensor and the second coordinate of the position of the center of gravity are obtained and recorded for each loading state, the coefficient τ of the second coordinate of the position of the center of gravity of the structure is jy and the constant C y It is determined.

[0082] In order to determine such coefficients and constants for the second coordinate of the center of gravity, a calibration sensor set having at least two calibration sensors is selected and for each calibration sensor set the system of equations as defined in step viii') is solved by the method of least squares as for the first coordinates of the weight and the center of gravity.

[0083] In order to determine which of the calibration sensors will be the installed sensors for determining the second coordinate of the position of the center of gravity of the structure, a third group of calibration sensors is selected for which the third probability error is minimized, as defined in step x'). Thus, in this embodiment, the plurality of first installed sensors comprises the first group of calibration sensors selected in step vii), the second group of calibration sensors selected in step x) and the third group of calibration sensors selected in step x'). In order to determine the second coordinate of the position of the center of gravity, the third group of installed sensors is used.

[0084] The mounted sensor groups define the plurality of first mounted sensors positioned in sensitive load points of the structure and used to determine first and second coordinates of the position of the weight and / or center of gravity of the structure. One or more of the mounted sensors included in one of the mounted sensor groups may be included in one or both of the other mounted sensor groups.

[0085] Advantageously, the method improves the accuracy and reliability of determining the position of the centre of gravity, since the invention also allows determining the second coordinates of the position of the centre of gravity based on measurements obtained by sensors installed in at least one sensitive load point.

[0086] In a particular embodiment, the method comprises verifying, after step vii), step x) and / or step x'), for at least one loading state i:

[0087] The first set of calibration sensors meets the weight residual value (εw i ) is less than a first predetermined threshold, wherein, and / or

[0088] The second set of calibration sensors meets the X-coordinate residual value (εx i ) is less than a second predetermined threshold, wherein, and / or

[0089] The third set of calibration sensors meets the Y coordinate residual value (εy i ) is less than a third predetermined threshold,

[0090] in,

[0091] In an embodiment, the first predetermined threshold, the second predetermined threshold and / or the third predetermined threshold is 3%, preferably 2%.

[0092] Advantageously, this additional step of verifying whether the selected set of calibration sensors meets this requirement allows checking the accuracy of the equations.

[0093] In a specific embodiment, the method comprises performing the following steps before step a):

[0094] selecting at least one sensitive load point in the structure; and

[0095] At least one sensor is mounted on the at least one sensitive load point.

[0096] In a particular embodiment, at each iteration of step ii) of the method, the probe weight Wp is used i The structure is loaded in steps of percentages of the maximum permissible weight of the structure. For example, the probe weight Wp i The structure is loaded at 0%, 20%, 40%, 60%, 80% and 100% of the load. Advantageously, loading the structure in steps allows the linearity of the sensor to be verified.

[0097] In a specific embodiment of the method:

[0098] At step vii), a plurality of first groups of calibration sensors are selected, wherein the first group of calibration sensors satisfies that a first probability error is minimal, and / or

[0099] At step x), a plurality of second groups of calibration sensors are selected, wherein the second group of calibration sensors satisfies that the second probability error is the smallest, and / or

[0100] At step x′), a plurality of third groups of calibration sensors are selected, wherein the third groups of calibration sensors satisfy that a third probability error is minimum.

[0101] In this embodiment, more than one set of calibration sensors are selected for determining at least one of the coordinates of the weight and / or the position of the center of gravity, wherein each calibration sensor set has an associated equation for determining at least one of the coordinates of the weight and / or the position of the center of gravity. Thus, once a calibration has been performed on the structure, the weight and / or the position of the center of gravity of the structure loaded with an unknown weight can be determined using multiple equations. The redundancy in determining the weight and / or the position of the center of gravity of the structure allows verification that the method and / or sensors are functioning properly. In a preferred embodiment, at least two sensor sets with different numbers of sensors are selected.

[0102] In certain embodiments, the structure is a ground vehicle.

[0103] In a particular embodiment, the at least one sensitive load point of the structure is located in at least one bulkhead of the vehicle.

[0104] In the context of this specification, the bulkhead of a ground vehicle is to be understood as a region of the vehicle to which a support element is fixed. A support element of a ground vehicle is an element on which the vehicle sits on the ground. For example, the bulkhead may be a region that accommodates such a support element. In a specific embodiment in which the vehicle is an aircraft, the support element is understood to be a landing gear.

[0105] In certain embodiments, the ground vehicle is an aircraft.

[0106] In a particular embodiment, the at least one sensitive load point is located in at least one landing gear bulkhead.

[0107] In a particular embodiment, the at least one sensitive load point is located in a nose landing gear pin.

[0108] In a particular embodiment, the at least one sensitive load point is located in a main landing gear pin.

[0109] Unlike the prior art, in the method of the invention, the landing gear is not equipped with sensors. In this way, the measurements obtained by the sensors are independent of changes in geometry and independent of the shock absorber behavior. In this embodiment, the instrumentation is located in the area around the landing gear or in the equipped pins, so as to receive the loads without changes in direction or with very small changes in direction. Instrumentation performed in this way is independent of changes in geometry and independent of temperature or adhesion effects and other extraneous influences.

[0110] In a special embodiment, the position of the center of gravity and / or the weight is measured in the calibration step ii) using a scale and / or a jack with a load cell, preferably three hydraulic jacks.

[0111] In a specific embodiment, the method further comprises the following steps:

[0112] c) measuring responses of the plurality of second mounted sensors located in at least one lifting surface of the structure; and

[0113] d) determining the corrected weight of the structure and / or the corrected position of the center of gravity of the structure as:

[0114]

[0115]

[0116]

[0117] Where W is the calculated weight of the structure, (X, Y) is the calculated position of the center of gravity of the structure,

[0118] where M is the number of lifting surfaces considered at step c),

[0119] Among them, V h ' is the vertical component of the resultant force exerted on the lifting surface h of the structure,

[0120] Among them, X h ' and Y h ' are the X and Y coordinates through which the vertical component of the resultant force passes, respectively, where for each lifting surface, V h ', X h ' and Y h ' is determined based on the measured response as:

[0121]

[0122]

[0123]

[0124] Wherein, μ' is the response measured by the plurality of second mounted sensors, the subscript in the response indicates the sensor that has performed the measurement, L v , L x and L y is a natural number,

[0125] Among them, W, V' and W 校正 are expressed in the same axis system; X, X' and X 校正 are expressed according to the same coordinate system, and Y, Y' and Y 校正 is expressed according to the same coordinate system,

[0126] And among them,

[0127] To determine V', use the number L v The fourth group of sensors installed is the sensor,

[0128] To determine X', use the number L x The fifth set of sensors installed is

[0129] To determine Y', use the number L y The installed sensor is a sixth group of sensors, and wherein,

