A bridge model design method and system based on static and dynamic information fusion

Abstract

The application relates to a bridge model design method and system based on static and dynamic information fusion, and belongs to the technical field of bridge design. The bridge model design method based on static and dynamic information fusion comprises the following steps: obtaining physical quantities of a prototype and a scale model of a bridge; determining static dimensionless parameters based on the physical quantities and a dimensional analysis method; establishing a multi-degree-of-freedom motion equation; determining dynamic dimensionless parameters based on the multi-degree-of-freedom motion equation and the physical quantities; determining a similarity relationship between the prototype and the scale model based on the static dimensionless parameters and the dynamic dimensionless parameters; performing distortion analysis on the scale model based on the similarity relationship, determining an actual similarity relationship between the prototype and the scale model, and completing scale model design based on the actual similarity relationship.

Description

Technical Field

[0001] This invention relates to the field of bridge technology, and in particular to a bridge model design method and system based on static and dynamic information fusion. Background Technology

[0002] Structural testing is an effective method to understand the internal force distribution, working state, and failure mode of a structure under various loads. However, prototype testing conducted directly on actual structures has problems such as long testing cycles, unstable on-site testing conditions, and the inability to conduct destructive tests. Scaled-down model testing has the advantages of low excitation and testing costs, controllable testing conditions, and repeatable multi-condition testing. It is an effective method to simulate the characteristics of actual structures and ensure structural safety.

[0003] The key to scaled-down model testing lies in establishing a scaled-down model that reflects the static and dynamic characteristics of the actual structure. Its core is to establish the similarity relationship between the prototype structure and the scaled-down structure.

[0004] Existing research mainly focuses on the static or dynamic similarity of models, with few studies considering the integration of static and dynamic similarity relationships. Moreover, most of the models involved are simple in structure and have a large scale. Small-scale models of complex structures are subject to dual constraints of similarity relationships and manufacturing processes in terms of cross-section design, node connection, and boundary condition setting. Summary of the Invention

[0005] In view of this, it is necessary to provide a bridge model design method and system based on static and dynamic information fusion to solve the technical problem of considering static similarity or dynamic similarity separately when designing scaled-down models.

[0006] To address the aforementioned problems, this invention provides a bridge model design method based on static and dynamic information fusion, comprising:

[0007] Obtain the physical quantities of the prototype and scaled-down model of the bridge, and determine the static dimensionless parameters based on the physical quantities and dimensional analysis method.

[0008] Establish multi-degree-of-freedom motion equations, and determine the dynamic dimensionless parameters based on the multi-degree-of-freedom motion equations and the physical quantities;

[0009] The similarity relationship between the prototype and the scaled-down model is determined based on the static dimensionless parameters and the dynamic dimensionless parameters. Distortion analysis is performed on the scaled-down model based on the similarity relationship to determine the actual similarity relationship between the prototype and the scaled-down model. The scaled-down model design is completed based on the actual similarity relationship.

[0010] In one possible implementation, determining the static dimensionless parameters based on the physical quantity using dimensional analysis includes:

[0011] A material mechanics model is constructed, and similarity constants between the prototype and the scaled-down model are determined based on the material mechanics model and the physical quantities. The physical quantities include at least length, mass, time, velocity, and density, and the similarity constants include elastic modulus, geometric dimensions, response acceleration, Poisson's ratio, response displacement, cross-sectional area, cross-sectional moment of inertia, load, mass, frequency, and density.

[0012] Based on the aforementioned similarity constant, the static dimensionless parameters are determined using dimensional analysis. These static dimensionless parameters include a first static dimensionless parameter, a second static dimensionless parameter, a third static dimensionless parameter, a fourth static dimensionless parameter, a fifth static dimensionless parameter, a sixth static dimensionless parameter, a seventh static dimensionless parameter, and an eighth static dimensionless parameter.

[0013] In one possible implementation, the formula for calculating the static dimensionless parameter is:

[0014] ,

[0015] ,

[0016] ,

[0017] ,

[0018] ,

[0019] ,

[0020] ,

[0021] ,

[0022] in, The first static dimensionless parameter, This is the second static dimensionless parameter. The third static dimensionless parameter, The third static dimensionless parameter, The fifth static dimensionless parameter, The sixth static dimensionless parameter, The seventh static dimensionless parameter, The eighth static dimensionless parameter, For the material's Poisson's ratio, For linear displacement, For material density, For the length of the component, It is the acceleration due to gravity. For the intensity of the distributed surface load, As an external force, The elastic modulus of the material, For stress, In response, The bending moment experienced by the cross section, Let be the distance from the point in question to the neutral axis. Let be the moment of inertia of the cross section.

[0023] In one possible implementation, determining the dimensionless dynamic parameters based on the multi-degree-of-freedom equations of motion and the physical quantities includes:

[0024] Construct a dimensional matrix of the multi-degree-of-freedom physical quantities based on the aforementioned multi-degree-of-freedom motion equations and the aforementioned physical quantities;

[0025] According to the second similarity theory, the dynamic dimensionless parameters are determined based on the dimensional matrix of the multi-degree-of-freedom physical quantities, wherein the dynamic dimensionless parameters include a first dynamic dimensionless parameter, a second dynamic dimensionless parameter, a third dynamic dimensionless parameter, and a fourth dynamic dimensionless parameter.

[0026] In one possible implementation, the formula for calculating the dimensionless dynamic parameter is:

[0027] ,

[0028] ,

[0029] ,

[0030] ,

[0031] in, The first dynamic dimensionless parameter, As an external force, The elastic modulus of the material, For geometric scaling ratio, For the second dynamic dimensionless parameter, It is the natural frequency. For density, For the dimensionless parameter of the third dynamic force, In response to acceleration, For linear displacement, For the fourth dynamic dimensionless parameter, For speed.

