A method for detecting out-of-tolerance of quay crane cantilever track based on strain measurement

Abstract

The present invention provides a method for detecting out-of-tolerance (OTO) of a quay crane cantilever track based on strain measurement. The method constructs a unified coordinate system for two cantilever beams, divides each cantilever beam into multiple monitoring units, and constructs an analysis unit within each monitoring unit. After monitoring and acquiring strain information from each analysis unit, the deformation information of each cantilever beam is calculated and acquired. The deformation information of the two cantilever beams is compared to analyze and acquire out-of-tolerance information of the cantilever track. The method divides each cantilever beam into multiple monitoring units and constructs analysis units for each unit. A strain mapping relationship associated with the actual deformation is constructed for each analysis unit. After monitoring and analyzing each analysis unit, the strain information of each analysis unit can be acquired. After assembling and analyzing the units, the deformation information of each cantilever beam can be acquired. Furthermore, by comparing and analyzing the deformation information of the two cantilever beams with standard data, it can be determined whether the cantilever track has an OTO problem. The method has the advantages of saving time and effort, and being stable and reliable.

Description

Technical Field

[0001] The invention relates to the field of deformation monitoring of double tracks of a quay crane cantilever, and in particular to a method for detecting out-of-tolerance of quay crane cantilever tracks based on strain measurement. Background Art

[0002] Shore-to-shore container cranes, also known as quay cranes, are crucial equipment for port container loading and unloading operations. Due to their prolonged, heavy-load operation, quay cranes are prone to structural deformation, which not only seriously impacts operational efficiency but can also pose significant safety risks. Track deviations caused by track deformation are one of the most common and significant issues in loading and unloading operations.

[0003] Quay cranes typically have two sets of tracks: running tracks and cantilever tracks. The running tracks are installed directly on the ground and bear the entire weight of the quay crane. Their deformation is primarily caused by overall deformation of the foundation, particularly settlement of the seaward side. The running tracks have a longer deformation cycle, allowing for long-term offline testing to measure and adjust deviations. The cantilever tracks, on the other hand, are typically tens of meters above the shore and are used to carry trolleys for lifting containers. Due to their shorter deformation cycle, cantilever tracks are more difficult to measure, and currently rely primarily on human inspections, making it difficult to detect track deviations in unmanned environments. Summary of the Invention

[0004] In order to solve the problems existing in the background technology, the present invention proposes a method for detecting out-of-tolerance of a quay crane cantilever track based on strain measurement.

[0005] A method for detecting out-of-tolerance of a quay crane cantilever track based on strain measurement comprises the following steps:

[0006] S100, constructing a unified coordinate system for the two cantilever beams of the cantilever track;

[0007] S200, dividing the surface of each cantilever beam into a plurality of adjacent monitoring units, and constructing an analysis unit in each monitoring unit;

[0008] S300, after monitoring and acquiring the strain detection information of each analysis unit, calculating and acquiring the deformation information of each cantilever beam;

[0009] S400: Compare deformation information of the two cantilever beams, analyze and obtain deviation information of the cantilever track.

[0010] Based on the above, in step S200, the analysis unit constructs a deformation field at any position corresponding to the monitoring unit, and constructs a theoretical strain corresponding to any point on the surface of the cantilever beam.

[0011] Based on the above, step S300 includes the following steps:

[0012] S310, setting a strain sensor on the monitoring unit, and obtaining strain detection information of the analysis unit through the strain sensor;

[0013] S320, obtaining a deformation mapping model of the analysis unit in combination with the theoretical strain corresponding to the analysis unit;

[0014] S330, constructing the relationship between the theoretical strain and the measured strain of the analysis unit through the least square variation principle, and obtaining the mapping relationship of the single analysis unit;

[0015] S340. A unified assembly matrix is ​​constructed for all monitoring units of each cantilever beam, and after constructing a global deformation relationship of each cantilever beam according to the deformation mapping relationship in step S330, the deformation information of each cantilever beam is calculated based on the strain information of each analysis unit obtained by monitoring.

[0016] Based on the above, the deformation field at any position in the monitoring unit is:

[0017]

[0018] u z (x,y,z)=w(x,y)

[0019] Where u x (x,y,z),u y (x,y,z),u z (x, y, z) represents the deformation of any point in the plate structure along the three axial directions, u(x, y), v(x, y), w(x, y) represent the deformation of the neutral surface of the plate structure along the x, y, z directions, respectively, z represents the distance coordinate from any position to the neutral surface, They represent the rotation effects of the neutral plane along the x and y directions respectively.