[0130] where j v =1,...,L v The coefficient of where j x =1,...,L x The coefficient of and among them y =1,...,L y The coefficient of and the constant C v '、C x '、C y ' is predetermined by applying the following calibration steps:

[0131] si) positioning a plurality of calibration sensors in at least one lifting surface of the structure, wherein the number of calibration sensors is m', m' being a natural number,

[0132] s-ii) applying a probing force to the at least one lifting surface of the structure to obtain a force state, and measuring a vertical component of the resultant force under the force state, an X coordinate and a Y coordinate through which the vertical component of the resultant force passes, respectively,

[0133] s-iii) for each calibrated sensor, measuring a response associated with a force state,

[0134] s-iv) repeating steps s-ii) and s-iii) for a plurality of force states f, where f=1, ..., s', s' being the number of force states, wherein for each force state a different probing force is applied to the at least one lifting surface, s' being a natural number,

[0135] sv) select a calibration sensor group having at least two calibration sensors, and for each calibration sensor group, solve the problem of having a number greater than N v +1 equation system, N v is the number of calibration sensors in the calibration sensor set, where the system of equations is:

[0136]

[0137] where μ' n,q is the measured response of the calibrated sensor, where n = 1, ..., N v , and V' q is the vertical component of the resultant force measured for the corresponding force state q, where q = 1, ..., P,

[0138] The system of equations is solved by the least squares method, thereby obtaining for n=1,...,N v The vertical force coefficient β n ', and the constant C v ',

[0139] s-vi) For each calibration sensor set, the estimated vertical force Ve for each force state f is f 'Determined as:

[0140]

[0141] Among them, μ' n,f is the response of the calibration sensor in the calibration sensor set associated with the force state f,

[0142] s-vii) Select the fourth probability error PE' v is the smallest fourth group of calibration sensors, where PE' v yes:

[0143]

[0144] s' is the total number of force states, N v is the number of calibration sensors in the calibration sensor set, C E is a positive real number, Ve f ' is the estimated vertical force for the force state f, and V' fis the vertical component of the resultant force measured for the force state f,

[0145] s-viii) Select a calibration sensor group having at least two calibration sensors, and for each calibration sensor group, solve the problem of having a number of sensors equal to or greater than N x +1 equation system, N x is the number of calibration sensors in the calibration sensor set, where the system of equations is:

[0146]

[0147] μ' n,q is the measured response of the calibrated sensor, and X q ' is the X coordinate associated with the corresponding force state q through which the measured vertical component of the resultant force passes, where q = 1, ..., P,

[0148] The system of equations is solved by the least squares method, thereby obtaining for n=1,...,N x X coefficient γ n ', and X constant C x ',

[0149] s-ix) For each calibration sensor set, the estimated X coordinate Xe through which the vertical component of the resultant force passes for each force state f f 'Determined as:

[0150]

[0151] Among them, μ' n,f is the response of the calibration sensor in the calibration sensor set associated with the force state f,

[0152] sx) selects the fifth probability error PE' X is the smallest fifth set of calibrated sensors, where PE' X yes:

[0153]

[0154] s' is the total number of force states, N x is the number of calibration sensors in the calibration sensor set, C E is a positive real number, Xe f ' is the estimated X coordinate through which the vertical component of the resultant force passes for the force state f, and X' f is the X coordinate through which the measured vertical component of the resultant force for the force state f passes,

[0155] s-xi) Select a calibration sensor group having at least two calibration sensors, and for each calibration sensor group, solve the problem of having a number P equal to or greater than N y +1 equation system, N y is the number of calibration sensors in the calibration sensor set, where the system of equations is:

[0156]

[0157] μ' n,q is the measured response of the calibrated sensor, and Y q ' is the Y coordinate associated with the corresponding force state q through which the measured vertical component of the resultant force passes, where q = 1, ..., P,

[0158] The system of equations is solved by the least squares method, thereby obtaining for n=1,...,N y Y coefficient τ n ', and Y constant C y ',

[0159] s-xii) For each calibration sensor set, the estimated Y coordinate (Ye) through which the vertical component of the resultant force passes for each force state f ') is determined as:

[0160]

[0161] Among them, μ' n,f is the response of the calibration sensor in the calibration sensor set associated with the force state f,

[0162] s-xiii) Select the sixth probability error PE' Y is the smallest sixth set of calibration sensors, where PE' Y yes:

[0163]

[0164] s' is the total number of force states, N y is the number of calibration sensors in the selected calibration sensor set, and C E is a positive real number,

[0165] s-xiv) selecting a plurality of calibration sensors as the plurality of second installed sensors, the plurality of calibration sensors comprising:

[0166] the fourth set of calibration sensors selected in step s-vii);

[0167] the fifth set of calibration sensors selected in step sx); and

[0168] the sixth set of calibration sensors selected in step s-xiii),

[0169] Among them, L v is the number of sensors in the fourth set of calibration sensors, L x is the number of sensors in the fifth set of calibration sensors, and L y is the number of sensors in the sixth set of calibration sensors. v , L x and L y Less than or equal to m'.

[0170] In addition to determining the total weight of the structure and the position of the center of gravity, the method also allows the determination of external forces acting on the lifting surface of the structure. Therefore, the results of the weight and the position of the center of gravity obtained in step b) can advantageously be corrected based on said external forces acting on the lifting surface of the structure.

[0171] Throughout this document, the coordinates through which the vertical forces or vertical resultant forces pass are defined relative to the same coordinate system of the centre of gravity. The external forces acting on the lifting surface are defined relative to an axis system which is to be understood as the previous coordinate system.

[0172] Before determining the corrected weight and corrected center of gravity of the structure based on the vertical components of the resultant force applied to the lifting surface of the structure and the X- and Y-coordinates through which such vertical components of the resultant force pass, it is necessary to determine such components and coordinates based on the measured responses of the plurality of second mounted sensors located in the lifting surface of the structure, and it is also necessary to determine which sensors are to be used. The determination of such plurality of second mounted sensors is performed by a calibration step.

[0173] The calibration steps for determining the weight and the location of the center of gravity are defined to be similar to the calibration steps for determining the resultant force from each lifting surface of the structure and the X and Y coordinates through which the vertical component of the resultant force passes.

[0174] In the calibration steps si) to s-xi) of the method, a plurality of calibration sensors are mounted in at least one lifting surface h of the structure. In the context of the present description, a lifting surface of a structure is understood to be a structural body shaped to produce a normal reaction to its movement through the air.

[0175] Once a plurality of calibration sensors are mounted in at least one lifting surface, different probing forces are applied to the lifting surface, thereby obtaining different force states. The vertical component at each force state, and the X and Y coordinates through which such vertical component of the resultant force respectively passes, can be measured in a conventional manner. In addition, for each force state, the measured response of each calibration sensor is recorded. Once the response of the calibration sensor and the vertical component of the resultant force and the X and Y coordinates are obtained and recorded for each force state, the coefficient β' jv , γ' jx and τ' jy and the constant C v '、C x '、C y ' are determined separately.