[0032] In one possible implementation, the similarity relationship between the prototype and the scaled-down model is calculated as follows:

[0033] ,

[0034] ,

[0035] ,

[0036] in, The elastic modulus of the prototype. For similarity ratios of elastic modulus, The elastic modulus of the scaled-down model. Based on the geometric dimensions of the prototype, For the geometric dimensions of the scaled-down model, The geometric similarity ratio, In response to acceleration similarity ratio, For the prototype's response acceleration, The response acceleration of the scaled model.

[0037] In one possible implementation, the step of performing distortion analysis on the scaled model based on the similarity relationship to determine the actual similarity relationship between the prototype and the scaled model includes:

[0038] Based on the similarity relationship, the similarity constants of the scaled-down model are obtained, and based on the similarity constants, the material type of the scaled-down model is determined.

[0039] Determine the geometric scaling ratio between the prototype and the scaled-down model, and determine the similarity coefficient between the prototype and the scaled-down model based on the similarity relationship, material type, and geometric scaling ratio.

[0040] Based on the similarity relationship and similarity coefficient, distortion analysis is performed on the scaled model to determine the actual similarity relationship between the prototype and the scaled model.

[0041] In one possible implementation, the distortion analysis of the scaled model based on the similarity relationship and similarity coefficient includes:

[0042] Obtain the volume of the scaled-down model, obtain the density similarity ratio based on the similarity relationship, and determine the additional mass of the scaled-down model based on the density similarity ratio and the volume.

[0043] Obtain the actual mass of the scaled-down model, and determine the equivalent density of the scaled-down model based on the added mass, the actual mass of the scaled-down model, and the volume.

[0044] The theoretical density similarity ratio of the main beam and the theoretical density similarity ratio of the bridge tower are determined based on the similarity coefficient and the equivalent density of the scaled model.

[0045] The density similarity ratio of the main beam and the density similarity ratio of the bridge tower are determined based on the equivalent density of the scaled model.

[0046] The weights of the main beam and the bridge tower are determined based on the density similarity ratio of the main beam and the density similarity ratio of the bridge tower, respectively.

[0047] Based on the weights of the main beam and the bridge tower, and the similarity relationship, the equivalent density similarity ratio and the equivalent elastic modulus similarity ratio are determined. Based on the equivalent density similarity ratio and the equivalent elastic modulus similarity ratio, the dynamic dimensionless parameters are adjusted to determine the actual similarity relationship between the prototype and the scaled-down model.

[0048] In one possible implementation, the process of designing the scaled model based on the actual similarity relationship includes:

[0049] Based on the actual similarity relationship and the geometric scaling ratio, the truss section similarity coefficient, main beam section parameters, and bridge tower section similarity coefficient of the scaled model are determined. The truss section includes the upper chord section, the horizontal bracing section, and the web member section. The main beam section parameters include the axial stiffness, transverse bending stiffness, and torsional stiffness of the main beam. The bridge tower section includes the upper column section and the middle column section of the bridge tower.

[0050] Obtain the bridge parameters, and complete the scaled-down model design based on the bridge parameters, truss section similarity coefficient, main beam section parameters, and bridge tower section similarity coefficient.

[0051] On the other hand, the present invention also provides a bridge model design system based on static and dynamic information fusion, comprising:

[0052] The static dimensionless parameter determination module is used to obtain the physical quantities of the prototype and scaled-down model of the bridge, and determine the static dimensionless parameters based on the physical quantities and dimensional analysis method.

[0053] The dynamic dimensionless parameter determination module is used to establish multi-degree-of-freedom motion equations and determine dynamic dimensionless parameters based on the multi-degree-of-freedom motion equations and the physical quantities.

[0054] The scaled-down model design module is used to determine the similarity relationship between the prototype and the scaled-down model based on the static dimensionless parameters and the dynamic dimensionless parameters, perform distortion analysis on the scaled-down model based on the similarity relationship, determine the actual similarity relationship between the prototype and the scaled-down model, and complete the scaled-down model design based on the actual similarity relationship.

[0055] The beneficial effects of this invention are as follows: Based on dimensional analysis, static dimensionless parameters are determined, transforming various physical quantities in the prototype structure into dimensionless forms, and converting complex physical relationships into more easily understood and processed problems. On the basis of dimensionlessness, key physical parameters that significantly influence system behavior are identified by analyzing the similarity of physical quantities. Dynamic dimensionless parameters are determined based on multi-degree-of-freedom motion equations and physical quantities, describing the relationships between various physical quantities in the prototype structure. These parameters are unitless, making them more applicable. The similarity relationship between the prototype and the scaled-down model is determined based on both static and dynamic dimensionless parameters. By integrating static and dynamic similarity, a similarity equation reflecting the relationship between the prototype and scaled-down structures is established, linking each physical quantity in the prototype structure to its corresponding physical quantity in the scaled-down structure, ensuring that the characteristics of the scaled-down structure are similar to those of the prototype structure. Distortion analysis is performed on the scaled-down model based on the similarity relationship, considering the inconsistency in the added mass of the bridge model's tower and beam. The scaled-down model design is completed based on actual similarity relationships, ensuring that the scaled-down model can indirectly reflect the stress state of the prototype structure, thus proving the feasibility and correctness of the scaled-down model design approach. Attached Figure Description

[0056] Figure 1 A flowchart illustrating an embodiment of the bridge model design method based on static and dynamic information fusion provided by the present invention;

[0057] Figure 2 A schematic diagram of the overall structure of a scaled-down model of the bridge model design method based on static and dynamic information fusion provided by this invention;

[0058] Figure 3 A schematic diagram comparing the finite element analysis vibration modes of the prototype structure and the scaled-down structure of the bridge model design method based on static and dynamic information fusion provided by this invention.