[0020] Based on the above, the theoretical strain at any point P in the deformation field is expressed as:

[0021] ε(x,y,z)={ε x ,ε y ,ε z ,γ xy ,γ xz ,γ yz} T =Lu

[0022] Where ε(x, y, z) is the strain vector of any point in the analysis unit, u={u x (x,y,z),u y (x,y,z)} T represents the three-dimensional deformation vector of any point in the analysis unit, and L represents the differential operator.

[0023] Based on the above, in step S320, the deformation mapping model includes a plane strain model and a transverse shear strain model. The plane strain model is represented by e (s) (u e )=m(θ)L1u e , the transverse shear strain model is expressed as g (s) (u e )=L2u e ,in:

[0024]

[0025] Where, ε e Representation and analysis of the deformation freedom of the four nodes of the unit The strain vector, Represented as a submatrix of the transformation matrix and L; and denote plane strain and transverse shear strain, respectively; Indicates any position within the analysis unit (x i ,y i ) makes an angle θ with the x direction i The measured strain, Represents the strain component of the measuring point, m(θ)={cos 2 θ i ,sin 2 θ i ,sinθ i cosθ i} is a vector representing the angle of the strain sensor.

[0026] Based on the above, in step S330, the relationship between the theoretical strain and the measured strain of the analysis unit is expressed as:

[0027]

[0028] in, represents the inverse proportional boundary finite element functional symbol, e (s) (u e ), g (s) (u e ) represent the theoretical plane strain and transverse shear strain of the analysis unit, represents the planar measured strain of the analysis unit, represents the transverse shear measurement strain of the analysis unit, w e ,w g denote the least square weight coefficients of plane strain and transverse shear strain, respectively.

[0029] Based on the above, in step S330, the local and global mapping relationship of a single analysis unit is expressed as:

[0030]

[0031] in, represents the inverse-scale boundary finite element class stiffness matrix, represents the inverse-scale boundary finite element class load vector, Represents the deformation degrees of freedom of the inversely proportional boundary finite element nodes.

[0032] Based on the above, in step S340, the assembly matrix is ​​expressed as:

[0033]

[0034] Among them, k nn Represents the stiffness matrix, M, N and O represent the abbreviation of the stiffness matrix, u n represents the node displacement matrix, f n represents the strain matrix.

[0035] Based on the above, in step S340, after the deformation information of the two cantilever beams is obtained, the deformation information of the cantilever track is obtained, and then compared and analyzed according to the standard data information of the cantilever track to determine whether the deformation of the cantilever track causes the track to exceed the tolerance.

[0036] Compared with the existing technology, the present invention has outstanding substantial features and significant progress. Specifically, the present invention divides each cantilever beam into multiple monitoring units and constructs analysis units respectively, and constructs a strain mapping relationship associated with the actual deformation for each analysis unit. After monitoring and analyzing each analysis unit, the strain information of each analysis unit can be obtained. After assembling and analyzing the strain information of each analysis unit, the deformation information of each cantilever beam can be obtained. Then, after comparing and analyzing the deformation information of the two cantilever beams with the standard data, it can be determined whether the cantilever track has an out-of-tolerance problem. It has the advantages of saving time and effort, being stable and reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic block diagram of the process structure of the present invention;

[0038] Figure 2 This is a schematic structural diagram of the quay crane of the present invention;

[0039] Figure 3 Schematic diagram of the structure of the monitoring unit of the present invention;

[0040] Figure 4 It is a three-dimensional structural configuration diagram based on the ratio boundary finite element of the present invention;

[0041] Figure 5 Schematic diagram of the installation of the plate structure and strain sensor of the present invention;

[0042] Figure 6 It is a structural schematic diagram of the measuring surface of a single cantilever beam of the present invention.

[0043] Explanation of the accompanying symbols: 1. Quay crane; 2. Cantilever beam; 3. Monitoring unit; 4. Strain sensor; 5. Inner surface of cantilever beam; 6. Outer surface of cantilever beam; 7. Neutral plane. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0045] In reality, the cantilever track of the quay crane 1 includes two cantilever beams 2, on which a track for a trolley for lifting containers is provided, such as Figure 2 shown.