[0176] To determine such coefficients and constants, a calibration sensor set having at least two calibration sensors is selected and, for each calibration sensor set, a system of equations as defined in step sv), step s-viii) and step s-xi) is solved by the least squares method. In the system of equations, each equation corresponds to a loading state and the number of equations is equal to or greater than the number of calibration sensors in the calibration sensor set plus one.

[0177] To determine which of the calibration sensors will be the installed sensors for determining the vertical component of the resultant force on the lifting surface, the X and Y coordinates through which the vertical component of the resultant force passes, respectively, select:

[0178] a fourth group of calibration sensors satisfying that a fourth probability error is minimum;

[0179] a fifth group of calibration sensors satisfying that a fifth probability error is minimal; and

[0180] A sixth group of calibration sensors satisfying a sixth probability error is the smallest;

[0181] In this case, the probability error is defined in steps s-vii), sx) and s-xiii) of the method, respectively.

[0182] To determine the vertical component of the resultant force applied to the lifting surface, a fourth group of sensors is used; to determine the X coordinate through which the vertical component of the resultant force on the lifting surface passes, a fifth group of sensors is used; and to determine the Y coordinate through which the vertical component of the resultant force passes, a sixth group of sensors is used. These three groups of sensors are predetermined in the calibration step and define the plurality of second mounted sensors, which are located in the lifting surface of the structure and are used to determine the corrected weight and / or the corrected center of gravity of the structure. One or more of the mounted sensors included in one of the sensor groups may also be included in one or both of the other sensor groups. In a specific embodiment in which only one of the coordinates of the position of the center of gravity is determined, it should be understood that the method can independently correct this coordinate of the center of gravity.

[0183] Advantageously, since this embodiment allows determining the position and weight of the centre of gravity based on measurements obtained by sensors located in at least one lifting surface taking into account external forces exerted on the lifting surface, the method improves the accuracy and reliability of determining the weight and centre of gravity.

[0184] In a more specific embodiment, the structure is an aircraft comprising a lifting surface, and in steps s-ii) and s-iv) of the calibration step, a plurality of probing forces are applied on at least one lifting surface of the aircraft.

[0185] In a second inventive aspect, the present invention provides a system configured for determining at least a first coordinate of a position of a weight and / or a center of gravity of a structure, the system comprising:

[0186] a plurality of mounted sensors located on the structure;

[0187] a data acquisition module configured to record data from the plurality of mounted sensors located on the structure; and

[0188] A data processing device configured to perform at least step b) of the method according to the first inventive aspect.

[0189] The data acquisition module and the data processing device may be implemented as two different elements in data communication or as a single processor.

[0190] In a third inventive aspect, the present invention provides a vehicle comprising a system according to the second aspect. Preferably, the vehicle is an aircraft.

[0191] Except for mutually exclusive combinations of features and / or steps, all features described in this specification (including claims, description and drawings) and / or all steps of the described methods may be combined in any combination. BRIEF DESCRIPTION OF THE DRAWINGS

[0192] These and other features and advantages of the present invention will be clearly understood from the detailed description of the present invention, which becomes apparent from the preferred embodiments of the present invention which are given by way of example only and not as a limitation of the present invention with reference to the accompanying drawings.

[0193] Figure 1 Sensitive load points used in embodiments of the present invention are shown.

[0194] Figure 2 Sensitive load points used in embodiments of the present invention are shown.

[0195] Figure 3a to Figure 3b The installation of a sensor in at least one sensitive load point according to an embodiment of the invention is shown.

[0196] Figure 4 An aircraft is shown loaded with a weight probe according to an embodiment of the present invention.

[0197] Figure 5 A method for obtaining the weight and the center of gravity by means of a jack with a load cell according to an embodiment of the invention is shown. DETAILED DESCRIPTION

[0198] Having outlined the purpose of the invention, a specific non-limiting embodiment will be described below. In particular, an embodiment of a method for determining the weight (W) and the position of the center of gravity (X, Y) of an aircraft (6) as a first coordinate of the X coordinate is described. In this particular embodiment, the position of the center of gravity is defined relative to a coordinate system, the origin of which is a predetermined point. In this particular example, the origin is located on the X axis in front of the nose of the aircraft (6), in particular at a distance of 1587 mm from the nose, when viewed from the side. In this aircraft (6), the X axis is chosen as the projection on the horizontal plane along the longitudinal direction of the fuselage (roll axis).

[0199] Figure 1 and Figure 2 A main landing gear bulkhead (1) and a nose landing gear (2) of an aircraft (6) are shown, respectively. Selected sensitive load points (3) in the main landing gear bulkhead (1) and in the pins (7) of the nose landing gear (2) are shown in these figures. In the context of the present invention, the sensitive load points (3) of a structure whose weight and / or center of gravity are to be determined are the points in the case where the structure is sitting on the ground. In this particular example, respectively Figure 1 and Figure 2As shown in , four of the sensitive load points ( 3 ) are located in the main landing gear bulkhead ( 1 ), and three of the sensitive load points ( 3 ) are located in the pins ( 7 ) of the nose landing gear ( 2 ).

[0200] After the sensitive load points (3) are selected, at least one sensor (4) is positioned in each sensitive load point (3). In this particular example, the sensor (4) is a strain gauge bridge. Figure 3a and Figure 3b In FIG. 1 , some of the strain gauge bridges ( 4 ) mounted on a structure are schematically shown. The strain gauge bridges ( 4 ) are attached to the structure by abrasion, application of adhesive, application of pressure and heat curing. Figure 3a In the example shown in , the strain gauge bridge (4) is attached to the main landing gear bulkhead (1). Figure 3b In the strain gauge bridge (4) is attached to the nose landing gear pin (7). Figure 3b In this particular example, the sensor (4) is embedded in one of the nose landing gear pins (7).

[0201] Example

[0202] For a specific example, before determining the weight (W) of the aircraft (6) and the X coordinate (X) of the position of the center of gravity (X, Y), the following calibration steps are performed:

[0203] i) 19 calibration sensors are positioned in sensitive load points (3) of the aircraft (6). Thus, in this particular example, m=19. In this particular example, all positioned calibration sensors are strain gauge bridges. Furthermore, calibration sensors 1 to 16 are positioned in the main landing gear bulkhead and calibration sensors 17 to 19 are positioned in the nose landing gear pin (7).

[0204] ii) Using the detection weight Wp 1 The structure is loaded to obtain a first loading state (i=1), and for this loading state i=1, the weight of the aircraft (W 1 ) and the X coordinate of the center of gravity (X 1 ). In this particular example, the Y coordinate of the center of gravity is not illustrated below because the Y coordinate is obtained like the X coordinate.