[0059] Figure 4 A schematic diagram of the measured modal vibration modes of the bridge model design method based on static and dynamic information fusion provided by the present invention;

[0060] Figure 5 This is a schematic diagram of an embodiment of the bridge model design system based on static and dynamic information fusion provided by the present invention. Detailed Implementation

[0061] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0062] A specific embodiment of the present invention discloses a bridge model design method based on static and dynamic information fusion. Figure 1This is a flowchart of the bridge model design method based on static and dynamic information fusion provided in an embodiment of the present invention. Please refer to [link / reference]. Figure 1 Bridge model design methods based on static and dynamic information fusion include:

[0063] S101. Obtain the physical quantities of the prototype and scaled-down model of the bridge, and determine the static dimensionless parameters based on the physical quantities and dimensional analysis method.

[0064] S102. Establish multi-degree-of-freedom motion equations and determine the dimensionless dynamic parameters based on the multi-degree-of-freedom motion equations and physical quantities.

[0065] S103. Based on the static dimensionless parameters and the dynamic dimensionless parameters, determine the similarity relationship between the prototype and the scaled-down model. Based on the similarity relationship, perform distortion analysis on the scaled-down model to determine the actual similarity relationship between the prototype and the scaled-down model. Based on the actual similarity relationship, complete the design of the scaled-down model.

[0066] To ensure that the scaled-down model accurately reflects the mechanical properties of the prototype structure, an appropriate similarity relationship must be established between the scaled-down model and the prototype structure. Similarity analysis involves two requirements: first, determining the similarity constant, i.e., the ratio of the same physical quantity between the scaled-down model and the prototype structure must be constant; second, the relationships between physical quantities in the scaled-down model should be consistent with the corresponding relationships between physical quantities in the prototype structure, based on dimensional analysis and... Theorem derivation of static and dynamic similarity relationships of structures.

[0067] Compared with existing technologies, the bridge model design method based on static and dynamic information fusion provided in this embodiment obtains the physical quantities of the prototype and scaled-down model of the bridge, determines the static dimensionless parameters based on physical quantities and dimensional analysis, establishes multi-degree-of-freedom motion equations, determines the dynamic dimensionless parameters based on the multi-degree-of-freedom motion equations and physical quantities, determines the similarity relationship between the prototype and scaled-down model based on the static and dynamic dimensionless parameters, establishes similarity equations reflecting the relationship between the prototype structure and the scaled-down structure by fusing static and dynamic similarity, associates each physical quantity in the prototype structure with the corresponding physical quantity in the scaled-down structure to ensure that the characteristics of the scaled-down structure are similar to those of the prototype structure, performs distortion analysis on the scaled-down model based on the similarity relationship to determine the actual similarity relationship between the prototype and scaled-down model, completes the scaled-down model design based on the actual similarity relationship, considers the problem of inconsistent additional mass of the bridge model tower and beam, ensures that the scaled-down model can indirectly reflect the stress state of the prototype structure, and proves the feasibility and correctness of the scaled-down model design approach.

[0068] In some embodiments, in step S101, the physical quantities of the prototype and scaled-down model of the bridge are obtained. These physical quantities include at least length, mass, time, velocity, and density. Based on these physical quantities, static dimensionless parameters are determined using dimensional analysis. Specifically, the steps are: constructing a materials mechanics model; determining similarity constants between the prototype and scaled-down model based on the materials mechanics model and the physical quantities; these similarity constants include elastic modulus, geometric dimensions, response acceleration, Poisson's ratio, response displacement, cross-sectional area, cross-sectional moment of inertia, load, mass, frequency, and density; and determining static dimensionless parameters based on these similarity constants using dimensional analysis. These static dimensionless parameters include a first static dimensionless parameter, a second static dimensionless parameter, a third static dimensionless parameter, a fourth static dimensionless parameter, a fifth static dimensionless parameter, a sixth static dimensionless parameter, a seventh static dimensionless parameter, and an eighth static dimensionless parameter. The calculation formula for the materials mechanics model is:

[0069] ,

[0070] ,

[0071] in, The elastic modulus of the material, The external force acting on the cross section The area of ​​the cross section. The bending moment experienced by the cross section, Let be the distance from the point in question to the neutral axis. Let the moment of inertia of the cross section be... For stress, For strain, which is a dimensionless quantity, the static dimensionless parameters are obtained using dimensional analysis. The formula for calculation is:

[0072] , , , ,

[0073] , , , ,

[0074] in, Let be the first static dimensionless parameter, indicating that the strain of the scaled-down model and the prototype are equal. This is the second static dimensionless parameter. The third static dimensionless parameter, The third static dimensionless parameter, This is the fifth static dimensionless parameter, indicating that the Poisson's ratio of the materials in the scaled-down model and the prototype are equal. Once the material is selected, its Poisson's ratio, elastic modulus, and mass density are also determined. The sixth static dimensionless parameter indicates that the linear displacement of the structure is proportional to the geometrical scaling. This is the seventh static dimensionless parameter, indicating that when the elastic modulus of a material is the same, density is inversely proportional to geometrical scaling. This similarity relationship is difficult to achieve and is usually realized by adding mass. The eighth static dimensionless parameter, For the material's Poisson's ratio, For linear displacement, For material density, For the length of the component, It is the acceleration due to gravity. The intensity of the distributed surface load.