[0046] like Figure 1 As shown in FIG, a method for detecting out-of-tolerance of a quay crane cantilever track based on strain measurement is specifically as follows:

[0047] The cantilever beam of the quay crane is taken as the object to be measured. According to the characteristics of the cantilever beam structure of the quay crane, the cantilever beam structure is divided into multiple monitoring units 3. Each monitoring unit 3 is regarded as a pseudo plate unit / boundary surface unit / boundary surface structure. Each unit of the pseudo plate unit has four nodes (i.e., the four corner points n-1, n-2, n-3 and n-4 of the square), as shown in Figure 2. Figure 3 As shown, a node includes six degrees of freedom (two degrees of freedom along the x-axis, y-axis, and z-axis), and is analyzed using scaled boundary finite element theory. The scaled boundary finite element method is a structural analysis method that describes the deformation field characteristics of a structure's boundary domain by introducing a scaling factor. In this example, it is associated with the boundary surface theory strain and deformation degrees of freedom.

[0048] Depend on Figure 4 Based on the three-dimensional structural configuration diagram of the proportional boundary finite element, the position of any point X on the geometric boundary domain can be expressed as:

[0049]

[0050] Among them, x(ξ,η), y(ξ,η), z(ξ,η) are the position coordinates of the structure boundary along the three axial directions, ζ is the scaling factor coordinate along the radial direction, (ξ,η) is the isoparametric coordinate of the boundary element plane, x a ={x1,x2...,x4} T ,y a={y1,y2...,y4} T , z a ={z1,z2...,z4} T Represent the coordinates of the four nodes of the boundary surface element in the global coordinate system, (x0, y0, z0) represents the position coordinates of the scaling center, and N(ξ,η) is the element shape function interpolation matrix, which can be expressed as:

[0051]

[0052] Where N i (ξ,η), (i=1,2...m) represents the element shape function of m nodes.

[0053] Based on the classical Kirchhoff plate structure theory, the deformation field at any position in the plate structure of the pseudo-plate element is:

[0054]

[0055] u z (x,y,z)=w(x,y)

[0056] Where u x (x,y,z),u y (x,y,z),u z (x, y, z) represent the deformation of any point in the plate structure along the three axial directions, u(x, y) and v(x, y) represent the deformation of the neutral surface 7 of the plate structure along the x and y directions, w(x, y) represents the deformation of the neutral surface 7 of the plate structure along the z direction, and z represents the distance coordinate from any position to the neutral surface 7. They represent the rotation effects of the neutral plane 7 along the x and y directions respectively. The plate structure is as follows Figure 5 shown.

[0057] According to the elastic assumption of cantilever beam structure deformation and strain, the theoretical strain of any point P on the cantilever beam surface is expressed as:

[0058] ε(x,y,z)={ε x ,ε y ,ε z ,γ xy ,γ xz ,γ yz} T =Lu

[0059] Where ε(x, y, z) is the strain vector of any point on the cantilever beam surface, u={u x (x,y,z),u y (x,y,z)} T represents the three-dimensional deformation vector of any point in the plate structure, and L represents the differential operator.

[0060] According to the method of describing the three-dimensional deformation field of the cantilever beam structure by using the scaled boundary finite element, the inner surface 5 or the outer surface 6 of the cantilever beam structure is selected as the structural boundary surface. The scaling center coincides with the origin of the global coordinate system. The geometric position of the point P inside the boundary surface element of the cantilever beam can be expressed as:

[0061]

[0062] Where N i (ξ,η), (i=1,2…4) represents the cubic isoparametric element shape function. By constructing the Jacobian matrix J, the Jacobian transformation of the differential operator L is performed. The transformation relationship between the partial differential under the global coordinate system (x, y, z) and the local coordinate system (ξ,η,ζ) can be expressed as:

[0063]

[0064] Where, Represents the partial derivatives along the three axial directions of x, y, and z, respectively, J -1 represents the inverse of the Jacobian matrix, Denote the partial derivatives along the global coordinate system ξ, η, ζ respectively. From this, the differential operator L can be expressed as Where |J| represents the determinant of the Jacobian matrix, b 1 ,b 2 ,b 3 Represents the matrix associated with the derivatives of the shape functions for the boundary surface elements.

[0065] The strain of the boundary surface unit of the cantilever beam is detected by the strain sensor 4, and the deformation mapping model is obtained by combining the corresponding theoretical strain. The strain vector based on the unit form can be expressed as

[0066]

[0067] Where, ε e Denotes the degree of freedom of deformation of the element nodes The strain vector, Represents the transformation matrix and the submatrix of L; and denote plane strain and transverse shear strain, respectively.

[0068] The strain at any position in the xy plane within the monitoring unit can be expressed as:

[0069]

[0070] Where, Indicates any position within the unit (x i ,y i ) makes an angle θ with the x directioni The measured strain, Represents the strain component of the measuring point, m(θ)={cos 2 θ i ,sin 2 θ i ,sinθ i cosθ i} is a vector representing the angle of the strain sensor.