[0205] iii) For each calibrated sensor r, measure the response μ associated with loading state i=1 r,1 , where r=1,…19.

[0206] iv) Repeat steps ii) and iii) for multiple loading states i). In this example, nine different configurations of loading probe weights are used, and different loading states are obtained by modifying the weight and / or position of the probe weight loaded on the aircraft (6). Figure 4 As schematically shown in FIG. 1 , twelve water tanks (8) are arranged at specific locations in the aircraft (6). In this example, the loading state is obtained by filling different combinations of water tanks to different water levels. Tables 1A to 1B show the water tanks filled with water and the maximum probe weight in each configuration. In Tables 1A to 1B and Figure 4 In the figure, the twelve water tanks (8) are labeled as T1, T2, ... T12.

[0207]

[0208] Table 1A

[0209]

[0210] Table 1B

[0211] In addition, for each of the configurations of the water tank (8) filled with water in Tables 1A to 1B, a plurality of filling percentages are considered. For example, for configuration 1 as shown in Tables 1A to 1B, the increasing water tank filling percentages under consideration are 33%, 66%, 100%, and the decreasing water tank filling percentages are 66%, 33% and 0%. Thus, for configuration 1 of the water tank (8) shown in Table 1, six loading states are obtained.

[0212] During these calibration steps, the weight (W i ) and the X coordinate of the center of gravity (X i ) has already Figure 5 As schematically shown in FIG. 1 , the load cell (10) is attached to the hydraulic jack (9) at the lifting point (11) to measure the actual weight value (W) of the aircraft (6) at each loading state i. i ) and the actual X coordinate of the center of gravity (X i The load cell (10) is connected to a weight indicator system (5) which records these measurements.

[0213] The following Tables 2A to 2E to 10A to 10E show the weight (W) measured for each loading state i. i ), the X coordinate of the center of gravity (X i ) and the response of each sensor (sensors are identified as "bridge"):

[0214]

[0215] Table 2A

[0216]

[0217]

[0218] Table 2B

[0219]

[0220] Table 2C

[0221]

[0222] Table 2D

[0223]

[0224] Table 2E

[0225]

[0226] Table 3A

[0227]

[0228]

[0229] Table 3B

[0230]

[0231] Table 3C

[0232]

[0233] Table 3D

[0234]

[0235] Table 3E

[0236]

[0237] Table 4A

[0238]

[0239]

[0240] Table 4B

[0241]

[0242] Table 4C

[0243]

[0244] Table 4D

[0245]

[0246]

[0247] Table 4E

[0248]

[0249] Table 5A

[0250]

[0251] Table 5B

[0252]

[0253] Table 5C

[0254]

[0255] Table 5D

[0256]

[0257]

[0258] Table 5E

[0259]

[0260] Table 6A

[0261]

[0262] Table 6B

[0263]

[0264]

[0265] Table 6C

[0266]

[0267] Table 6D

[0268]

[0269]

[0270] Table 6E

[0271]

[0272] Table 7A

[0273]

[0274] Table 7B

[0275]

[0276]

[0277] Table 7C

[0278]

[0279] Table 7D

[0280]

[0281] Table 7E

[0282]

[0283] Table 8A

[0284]

[0285] Table 8B

[0286]

[0287]

[0288] Table 8C

[0289]

[0290] Table 8D

[0291]

[0292] Table 8E

[0293]

[0294] Table 9A

[0295]

[0296] Table 9B

[0297]

[0298]

[0299] Table 9C

[0300]

[0301] Table 9D

[0302]

[0303] Table 9E

[0304]

[0305]

[0306] Table 10A

[0307]

[0308] Table 10B

[0309]

[0310] Table 10C

[0311]

[0312]

[0313] Table 10D

[0314]

[0315] Table 10E

[0316] Considering all filling percentages, a total of 51 loading states were obtained.

[0317] Once the measurements of each sensor (4) are obtained for each loading state i, the following calibration steps are performed:

[0318] v) Form a system with four calibration sensors (N w =4), and for each calibration sensor group, an equation system having a number P = 51 equations is solved by the least square method. In addition, a system having three calibration sensors (N) is formed. w =3) and for each calibration sensor set, the system of equations with the number P = 51 equations is also solved by the least squares method. In this example, all combinations of 3 sensors and 4 sensors are considered. For each calibration sensor set, the weight coefficient β is obtained for n = 1, ..., 4 and for n = 1, ..., 3, respectively n .

[0319] vi) Using the measured responses and the obtained weight coefficients, for a system with 4 sensors (N w =4) and each sensor group with 3 sensors (N w=3), determine the estimated weight (We i ), and the first probability error (PE w ).

[0320] The following shows the obtained results in steps v) and vi) for a system with four sensors (N w =4) and a plurality of (but not all) equations for some sensor groups in the sensor group, and a first probability error (PE w ):

[0321] Equation 1: We Eq1 =(-86556.3xμ 桥1 )+(-73945.4xμ 桥2 )+(-63713.4xμ 桥9 )+(11350.0xμ 桥17 )

[0322] For the first probability error of Equation 1: PE w =736.0

[0323] Equation 2: We Eq2 =(-72791.4xμ 桥1 )+(-75957.2xμ 桥9 )+(-65926.8xμ 桥10 )+(11083.7xμ 桥17 )

[0324] For the first probability error of Equation 2: PE w =684.3

[0325] Equation 3: We Eq3 =(-29698.7xμ 桥3 )+(-75203.4xμ 桥9 )+(24293.0xμ 桥17 )+(-25100.2xμ 桥19 )

[0326] For the first probability error of Equation 3: PE w =713.8

[0327] Equation 4: We Eq4 =(-28387.9xμ 桥3 )+(-44809.5xμ 桥5 )+(-72570.8xμ 桥9 )+(11039.6xμ 桥17 )

[0328] For the first probability error of Equation 4: PE w =704.4

[0329] Equation 5: We Eq5 =(-85744.5xμ 桥1 )+(-81280.3xμ 桥2 )+(-67149.1xμ 桥9 )+(18817.2xμ 桥18 )

[0330] For the first probability error of Equation 5: PE w =935.3

[0331] Equation 6: We Eq6 =(-80364.5xμ 桥1 )+(-57544.1xμ 桥2 )+(-67523.6xμ 桥9 )+(20592.7xμ 桥19 )

[0332] For the first probability error of Equation 6: PE w =1036.4

[0333] Equation 7: We Eq7 =(-156095.0xμ 桥1 )+(-335755.3xμ 桥2 )+(181157.1xμ 桥10 )+(23123.7xμ 桥18 )

[0334] For the first probability error of Equation 7: PE w =1749.8

[0335] Among them, We Eq1 represents the estimated weight obtained using the first combination of sensors, namely, sensors 1, 2, 9 and 17, and wherein the first probability error (PE) for each sensor group has been obtained according to the following expression w )

[0336]

[0337] Where, s = 51, N w =4 and C E = 0.6745, i represents the loading state. In this particular example, the weight constant C obtained in the above equation W is 0.