[0075] In some embodiments, in step S102, a multi-degree-of-freedom motion equation is established, and the dimensionless dynamic parameters are determined based on the multi-degree-of-freedom motion equation and the physical quantities. First, a dimensional matrix of the multi-degree-of-freedom physical quantities is constructed based on the multi-degree-of-freedom motion equation and the physical quantities. The dynamic similarity relationship is established on the basis of the motion equation, and the calculation formula of its multi-degree-of-freedom motion equation is:

[0076] ,

[0077] in, , , These are the system's acceleration, velocity, and displacement, respectively. , , These are the system's mass matrix, damping matrix, and stiffness matrix, respectively. The external stimulus received by the system It is related to the material density and component size. The dynamic characteristics of the system are determined by the above physical quantities, which are related to the material's elastic modulus and the component dimensions, together with the displacement transfer function. For the dimensional matrices of its multi-degree-of-freedom physical quantities, please refer to Table 1.

[0078] Table 1

[0079]

[0080] Secondly, based on the second similarity theory, the dimensionless parameters of the dynamics are determined based on the dimensional matrix of the multi-degree-of-freedom physical quantities. According to the second similarity theory, the relationship between the physical quantities can be expressed as follows:

[0081] ,

[0082] in, For the dimensionless term composed of dynamic parameter physical quantities, the formula for calculating its dynamic dimensionless parameter is:

[0083] ,

[0084] ,

[0085] ,

[0086] ,

[0087] in, The first dimensionless parameter of dynamics indicates that, when the elastic modulus of the material is the same, the external force is proportional to the square of the geometric scaling ratio. As an external force, The elastic modulus of the material, For geometric scaling ratio, Let be the second dimensionless dynamic parameter, indicating that the natural frequencies of the scaled model and prototype are inversely proportional to the product of the square roots of the geometric scaling ratio and the density scaling ratio. It is the natural frequency. For density, The third dimensionless parameter represents the linear displacement similarity ratio, which is equal to the square of the frequency similarity ratio, when the accelerations of the scaled model and the prototype are the same. In response to acceleration, For linear displacement, The fourth dynamic dimensionless parameter indicates that when the velocities of the scaled model and the prototype are the same, the linear displacement similarity ratio is equal to the frequency similarity ratio. For speed.

[0088] In some embodiments, in step S103, the similarity relationship between the prototype and the scaled-down model is determined based on static dimensionless parameters and dynamic dimensionless parameters. The scaled-down model of the bridge is designed according to the similarity criteria of static and dynamic dimensionless parameters. Among them, the similarity constants of elastic modulus, system response acceleration, and geometric dimensions are used as basic variables, and other similarity constants are derived quantities. The similarity relationship of various physical quantities between the prototype and the scaled-down model is shown in Table 2.

[0089] Table 2

[0090]

[0091] Distortion analysis of the scaled model based on similarity relationships was performed. First, based on the similarity relationship between the prototype and the scaled model, the similarity constant of the scaled model was obtained. Based on the similarity constant, the material type of the scaled model was determined, and the geometric scaling ratio between the prototype and the scaled model was determined. Considering factors such as laboratory space size, model fabrication and assembly, and experimental objectives, the geometric scaling ratio was determined to be 1:100. Second, based on the similarity relationship, material type, and geometric scaling ratio, the similarity coefficient between the prototype and the scaled model was determined. The similarity coefficients between the prototype and the scaled model are shown in Table 3.

[0092] Table 3

[0093]

[0094] Finally, distortion analysis is performed on the scaled model based on similarity relationships and similarity coefficients to determine the actual similarity between the prototype and the scaled model. When the similarity relationship and similarity coefficient between the scaled model and the bridge prototype are fully satisfied, the scaled model is a fully similar model. When one or more of the similarity relationships and similarity coefficients between the scaled model and the bridge prototype are not satisfied, the scaled model is distorted, and the actual similarity relationship needs to be determined through distortion analysis. The process of distortion analysis for the scaled model is as follows: First, the volume of the scaled model is obtained. Based on the similarity relationship, the density similarity ratio is obtained. Based on the density similarity ratio and volume, the additional mass of the scaled model is determined. The formula for calculating the density similarity ratio is:

[0095] ,

[0096] in, For density similarity ratio, For similarity ratios of elastic modulus, In response to acceleration similarity ratio, This represents the geometric similarity ratio. For models with small scaling ratios, the density similarity constant is very large, and it is difficult for general model materials to meet this similarity constant requirement. Typically, an additional mass is added to the model to compensate for the density difference caused by the material. The added mass is the difference between the theoretical mass and the actual mass of the scaled model, and its calculation formula is:

[0097] ,

[0098] in, The theoretically added mass that should be applied to the model, Density of the prototype For the density of the model, The theoretical density similarity ratio, The volume of the scaled-down model;

[0099] Due to limitations such as model size, load-bearing capacity, and the location of counterweights, the actual production of small-scale scale models cannot be based on the calculated theoretical additional mass. Therefore, the equivalent density of the scale model is determined based on the additional mass, the actual mass of the scale model, and its volume. The formula for calculating the equivalent density is as follows:

[0100] ,

[0101] in, The equivalent density of the scaled-down model;

[0102] The theoretical density similarity ratios of the main girder and the bridge tower are determined based on the similarity coefficient and the equivalent density of the scaled model. The weights of the main girder and the bridge tower are then determined based on their respective density similarity ratios. The calculation formulas are as follows:

[0103] ,

[0104] in, It is the actual density similarity ratio of the main beam. It is the actual density similarity ratio of the bridge towers;

[0105] The equivalent density similarity ratio and equivalent elastic modulus similarity ratio are determined based on the weights of the main girder and the bridge towers, as well as similarity relationships. The formula for calculating the equivalent density similarity ratio is as follows:

[0106] ,

[0107] The formula for calculating the similarity ratio of its equivalent elastic modulus is:

[0108] ,

[0109] in, The equivalent density similarity ratio, The equivalent elastic modulus similarity ratio, It is the similarity ratio of the elastic modulus of the main beam. It is the similarity ratio of the elastic modulus of the bridge towers;

[0110] The dynamic dimensionless parameters are adjusted based on the equivalent density similarity ratio and the equivalent elastic modulus similarity ratio to determine the actual similarity relationship between the prototype and the scaled-down model. The adjustment primarily focuses on the second dynamic dimensionless parameter. .