[0071] The relationship between the deformation freedom of the xy plane and the unit node can be obtained from the strain vector based on the unit form and the strain at any position on the surface, which is expressed as e (s) (u e )=m(θ)L1u e .e (s) (u e ) is the plane strain of the boundary surface element; the relationship between the transverse shear strain and the degree of freedom of the element node deformation can be expressed as g (s) (u e )=L2u e , g (s) (u e ) represents the transverse shear strain of the boundary surface unit. Therefore, the strain field of the cantilever beam structure can be calculated by simply measuring the strain detection information of the structure boundary surface. The installation method of the strain sensor is as follows: Figure 5 As shown, the measurement surface of the cantilever beam structure is as follows Figure 6 shown.

[0072] The relationship between the theoretical strain and the measured strain of the cantilever beam structure boundary surface is constructed by the least square variation principle and expressed as:

[0073]

[0074] in, represents the inverse proportional boundary finite element functional symbol, e (s) (u e ), g (s) (u e ) represent the theoretical plane strain and transverse shear strain of the boundary surface, represents the measured strain on the boundary surface element plane, represents the transverse shear measurement strain of the boundary surface element, w e ,w g denote the least square weight coefficients of plane strain and transverse shear strain, respectively.

[0075] Find the node degree of freedom u e The partial derivative of , based on the proportional boundary finite element theory, can be expressed as in, represents the inverse-scale boundary finite element-like stiffness matrix, represents the inverse-scale boundary finite element class load vector, Represents the inverse-proportional boundary finite element node deformation degrees of freedom.

[0076] Substituting the initial boundary conditions, the solution can be directly obtained as U = K -1 F, U represent the displacement matrix, K -1 represents the inverse matrix of the stiffness matrix, and F represents the vector strain matrix. The operation is similar to the stiffness matrix operation in finite element theory. To facilitate the overall operation of the cantilever beam structure, it is necessary to assemble the relationship matrices of all monitoring units of the cantilever beam into a total matrix. This way, the deformation data of the entire cantilever beam can be obtained at one time.

[0077] Assembly Matrix Calculation and Track Out-of-Tolerance Detection: Each monitoring unit of a single cantilever beam structure is assembled to form an assembly matrix. By calculating the deformation of the cantilever beam structure in the assembly matrix, the deformation of each cantilever beam structure is determined, corresponding to the deformation of a single track. By comparing the deformation data of the two tracks, it can be determined whether the track has exceeded the allowable deformation range, that is, whether there is an out-of-tolerance situation.

[0078] According to the structure of a single track, it is only necessary to find out the matrix conversion relationship of a monitoring unit and then simply assemble the whole unit. in is a 24×24 square matrix, is a 24×1 column vector, which can be obtained by coordinate transformation

[0079]

[0080] Among them, T moment is a transformation matrix of order 24, and The matrix dimensions correspond.

[0081] The stiffness matrix for monitoring unit 1 is as follows

[0082]

[0083] When assembling based on common nodes later, each unit matrix needs to be expanded to the overall matrix dimension and then superimposed. Taking unit 1 as an example, its expansion form is as follows:

[0084]

[0085] Among them, the A matrix is ​​a sixth-order zero matrix, k ij The (i, j = 1, 2, 3, 4) matrix is ​​a sixth-order matrix. The matrix for monitoring unit n (when n is an even number) is as follows

[0086]

[0087] Among them, kij (i=(n-3),(n-2),(n-1),nj=1,2,3,4.), u i (i=(n-3),(n-2),(n-1),n.) and f i (i=(n-3),(n-2),(n-1),n.) is a six-dimensional vector, and the node order is the counterclockwise order of the unit nodes. The final assembly matrix is ​​as follows:

[0088]

[0089] Among them, M, N and O represent the abbreviation of the stiffness matrix, k ij (i=1,2,…,nj=1,2,3,4.) represents the stiffness matrix, u i (i=1,2,…,n.) represents the node displacement matrix, f i (i=1,2,…,n.) represents the strain matrix. The expanded form is

[0090]

[0091] A unified coordinate system is constructed for the two cantilever beams of the cantilever track. The individual monitoring units are assembled in the coordinate system. The monitoring units are assembled into an overall matrix based on the common nodes (the common nodes of two adjacent monitoring units). Each unit matrix is ​​first expanded to the overall dimension and then superimposed. It is important to pay attention to the order of the nodes, and the unit order should be adjusted as needed. After the grouped units are assembled into the overall structural matrix, it is generally singular and requires boundary adjustment to solve. The fixed end needs to be determined and then brought into the equation to solve, and the displacement data of other nodes can be obtained. The superimposed assembly matrix is ​​converted to the global coordinate system to obtain the deformation of the single-sided cantilever beam. The same calculation is performed on the cantilever beams on both sides to obtain the deformation of the cantilever beams on both sides, that is, the deformation of the cantilever track. Then, the deformation of the two tracks is compared according to the standard data to see if it causes the track to exceed the tolerance.