[0338] According to the above results, Equation 2 and Equation 4 are selected due to their lower values ​​for the first probability error. The sensors corresponding to the equations are sensors 1, 9, 10 and 17 for Equation 2 and sensors 3, 5, 9 and 17 for Equation 4.

[0339] The following shows the obtained results in steps v) and vi) for a system with three sensors (N w =3) and a plurality of (but not all) equations for some of the sensor groups, and a first probability error (PE) obtained for the sensor group w ):

[0340] Equation 1: We Eq1 =(-67486.3xμ 桥1 )+(-141344.7xμ 桥2 )+(-114424.1xμ 桥9 ) For the first probability error of Equation 1: PE w =2989.5

[0341] Equation 2: We Eq2 =(-67642.3xμ 桥1 )+(-74448.0xμ 桥2 )+(-46822.8xμ 桥11 ) For the first probability error of Equation 2: PE w =3142.9

[0342] Equation 3: We Eq3 =(-74227.1xμ 桥1 )+(-71078.6xμ 桥9 )+(11693.7xμ 桥17 ) For the first probability error of equation 3: PE w =899.9

[0343] Equation 4: We Eq4 =(-42357.3xμ 桥1 )+(-132662.4xμ 桥9 )+(9092.1xμ 桥13 ) For the first probability error of Equation 4: PE w =3159.1

[0344] Equation 5: We Eq5 =(-125553.4xμ 桥1 )+(-87136.1xμ 桥7 )+(-253449.0xμ 桥10 ) For the first probability error of Equation 5: PEw =5497.9

[0345] Equation 6: We Eq6 =(-28267.7xμ 桥3 )+(-75931.5xμ 桥9 )+(10896.8xμ 桥17 ) For the first probability error of Equation 6: PE w =856.5

[0346] Among them, the first probability error (PE) for each sensor group has been obtained according to the following expression: w )

[0347]

[0348] Where, s = 51, N w =3 and C E =0.6745, i represents the loading state.

[0349] According to the above results, Equation 3 and Equation 6 are selected due to their lower values ​​for the first probability error. The sensors corresponding to the equations are sensors 1, 9 and 17 for Equation 3 and sensors 3, 9 and 17 for Equation 6.

[0350] vii) Based on the previous w =4,N w =3) Determine the first probability error (PE w ), a first group of four sensors is selected from a plurality of calibration sensors (4). The sensors included in the four groups of sensors are sensors 1, 3, 5, 9, 10 and 17. The six sensors (4) are thus selected as installed sensors that can be used to determine the weight (W) of the aircraft (6). Once the calibration step is performed, the determination of the weight (W) of the aircraft (6) can be performed based on the responses of the sensors according to one or more of the following expressions:

[0351] Calculation method 1: We App1 =(-72791.4xμ 桥1 )+(-75957.2xμ 桥9 )+(-65926.8xμ 桥10 )+(11083.7xμ 桥17 )

[0352] Calculation 2: We App2 =(-28387.9xμ 桥3 )+(-44809.5xμ 桥5 )+(-72570.8xμ桥9 )+(11039.6xμ 桥17 )

[0353] Calculation 3: We App3 =(-74227.1xμ 桥1 )+(-71078.6xμ 桥9 )+(11693.7xμ 桥17 ) Calculation method 4: We App4 =(-28267.7xμ 桥3 )+(-75931.5xμ 桥9 )+(10896.8xμ 桥17 )

[0354] In a preferred embodiment, at least two groups of sensors are selected having different numbers of sensors.

[0355] Perform the following calibration steps to obtain the X coordinate of the center of gravity:

[0356] viii) forming a system with four calibration sensors (N x =4), and for each calibration sensor group, an equation system having a number P = 51 equations is solved by the least square method. In addition, a system having three calibration sensors (N) is formed. x =3), and for each calibration sensor group, the equation system with the number of equations P=51 is also solved by the least square method. For each calibration sensor group, the constant C is obtained respectively x and the X-coordinate coefficients γ for n = 1, ..., 4 and for n = 1, ..., 3 n .

[0357] ix) Using the measured response, the obtained X-coordinate coefficients and the obtained X-constant C x , for a system with 4 sensors (N x =4) and each sensor group with 3 sensors (N x =3), determine the estimated X coordinate (Xe) for each loading state i i ), and the second probability error (PE x ).

[0358] The following shows the obtained results in steps viii) and ix) for a system with four sensors (N x =4), and a plurality of (but not all) equations for some of the sensor groups of the sensor group, and a second probability error (PE x ):

[0359] Equation 1: Xe Eq1=(-2501.7xμ 桥5 )+(-299.5xμ 桥7 )+(2695.3xμ 桥10 )+(-1031.6xμ 桥19 )+12040.8

[0360] For the second probability error of Equation 1: PE x =48.0

[0361] Equation 2: Xe Eq2 =(-498.6xμ 桥5 )+(-569.2xμ 桥8 )+(-654.5xμ 桥9 )+(-979.6xμ 桥19 )+11555.4

[0362] For the second probability error of Equation 2: PE x =31.3

[0363] Equation 3: Xe Eq3 =(-2330.6xμ 桥13 )+(-580.9xμ 桥15 )+(-953.6xμ 桥17 )+(616.9xμ 桥19 )+11934.0

[0364] For the second probability error of Equation 3: PE x =38.4

[0365] Equation 4: Xe Eq4 =(-17814.8xμ 桥1 )+(4114.3xμ 桥7 )+(12056.8xμ 桥8 )+(1118.8xμ 桥11 )+8539.4

[0366] For the second probability error of Equation 4: PE x =98.4

[0367] Equation 5: Xe Eq5 =(-302.2xμ 桥3 )+(-2523.8xμ 桥10 )+(-393.1xμ 桥11 )+(-570.3xμ 桥17 )+11223.3

[0368] For the second probability error of Equation 5: PE x =16.6

[0369] Equation 6: Xe Eq6 =(-272.6xμ 桥3 )+(-807.4xμ 桥9 )+(-1508.3xμ 桥10 )+(-571.7xμ 桥17 )+11341.5

[0370] For the second probability error of Equation 6: PE x =16.7

[0371] Among them, Xe Eq1 represents the estimated X coordinate obtained using the first combination of sensors, namely sensors 5, 7, 10 and 19, and wherein the second probability error (PE) for each group of sensors has been obtained according to the following expression X )

[0372]

[0373] Where, s = 51, N w =3 and C E =0.6745, i represents the loading state.