[0111] Based on the actual similarity relationship and geometric scaling ratio, the similarity coefficients of the truss section, the main beam section parameters, and the bridge tower section of the scaled-down model are determined. The truss section includes the upper chord section, the horizontal bracing section, and the web section. The main beam section parameters include the axial stiffness, lateral bending stiffness, and torsional stiffness of the main beam. The bridge tower section includes the upper column section and the middle column section. The parameters of the bridge are obtained. Based on the parameters of the bridge, the similarity coefficients of the truss section, the main beam section parameters, the similarity coefficients of the bridge tower section, and the parameters of the bridge, the scaled-down model design is completed.

[0112] The parameters of the bridge prototype are as follows: the track type is CRTS-Ⅲ slab track, set as a double-track track with a spacing of 5.0 m; the railway grade is a passenger dedicated line; the design speed is 360 km / h; the total bridge length is 684 m; the bridge span arrangement is: first side span 60 m, first middle span 120 m, main span 324 m, second middle span 120 m, second side span 60 m; the main girder consists of a lower chord steel box girder and an upper chord steel truss girder, the steel plate material is Q370qD; the center distance of the upper chord of the main truss is 14 m; the center distance of the lower chord truss is 14 m; the truss height is 12 m; the towers are reinforced concrete structures with a concrete strength grade of C60; the tower top elevation is 130.9143 m; the tower bottom elevation is 9.9130 m; the stay cables are spatial double-plane cables; each bridge tower has 13 pairs of cables on both sides on the elevation; the entire bridge has a total of 104 cables; the standard value of their tensile strength is 1670 Nm. MPa; geometric scaling ratio is 1:100. The total length of the scaled-down model bridge is determined to be 6.84 m, meaning the span arrangement is 6.84 m, with a total of 52 pairs of cables. The entire bridge is designed as a symmetrical structure, with the mid-span as the axis of symmetry. Please refer to the overall structural diagram of the scaled-down model. Figure 2 Based on similarity relationships, similarity constants for the scaled-down model are obtained. Based on similarity constants, the material type of the scaled-down model is determined. Material properties to be considered also need to take into account the effects of temperature and humidity, loading rate and strain rate, size and shape on material properties. Material properties include elastic modulus, stress characteristics, shrinkage and creep. Therefore, the beams, towers and piers of the scaled-down model are made of stainless steel, and the stay cables are made of steel wire rope. The beams are connected by a combination of bolts and welding. The stay cables are connected to the beams and towers by adjusting bolts. The beams are connected to the piers and towers by hinged supports. The bottom of the piers and towers is fixed to the workbench with bolts.

[0113] Based on the geometric scaling ratio, and according to the parameters of the prototype and the similarity relationship with the actual structure, the truss design parameters were calculated. The model truss does not include vertical members; the transverse spacing between the centers of the top chord members is 14.0 cm, the transverse spacing between the bottom chord members is 14.0 cm, the height difference between the top and bottom chord members is 12.0 cm, the segment length is 12.0 cm, the inclination angle of the diagonal members is 63.43°, and the truss structure consists of 57 connected segments. Based on the similarity coefficient requirements and actual fabrication needs, the final proposed truss cross-sectional dimensions are: a rectangular cross-section of 5.5 mm * 6.5 mm for the top chord, a rectangular cross-section of 2 mm * 4 mm for the horizontal bracing, and a rectangular cross-section of 5.5 mm * 5.5 mm for the web members. The similarity coefficients for the scaled model truss cross-sections are shown in Table 4.

[0114] Table 4

[0115]

[0116] in, For axial stiffness, For lateral bending stiffness, For torsional stiffness.

[0117] By designing the complex structural parts of the prototype cross-section according to a similarity ratio, the cross-sectional dimensions of the scaled-down model will be less than 1 mm, which is difficult to manufacture in practice. Therefore, the effect of the longitudinal ribs in the main beam cross-section is equivalent to the thickness, and the thickness of the main beam cross-section is set to 1 mm. The design of the main beam cross-section of the scaled-down model needs to meet the similarity coefficients for axial stiffness, transverse bending stiffness, and torsional stiffness. For the cross-sectional parameters of the main beam of the scaled-down model, please refer to Table 5.

[0118] Table 5

[0119]

[0120] Since the moment of inertia of the bridge cable section has no significant impact on the stress of the scaled-down structure, the similarity of the moment of inertia of the cable section is ignored, and the focus is on the similarity of the cable cross-sectional area. A single steel wire rope with a diameter of 3 mm is selected to simulate the cable stay. There are a total of 104 steel wires in the whole bridge. The bridge tower end is connected to the tower column of the bridge tower through cable sleeve, and the main beam end is anchored through cable adjustment bolts.

[0121] The bridge towers are designed in the same H-shape as the prototype bridge, with the same rectangular cross-section and axial stiffness. Longitudinal bending stiffness Transverse bending stiffness of bridge Based on the similarity relationship between the scaled-down model and the prototype, the final cross-sectional dimensions of the bridge towers were determined: the upper column is 40 mm long and 40 mm high, with a hollow core of 30 mm x 24 mm; the middle column is 40 mm long and 69 mm high, with a hollow core of 39 mm x 24 mm. The similarity coefficients for the bridge tower cross-sections are shown in Table 6.