[0092] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

Claims

1. A method for detecting out-of-tolerance of a quay crane cantilever track based on strain measurement, characterized in that: Including steps: S100, constructing a unified coordinate system for the two cantilever beams of the cantilever track; S200, dividing the surface of each cantilever beam into a plurality of adjacent monitoring units, and constructing an analysis unit in each monitoring unit; S300, after monitoring and acquiring the strain detection information of each analysis unit, calculating and acquiring the deformation information of each cantilever beam; S400, comparing deformation information of the two cantilever beams, analyzing and obtaining deviation information of the cantilever track; In step S200, the analysis unit constructs a deformation field at any position corresponding to the monitoring unit and constructs a theoretical strain corresponding to any point on the cantilever beam surface; Step S300 includes the following steps: S310, after a strain sensor is provided on the monitoring unit and strain detection information of the analysis unit is obtained through the strain sensor; S320, obtaining a deformation mapping model of the analysis unit in combination with the theoretical strain corresponding to the analysis unit; S330, constructing the relationship between the theoretical strain and the measured strain of the analysis unit through the least square variation principle, and obtaining the mapping relationship of the single analysis unit; S340, uniformly constructing an assembly matrix for all monitoring units of each cantilever beam, and constructing a global deformation relationship of each cantilever beam based on the deformation mapping relationship in step S330, and then calculating the deformation information of each cantilever beam based on the strain information of each analysis unit obtained through monitoring; The deformation field at any position within the monitoring unit is: u z (x,y,z)=w(x,y) Where u x (x,y,z),u y (x,y,z),u z (x, y, z) represents the deformation of any point in the plate structure along the three axial directions, u(x, y), v(x, y), w(x, y) represent the deformation of the neutral surface of the plate structure along the x, y, z directions, respectively, z represents the distance coordinate from any position to the neutral surface, Respectively represent the rotation effect of the neutral plane along the x and y directions; The theoretical strain at any point P on the cantilever beam surface is expressed as: ε(x,y,z)={ε x ,he y ,he z ,c xy ,c xz ,c yz } T =Lu Where ε(x, y, z) is the strain vector of any point in the analysis unit, u={u x (x,y,z),u y (x,y,z)} T represents the three-dimensional deformation vector of any point in the analysis unit, and L represents the differential operator.

2. The method for detecting out-of-tolerance of a quay crane cantilever track based on strain measurement according to claim 1, characterized in that: In step S330, the relationship between the theoretical strain and the measured strain of the analysis unit is expressed as: in, represents the inverse proportional boundary finite element functional symbol, e (s) (u e ), g (s) (u e ) represent the theoretical plane strain and transverse shear strain of the analysis unit, represents the planar measured strain of the analysis unit, represents the transverse shear measurement strain of the analysis unit, w e ,w g denote the least square weight coefficients of plane strain and transverse shear strain, respectively. Represents the deformation degrees of freedom of the inversely proportional boundary finite element nodes.

3. The method for detecting out-of-tolerance of a quay crane cantilever track based on strain measurement according to claim 1, characterized in that: In step S330, the local and global mapping relationship of a single analysis unit is expressed as: in, represents the inverse-scale boundary finite element class stiffness matrix, represents the inverse-scale boundary finite element class load vector, Represents the deformation degrees of freedom of the inversely proportional boundary finite element nodes.

4. The method for detecting out-of-tolerance of a quay crane cantilever track based on strain measurement according to claim 1, characterized in that: In step S340, the assembly matrix is ​​expressed as: Among them, k nn Represents the stiffness matrix, M, N and O represent the abbreviation of the stiffness matrix, u n represents the node displacement matrix, f n represents the strain matrix.

5. The method for detecting out-of-tolerance of a quay crane cantilever track based on strain measurement according to claim 1, characterized in that: In step S340, after the deformation information of the two cantilever beams is obtained, the deformation information of the cantilever track is obtained, and then a comparative analysis is performed based on the standard data information of the cantilever track to determine whether the deformation of the cantilever track causes the track to exceed the tolerance.

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