[0374] According to the above results, equation 5 and equation 6 are selected due to their lower values ​​for probability error. The sensors (4) corresponding to the equations are sensors 3, 10, 11 and 17 for equation 5 and sensors 3, 9, 10 and 17 for equation 6.

[0375] The following shows the obtained results in steps viii) and ix) for a system with three sensors (N x =3) and a plurality of (not all) equations for some sensor groups of the sensor group, and a second probability error PE obtained for the sensor group X :

[0376] Equation 1: Xe Eq1 =(-274.9xμ 桥3 )+(-632.6xμ 桥9 )+(-570.8xμ 桥17 )+11428.6 The second probability error for equation 1: PE x =17.6

[0377] Equation 2: Xe Eq2 =(-6343.1xμ 桥1 )+(-21746.6xμ 桥2 )+(15172.6xμ 桥5 )+8477.4

[0378] For the second probability error of Equation 2: PE x =128.1

[0379] Equation 3: Xe Eq3 =(-924.9xμ 桥3 )+(6513.9xμ 桥5 )+(80.9xμ 桥11 )+10182.0For the second probability error of equation 3: PE x =145.2

[0380] Equation 4: Xe Eq4 =(-688.2xμ 桥1 )+(-559.8xμ 桥9 )+(-570.2xμ 桥17 )+11481.6 For the second probability error of equation 4: PE x =18.2

[0381] Equation 5: Xe Eq5 =(-667.9xμ 桥8 )+(-2024.6xμ 桥13 )+(-575.1xμ 桥17 )+11872.0For the second probability error of equation 5: PE x =25.1

[0382] Equation 6: Xe Eq6 =(-801.3xμ 桥5 )+(-834.1xμ 桥7 )+(-1015.7xμ 桥19 )+11903.2 The second probability error for equation 6: PE x =48.3

[0383] Among them, the second probability error PE for each sensor group has been obtained according to the following expression X

[0384]

[0385] Where, s = 51, N w =3 and C E =0.6745, i represents the loading state.

[0386] According to the above results, equation 1 and equation 4 are selected due to their lower values ​​for the second probability error. The sensors (4) corresponding to the equations are sensors 3, 9 and 17 for equation 1 and sensors 1, 9 and 17 for equation 4.

[0387] x) according to the previous w =4,N w =3) The second probability error (PE) determined X ), four second sensors are selected from a plurality of calibration sensors (4). The sensors included in the four sensors are sensors 1, 3, 9, 10, 11 and 17. The six sensors (4) are thus selected as installed sensors that can be used to determine the X coordinate of the center of gravity of the aircraft (6). Once the calibration step has been performed, the determination of the X coordinate of the center of gravity of the aircraft (6) can be performed based on the responses of the sensors (4) according to one or more of the following expressions:

[0388] Calculation Method 1: Xe App1 =(-302.2xμ 桥3 )+(-2523.8xμ 桥10 )+(-393.1xμ 桥11 )+(-570.3xμ 桥17 )+11223.3

[0389] Calculation 2: Xe App2 =(-272.6xμ 桥3 )+(-807.4xμ 桥9 )+(-1508.3xμ 桥10 )+(-571.7xμ 桥17 )+11341.5

[0390] Calculation 3: Xe App3 =(-274.9xμ 桥3 )+(-632.6xμ 桥9 )+(-570.8xμ 桥17 )+11428.6

[0391] Calculation 4: Xe App4 =(-688.2xμ 桥1 )+(-559.8xμ 桥9 )+(-570.2xμ 桥17 )+11481.6

[0392] xi) In this example, the first plurality of installed sensors includes calibration sensors in the first group of sensors selected in step vii) and calibration sensors in the second group of sensors selected in step x), specifically calibration sensors 1, 3, 5, 9, 10, 11 and 17.

[0393] Once the algorithm for determining the weight (W) of the aircraft (6) has been obtained in calibration step vii), the following is a check that the weight algorithm satisfies all loading states i. To this end, the weight residual value (εw i ) to verify the obtained weight residual value (εw i ) is small, where εw i =100×(We i -W i ) / W i .

[0394] The following tables 11A-11B to 19A-19B respectively show the estimated weights (We) obtained in the calibration step vi) for each weight calculation method and each loading state i. i )、We i Subtract W i The obtained value and the weight residual value (εw i In these tables, the weight residual value (εw i ) has been expressed as (error W) i .

[0395]

[0396] Table 11A

[0397]

[0398]

[0399] Table 11B

[0400]

[0401] Table 12A

[0402]

[0403]

[0404] Table 12B

[0405]

[0406] Table 13A

[0407]

[0408] Table 13B

[0409]

[0410] Table 14A

[0411]

[0412] Table 14B

[0413]

[0414]

[0415] Table 15A

[0416]

[0417] Table 15B

[0418]

[0419]

[0420] Table 16A

[0421]

[0422] Table 16B

[0423]

[0424] Table 17A

[0425]

[0426] Table 17B

[0427]

[0428] Table 18A

[0429]

[0430]

[0431] Table 18B

[0432]

[0433] Table 19A

[0434]

[0435] Table 19B

[0436] Furthermore, once the algorithm for determining the X coordinate of the center of gravity of the aircraft (6) has been obtained in the calibration step x), the following is a check that the algorithm for determining the X coordinate satisfies all loading states i. To this end, the error (error X) is determined. i To verify that the error obtained is small, where (error X)i =100×(Xe i -X i ) / 2561, where this error is calculated based on the overage chord length of the aircraft (6) in this example of 2561 mm.

[0437] The following tables 20A-20B to 28A-28B respectively show the estimated weights Xe obtained in the calibration step ix) for each weight calculation method and each loading state i. i 、Xe i Subtract X i The obtained value, and (error X) i .

[0438]

[0439] Table 20A

[0440]

[0441] Table 20B

[0442]

[0443] Table 21A

[0444]

[0445] Table 21B

[0446]

[0447]

[0448] Table 22A

[0449]

[0450] Table 22B

[0451]

[0452]

[0453] Table 23A

[0454]

[0455] Table 23B

[0456]

[0457] Table 24A

[0458]

[0459] Table 24B

[0460]

[0461] Table 25A

[0462]

[0463]

[0464] Table 25B

[0465]

[0466] Table 26A

[0467]

[0468]

[0469] Table 26B

[0470]

[0471] Table 27A

[0472]

[0473] Table 27B

[0474]

[0475]

[0476] Table 28A

[0477]

[0478] Table 28B

[0479] Thus, this example performed on an aircraft shows that the method of the invention provides an effective estimation of the value of the weight of the aircraft and the value of the X coordinate of the position of the center of gravity. Furthermore, it has been shown that the method allows obtaining a plurality of mathematical expressions for determining the value of the weight and the value of the position of the center of gravity. The fact that different mathematical expressions provide very similar results shows that the results are precise and reliable.