[0122] Table 6

[0123]

[0124] in, The unit is N. , The unit is .

[0125] In some embodiments, the similarity ratio is analyzed, and finite element models of the prototype structure and the scaled-down model structure are established respectively. The prototype structure has 1353 elements and 1186 nodes, and the scaled-down model structure has 1279 elements and 1137 nodes. Both models are established as follows: the cables are simulated using tension-only truss elements, and the remaining parts are simulated using beam elements; the side piers, auxiliary piers, and the bottom of the bridge towers are fixed; the main beams are elastically connected to the piers; and the cables are rigidly connected to the main beams and the upper columns of the bridge towers. The mass of iron sand in the hollow parts of the box girder and the bridge tower is equivalent to the mass of the corresponding components. Therefore, the formula for calculating the unit weight of the box girder and the bridge tower is:

[0126] ,

[0127] ,

[0128] in, It is the mass of iron shot added. This refers to the volume of the corresponding components; through distortion analysis of the scaled-down model, the theoretical density similarity ratio of the main beam can be determined. Total volume of main beam Theoretical counterweight of main beam kg, the actual scaled-down model uses iron sand to fill the hollow parts of the box girder, the mass of the iron sand used is... kg, 57 pieces of 8 cm in size are evenly suspended at the bottom plate of the box girder. 8 cm A 15 cm solid iron block, total mass kg, the actual added mass of the main beam only reaches 13.7% of the theoretical value, the equivalent density of the main beam Density similarity ratio Bridge tower volume Theoretical counterweight kg, actually filling the hollow part of the bridge tower with iron sand, the mass of iron sand used kg, the actual added mass of the bridge tower is only 0.3% of the theoretical value. Equivalent density of the bridge tower. Density similarity ratio The modal frequency similarity ratio is determined by the following formula:

[0129] ,

[0130] The actual frequency similarity ratio between the model and the prototype was calculated based on the equivalent elastic modulus similarity ratio, the equivalent density similarity ratio, and the geometric scaling ratio. Based on the actual frequency similarity ratio, the unit weight of the box girder was calculated to be... The bridge tower's unit weight is The mass blocks suspended at the bottom of the main beam act on the finite element model as vertical nodal loads. Each block has a size of 74 N, and the element type and connection method are consistent with the prototype structure.

[0131] Modal analysis was performed on the finite element models of the scaled-down and prototype structures respectively. For a comparison of the vibration modes in the finite element analysis of the prototype and scaled-down structures, please refer to [link / reference]. Figure 3 The above six modes (third transverse, third vertical) are selected to verify whether the scaled-down model design satisfies the frequency similarity ratio between the model and the prototype derived above, and the error. Defined as:

[0132] ,

[0133] in, The frequency similarity ratio of the finite element model. For the results of deriving the frequency similarity ratio and modal frequencies, please refer to Table 7.

[0134] Table 7

[0135]

[0136] Table 7 shows that the errors in the same-order modal frequencies of both the prototype and scaled-down structures in the finite element analysis are less than 7%, with a maximum error of 6.99%, a minimum error of only 0.38%, and an average error of 3.74%. This error is attributed to the distortion analysis considering the additional mass and elastic modulus, which play a dominant role in modal frequencies, while other minor distortion terms are not considered. For example, the cross-sectional dimensions and shape of the scaled-down structure were rounded to ensure stiffness similarity, taking into account actual processing conditions; therefore, the cross-sectional design did not achieve complete similarity. The actual similarity ratio of the model matches the theoretically calculated similarity ratio well, proving the correctness of the aforementioned similarity and distortion analyses. This also demonstrates that the established finite element scaled-down model can effectively predict the working state of the actual bridge, providing reference data for the monitoring and analysis of actual bridges.

[0137] Modal analysis of the scaled-down model was conducted. The modal order can be determined by the mode shapes of the main beam; therefore, only the mode shapes of the main beam were measured. Due to the model's symmetry, only the mode shapes of half the structure needed to be measured. The modal order can be deduced based on the structural symmetry. To obtain the complete mode shapes of the main beam and compare them with those of the scaled-down finite element model, six modes (three transverse and three vertical) from the scaled-down model were selected for comparison with the measured modes. This verified the consistency of the dynamic characteristics between the model and the actual scaled-down model, and defined the modal frequency error. ,

[0138] ,

[0139] in, For the analysis of modal frequencies of the finite element scaled model, The measured modal frequencies of the scaled-down laboratory model are shown in Table 8. The measured modal frequencies were obtained from multiple measurements and the average value was taken. For the modal experimental analysis results, please refer to Table 8. For a schematic diagram of the measured modal shapes, please refer to [link to relevant documentation]. Figure 4 , Figure 4 In the diagram, the transverse vibration mode diagram is the top view of the steel box, and the vertical vibration mode diagram is the front view of the steel box.

[0140] Table 8

[0141]

[0142] Table 8 shows that the modal frequencies analyzed by the finite element method (FEM) are in good agreement with the measured modal frequencies of the first three transverse and three vertical modes. The frequency errors corresponding to the same mode shape are within 8%, with a maximum error of 7.85%, a minimum error of 0.97%, and an average error of 3.92%. The reasons for these errors are: FEM is difficult to accurately simulate the boundary conditions of actual structures, and the connection stiffness of members and the physical properties of materials in actual structures cannot be accurately calculated; noise interference and human error in modal testing affect the test results; furthermore, the modal analysis method used by the testing software itself can also produce errors. Considering all these results, the dynamic characteristics of the laboratory scaled-down model and the FEM scaled-down model show good consistency.