Claims

1. A method for determining the weight W of a structure and / or at least a first coordinate X of the position of the center of gravity, characterized in that The method comprises the following steps: a) measuring the responses μ of a plurality of first mounted sensors located in sensitive load points of the structure; and b) determining the weight W of the structure and / or the first coordinate X of the position of the centre of gravity based on the measured response μ as: Where W is the weight of the structure, X is the first coordinate of the position of the center of gravity of the structure on the projection plane, and k w and k x is a natural number, and μ is the response measured by the plurality of first installed sensors, wherein the subscript in the response μ indicates the sensor that has performed the measurement, wherein, To determine the weight W, use the number k w The first set of sensors installed is To determine the first coordinate X of the center of gravity, use a number k of x The second set of sensors of the installed sensor, and wherein, where j w =1,…k w The coefficient of where j x =1,…k x The coefficient of and the constant C w and C x is predetermined by applying the following calibration steps: i) positioning a plurality of calibration sensors in sensitive load points of the structure, wherein the number of the calibration sensors is m, where m is a natural number, ii) Using the detection weight Wp i The structure is loaded to obtain a loading state i, and a first coordinate X of the position of the center of gravity of the structure in the loading state i is measured. i and weight W i , iii) for each calibrated sensor r, measure the response μ associated with said loading state i r,i , where r = 1, ... m, r is a natural number, iv) repeating step ii) and step iii) for a plurality of said loading states i, wherein i=1, ...s, s is the number of said loading states, and s is a natural number, v) Selecting a calibration sensor group having at least two calibration sensors, and for each calibration sensor group, solving for a number P equal to or greater than N w +1 equation system, N w is the number of calibration sensors in the calibration sensor set, where the system of equations is: μ n,q is the measured response of the calibrated sensor, where n=1,...,N w , and W q is the weight associated with the corresponding loading state q, where q = 1, ..., P, The system of equations is solved by the least square method, thereby obtaining for n=1,...,N w The weight coefficient β n , and the weight constant C w , vi) For each calibration sensor set, the estimated weight We for each loading state i i Determined as: Among them, μ n,i is the response of the calibration sensor in the calibration sensor set associated with loading state i, vii) Select the first probability error PE w is the smallest first set of calibrated sensors, where PE w yes: s is the total number of loading states, N w is the number of calibration sensors in the calibration sensor set, and C E is a positive real number, viii) selecting a calibration sensor group having at least two calibration sensors, and for each calibration sensor group, solving for a number P equal to or greater than N x +1 equation system, N x is the number of calibration sensors in the calibration sensor set, where the system of equations is: μ n,q is the measured response of the calibrated sensor, where n=1,...,N x , and X q is the first coordinate of the center of gravity associated with the corresponding loading state q, where q=1,...,P, The system of equations is solved by the least square method, thereby obtaining for n=1,...,N x X coefficient γ n , and X constant C x , ix) For each calibration sensor set, the estimated first coordinate Xe of the center of gravity for each loading state i i Determined as: Among them, μ n,i is the response of the calibration sensor in the calibration sensor set associated with loading state i, x) Select the second probability error PE X is the smallest second set of calibration sensors, where PE X yes: s is the total number of loading states, N x is the number of calibration sensors in the calibration sensor set, and C E is a positive real number, xi) selecting a plurality of calibration sensors as the plurality of first installed sensors, the plurality of calibration sensors comprising: said first set of calibration sensors selected in step vii), and said second set of calibration sensors selected in step x), Among them, k w is the number of sensors in the first set of calibration sensors, and k x is the number of sensors in the second set of calibration sensors.

2. The method according to claim 1, characterized in that The method further comprises determining a second coordinate Y of the position of the center of gravity of the structure, wherein the second coordinate Y of the position of the center of gravity of the structure is determined based on the measured responses μ of the plurality of first mounted sensors as: where Y is the second coordinate of the position of the center of gravity of the structure on the projection plane, k y is a natural number, and μ is a response measured by the plurality of first installed sensors, wherein the subscript in the response μ indicates the sensor that has performed the measurement, In order to determine the second coordinate Y of the position of the center of gravity, a number k of y The third set of sensors of the installed sensors, and wherein, at least after steps i) to iv), the Y coefficient is predetermined by applying the following calibration steps and Y constant C y , where j y =1,…k y , wherein step ii) further comprises measuring a second coordinate Y of the position of the center of gravity of the structure in each loading state i i : viii') Selecting a calibration sensor group having at least two calibration sensors, and for each calibration sensor group, solving the problem of having a number P equal to or greater than N y +1 equation system, N y is the number of calibration sensors in the calibration sensor set, where the system of equations is: μ n,q is the measured response of the calibrated sensor, where n=1,...,N y , and Y q is the second coordinate of the center of gravity associated with the corresponding loading state q, where q=1,...,P, The system of equations is solved by the least square method, thereby obtaining for n=1,...,N y Y coefficient τ n , and the Y constant C y , ix') For each calibration sensor set, the estimated second coordinate Ye of the center of gravity for each loading state i i Determined as: Among them, μ n,i is the response of the calibration sensor in the calibration sensor set associated with loading state i, and x') selects the third probability error PE Y is the smallest third group of calibrated sensors, where PE Y yes: s is the total number of loading states, N y is the number of calibration sensors in the calibration sensor set, and C E is a positive real number, wherein said first plurality of installed sensors also includes said third set of calibration sensors selected in step x′), and wherein k y is the number of sensors in the third set of calibration sensors.

3. The method according to claim 2, characterized in that The method further comprises the following steps: c) measuring the responses μ' of a second plurality of mounted sensors located in at least one lifted surface h of the structure, and d) The corrected weight W of the structure 校正 and / or the corrected position of the center of gravity of the structure (X 校正 ,Y 校正 ) is determined as: Where W is the calculated weight of the structure, (X,Y) is the calculated location of the center of gravity of the structure, where M is the number of lifting surfaces considered at step c), Among them, V h ' is the vertical component of the resultant force exerted on the lifting surface h of the structure, Among them, X h ' and Y h ' are respectively the vertical components V of the resultant force h 'Through the X and Y coordinates, where for each lifting surface h, V h ', X h ' and Y h ' is determined based on the measured response μ' as: Wherein, μ' is the response measured by the plurality of second mounted sensors, the subscript in the response μ' indicates the sensor that has performed the measurement, L v , L x and L y is a natural number, Among them, W, V' and W 校正 are expressed in the same axis system; X, X' and X 校正 are expressed according to the same coordinate system, and Y, Y' and Y 校正 is expressed according to the same coordinate system, And among them, To determine V', use the number L v The fourth group of sensors installed is the sensor, To determine X', use the number L x The fifth set of sensors installed is To determine Y', use the number L y The installed sensor is a sixth group of sensors, and wherein, where j v =1,...,L v The coefficient of where j x =1,...,L x The coefficient of and where j y =1,...,L y The coefficient τ' jy and the constant C v '、C x '、C y ' is predetermined by applying the following calibration steps: si) positioning 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 detection force to the at least one lifting surface h of the structure, thereby obtaining a force state f, and measuring the vertical component V' of the resultant force under the force state f respectively f , providing the vertical component V' of the resultant force f The X and Y coordinates of the pass; s-iii) for each calibrated sensor r, measuring the response μ′ associated with the force state f r,f , where r = 1, ..., m', r is a natural number; s-iv) repeating steps s-ii) and s-iii) for a plurality of force states f, where f=1, ..., s', s' being the number of force states, wherein for each force state f, a different probing force is applied to the at least one lifting surface h, and s' being a natural number; sv) select a calibration sensor group having at least two calibration sensors, and for each calibration sensor group, solve the problem of having a number P greater than N v +1 equation system, N v is the number of calibration sensors in the calibration sensor set, where the system of equations is: where μ' n,q is the measured response of the calibrated sensor, where n=1,...,N v , and V' q is the vertical component of the resultant force measured for the corresponding force state q, where q = 1, ..., P, The system of equations is solved by the least square method, thereby obtaining for n=1,...,N v The vertical force coefficient β n ', and the constant C v '; s-vi) For each calibration sensor set, the estimated vertical force Ve for each force state f is f 'Determined as: Among them, μ' n,f is the response of a calibration sensor in the calibration sensor set associated with the force state f; s-vii) Select the fourth probability error PE' v is the smallest fourth group of calibration sensors, where PE' v yes: s' is the total number of force states, N v is the number of calibration sensors in the calibration sensor set, and C E is a positive real number; s-viii) Select a calibration sensor group having at least two calibration sensors, and for each calibration sensor group, solve the problem of having a number P equal to or greater than N x +1 equation system, N x is the number of calibration sensors in the calibration sensor set, where the system of equations is: μ' n,q is the measured response of the calibrated sensor, where n=1,...,N x , and X q ' is the measured vertical component V of the resultant force' q The X coordinate associated with the corresponding force state q, where q = 1, ..., P, The system of equations is solved by the least square method, thereby obtaining for n=1,...,N x X coefficient γ n ', and X constant C x '; s-ix) For each calibration sensor group, the vertical component V' of the resultant force for each force state f is f The estimated X coordinate Xe of the f 'Determined as: Among them, μ' n,f is the response of the calibration sensor in the selected calibration sensor set associated with the force state f; sx) selects the fifth probability error PE' X is the smallest fifth set of calibrated sensors, where PE' X yes: s' is the total number of force states, N x is the number of calibration sensors in the calibration sensor set, and C E is a positive real number; s-xi) Select a calibration sensor group having at least two calibration sensors, and for each calibration sensor group, solve the problem of having a number P equal to or greater than N y +1 equation system, N y is the number of calibration sensors in the calibration sensor set, where the system of equations is: μ' n,q is the measured response of the calibrated sensor, where n=1,...,N y , and Y q ' is the measured vertical component V of the resultant force' q The Y coordinate associated with the corresponding force state q, where q = 1, ..., P, The system of equations is solved by the least square method, thereby obtaining for n=1,...,N y Y coefficient τ n ', and Y constant C y '; s-xii) For each calibration sensor group, the vertical component V' of the resultant force for each force state f is f The estimated Y coordinate Ye passed through f 'Determined as: Among them, μ' n,f is the response of the calibration sensor in the selected calibration sensor set associated with the force state f; s-xiii) Select the sixth probability error PE' Y is the smallest sixth set of calibration sensors, where PE' Y yes: s' is the total number of force states, N y is the number of calibration sensors in the calibration sensor set, and C E is a positive real number; s-xiv) selecting a plurality of calibration sensors as the plurality of second installed sensors, the plurality of calibration sensors comprising: said fourth set of calibration sensors selected in step s-vii); said fifth set of calibration sensors selected in step sx); and said sixth set of calibration sensors selected in step s-xiii), Among them, L v is the number of sensors in the fourth set of calibration sensors, L x is the number of sensors in the fifth set of calibration sensors, and L y is the number of sensors in the sixth set of calibration sensors.

4. The method according to any one of claims 1 to 3, characterized in that The method comprises: After step vii) and / or step x), it is verified for at least one loading state i that: The first set of calibration sensors satisfies the weight residual value εw i is less than a first predetermined threshold, in, and / or The second set of calibration sensors satisfies the X-coordinate residual value εx i is less than a second predetermined threshold, in, 5. The method according to claim 2 or 3, characterized in that: The method comprises: After step x') it is verified for at least one loading state i that: The third set of calibration sensors satisfies the Y coordinate residual value εy i is less than a third predetermined threshold, in, 6. The method according to any one of claims 1 to 3, characterized in that At each iteration of step ii), the probe weight Wp is used i The structure is loaded in steps of predetermined percentages of the maximum allowable weight of the structure.

7. The method according to any one of claims 1 to 3, characterized in that The structure is a ground vehicle.

8. The method according to claim 7, characterized in that At least one of the sensitive load points is located in at least one bulkhead of the ground vehicle.

9. The method according to claim 7, characterized in that: The ground transportation vehicle is an aircraft.

10. The method according to claim 9, characterized in that At least one of said sensitive load points is located in at least one landing gear bulkhead.

11. The method according to claim 9, characterized in that At least one of said sensitive load points is located in a nose landing gear pin.

12. The method according to claim 9, characterized in that At least one of the sensitive load points is located in a main landing gear pin.

13. The method according to any one of claims 1 to 3, characterized in that In the calibration step ii) a first coordinate X of the position of the center of gravity is measured using a scale and / or a jack with a load cell. i and / or weight W i .

14. The method according to any one of claims 1 to 3, characterized in that At step vii), a plurality of the first group of calibration sensors are selected that satisfy the condition that the first probability error is the smallest, and / or, At step x), a plurality of the second group of calibration sensors that satisfy the condition that the second probability error is minimum are selected.

15. The method according to claim 2 or 3, characterized in that: At step x'), a plurality of the third group of calibration sensors that satisfy the condition that the third probability error is the smallest are selected.

16. The method according to claim 13, characterized in that In the calibration step ii) the first coordinate X of the position of the centre of gravity is measured using three hydraulic jacks. i and / or weight W i .

17. A system configured to determine at least a first coordinate of the position of the weight W and / or the center of gravity of a structure, characterized in that The system comprises: a plurality of mounted sensors located on the structure; a data acquisition module configured to record data from the plurality of mounted sensors located on the structure; and A data processing device configured to perform at least step b) of the method according to any one of claims 1 to 16.

18. A means of transport, characterized in that: The vehicle comprises the system according to claim 17.

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