[0143] Finite element models of the prototype structure and the scaled-down model were established. The modal frequency similarity ratio between the scaled-down model and the prototype structure was calculated based on the actual added mass of the scaled-down model. Finite element analysis verified that the analyzed modal frequency similarity ratio was in high agreement with the derived modal frequency similarity ratio, proving the feasibility and correctness of the scaled-down model design. Modal tests were conducted on the designed scaled-down model, and the first three transverse and first three vertical vibration modes of the test modes and the finite element modes of the scaled-down structure were matched. The modal frequencies of the same order of the test modes of the scaled-down model and the established finite element modes of the scaled-down structure are close, indicating that the test modes of the scaled-down model and the analyzed modes of the scaled-down finite element model are in good agreement. The relevant characteristics of the laboratory scaled-down structure were analyzed through simple and convenient model tests, and the similarity ratio was used to extrapolate to the prototype structure, thereby obtaining the relevant characteristics of the prototype structure. This provides a reference for research on damage identification and reliability assessment of the prototype structure.

[0144] To better implement the bridge model design method based on static and dynamic information fusion in the embodiments of the present invention, based on the bridge model design method based on static and dynamic information fusion, the corresponding method is as follows: Figure 5 As shown, this embodiment of the invention also provides a bridge model design system 500 based on static and dynamic information fusion, comprising:

[0145] The static dimensionless parameter determination module 501 is used to obtain the physical quantities of the prototype and scaled-down model of the bridge, and determine the static dimensionless parameters based on the physical quantities and dimensional analysis method.

[0146] The dynamic dimensionless parameter determination module 502 is used to establish multi-degree-of-freedom motion equations and determine dynamic dimensionless parameters based on multi-degree-of-freedom motion equations and physical quantities.

[0147] The scaled model design module 503 is used to determine the similarity relationship between the prototype and the scaled model based on static dimensionless parameters and dynamic dimensionless parameters, perform distortion analysis on the scaled model based on the similarity relationship, determine the actual similarity relationship between the prototype and the scaled model, and complete the scaled model design based on the actual similarity relationship.

[0148] In summary, the bridge model design method and system based on static and dynamic information fusion provided by this invention obtains the physical quantities of the prototype and scaled-down model of the bridge, determines the static dimensionless parameters based on the physical quantities and dimensional analysis, establishes multi-degree-of-freedom motion equations, determines the dynamic dimensionless parameters based on the multi-degree-of-freedom motion equations and physical quantities, determines the similarity relationship between the prototype and the scaled-down model based on the static and dynamic dimensionless parameters, performs distortion analysis on the scaled-down model based on the similarity relationship, determines the actual similarity relationship between the prototype and the scaled-down model, and completes the scaled-down model design based on the actual similarity relationship. This ensures that the scaled-down model can indirectly reflect the stress state of the prototype structure, proving the feasibility and correctness of the scaled-down model design approach.

[0149] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A bridge model design method based on static-dynamic information fusion, characterized in that, The method comprises the following steps: Obtaining physical quantities of a prototype and a scale model of a bridge, and determining static dimensionless parameters based on the physical quantities and a dimensional analysis method, wherein a calculation formula of the static dimensionless parameters is: ， ， ， ， ， ， ， ， wherein, is a first static dimensionless parameter, is a second static dimensionless parameter, is a third static dimensionless parameter, is a fourth static dimensionless parameter, is a fifth static dimensionless parameter, is a sixth static dimensionless parameter, is a seventh static dimensionless parameter, is an eighth static dimensionless parameter, is a Poisson's ratio of the material, is a linear displacement, is a density of the material, is a length of the member, is a gravitational acceleration, is a distributed load intensity, is an external force, is an elastic modulus of the material, is a stress, is a strain, is a bending moment to which the cross section is subjected, is a distance of the point of interest to the neutral axis, is a moment of inertia of the cross section; Establishing a multi-degree-of-freedom motion equation, and determining dynamic dimensionless parameters based on the multi-degree-of-freedom motion equation and the physical quantities, wherein a calculation formula of the dynamic dimensionless parameters is: ， ， ， ， wherein, is a first dynamic dimensionless parameter, is an external force, is an elastic modulus of the material, is a geometric scale ratio, is a second dynamic dimensionless parameter, is a natural frequency, is a density, is a third dynamic dimensionless parameter, is a response acceleration, is a linear displacement, is a fourth dynamic dimensionless parameter, is a velocity; Determining a similarity relationship between the prototype and the scale model based on the static dimensionless parameters and the dynamic dimensionless parameters, performing distortion analysis on the scale model based on the similarity relationship, determining an actual similarity relationship between the prototype and the scale model, and completing scale model design based on the actual similarity relationship, wherein a calculation formula of the similarity relationship between the prototype and the scale model is: ， ， ， wherein, Eprototypeis the elastic modulus of the prototype, Eprototypeis the elastic modulus of the prototype, Eprototypeis the elastic modulus of the prototype, Lprototypeis the geometric dimension of the prototype, Lprototypeis the geometric dimension of the prototype, Lprototypeis the geometric dimension of the prototype, Lprototypeis the geometric dimension of the prototype, Lprototypeis the geometric dimension of the prototype, Lprototypeis the geometric dimension of the prototype, The distortion analysis on the scale model based on the similarity relationship to determine the actual similarity relationship between the prototype and the scale model comprises: Obtaining a similarity constant of the scale model based on the similarity relationship, and determining a material type of the scale model based on the similarity constant; Determining a geometric scale ratio of the prototype and the scale model, and determining a similarity coefficient of the prototype and the scale model based on the similarity relationship, the material type and the geometric scale ratio; Performing distortion analysis on the scale model based on the similarity relationship and the similarity coefficient to determine the actual similarity relationship between the prototype and the scale model, wherein the distortion analysis on the scale model based on the similarity relationship and the similarity coefficient comprises: Obtaining a volume of the scale model, obtaining a density similarity ratio based on the similarity relationship, and determining an additional mass of the scale model based on the density similarity ratio and the volume; Obtaining an actual mass of the scale model, and determining an equivalent density of the scale model based on the additional mass, the actual mass of the scale model and the volume; Determining a theoretical density similarity ratio of a main beam and a theoretical density similarity ratio of a tower based on the similarity coefficient and the equivalent density of the scale model; Determining a density similarity ratio of the main beam and a density similarity ratio of the tower based on the equivalent density of the scale model; Determining a weight of the main beam and a weight of the tower based on the density similarity ratio of the main beam and the density similarity ratio of the tower, respectively; Determining an equivalent density similarity ratio and an equivalent elastic modulus similarity ratio based on the weight of the main beam, the weight of the tower and the similarity relationship, and adjusting the dynamic dimensionless parameters based on the equivalent density similarity ratio and the equivalent elastic modulus similarity ratio to determine the actual similarity relationship between the prototype and the scale model.

2. The bridge model design method based on static-dynamic information fusion according to claim 1, characterized in that, The static dimensionless parameters are determined based on the physical quantities and the dimensional analysis method, comprising: A material mechanics model is constructed, and similarity constants of the prototype and the scale model are determined based on the material mechanics model and the physical quantities, wherein the physical quantities at least include length, mass, time, velocity, density, and the similarity constants include elastic modulus, geometric size, response acceleration, Poisson's ratio, response displacement, cross-sectional area, cross-sectional moment of inertia, load, mass, frequency and density; Determine static dimensionless parameters according to dimensional analysis method based on the similarity constant, wherein the static dimensionless parameters include first, second, third, fourth, fifth, sixth, seventh and eighth static dimensionless parameters.

3. The bridge model design method based on static-dynamic information fusion according to claim 2, characterized in that, The determining the dynamic dimensionless parameters based on the multi-degree-of-freedom motion equation and the physical quantities comprises: Constructing a dimensional matrix of multi-degree-of-freedom physical quantities based on the multi-degree-of-freedom motion equation and the physical quantities; Determine dynamic dimensionless parameters based on the dimensional matrix of multi-degree-of-freedom physical quantities according to the second similarity theory, wherein the dynamic dimensionless parameters include first, second, third and fourth dynamic dimensionless parameters.

4. The bridge model design method based on static-dynamic information fusion according to claim 1, characterized in that, The completing the scale model design based on the actual similarity relationship comprises: Determine truss section similarity coefficients, main girder section parameters and bridge tower section similarity coefficients of the scale model based on the actual similarity relationship and a geometric scale ratio, wherein the truss section includes upper chord section, flat link section and web member section, the main girder section parameters include axial stiffness, lateral bending stiffness and torsional stiffness of the main girder, and the bridge tower section includes bridge tower upper column section and bridge tower middle column section. Obtain parameters of the bridge, and complete the scale model design based on the parameters of the bridge, the truss section similarity coefficients, the main girder section parameters and the bridge tower section similarity coefficients.

5. A bridge model design system based on static-dynamic information fusion, characterized in that, Comprise: The static dimensionless parameter determining module is configured to obtain physical quantities of a prototype and a scale model of a bridge, and determine static dimensionless parameters based on the physical quantities and dimensional analysis method, wherein a calculation formula of the static dimensionless parameters is: ， ， ， ， ， ， ， ， wherein, is a first static dimensionless parameter, is a second static dimensionless parameter, is a third static dimensionless parameter, is a fourth static dimensionless parameter, is a fifth static dimensionless parameter, is a sixth static dimensionless parameter, is a seventh static dimensionless parameter, is an eighth static dimensionless parameter, is a Poisson's ratio of the material, is a linear displacement, is a density of the material, is a length of the member, is a gravitational acceleration, is a distributed load intensity, is an external force, is an elastic modulus of the material, is a stress, is a strain, is a bending moment to which the cross section is subjected, is a distance of the point of interest to the neutral axis, is a moment of inertia of the cross section; The dynamic dimensionless parameter determining module is configured to establish a multi-degree-of-freedom motion equation, and determine dynamic dimensionless parameters based on the multi-degree-of-freedom motion equation and the physical quantities, wherein a calculation formula of the dynamic dimensionless parameters is: ， ， ， ， wherein, is a first dynamic dimensionless parameter, is an external force, is an elastic modulus of the material, is a geometric scale ratio, is a second dynamic dimensionless parameter, is a natural frequency, is a density, is a third dynamic dimensionless parameter, is a response acceleration, is a linear displacement, is a fourth dynamic dimensionless parameter, is a velocity; The scale model design module is configured to determine a similarity relationship between the prototype and the scale model based on the static dimensionless parameters and the dynamic dimensionless parameters, perform distortion analysis on the scale model based on the similarity relationship, determine an actual similarity relationship between the prototype and the scale model, and complete the scale model design based on the actual similarity relationship, wherein a calculation formula of the similarity relationship between the prototype and the scale model is: ， ， ， wherein, Eprototypeis the elastic modulus of the prototype, Eprototypeis the elastic modulus of the prototype, Emodelis the elastic modulus of the scaled model, Lprototypeis the geometric dimension of the prototype, Lmodelis the geometric dimension of the scaled model, Lprototypeis the geometric dimension of the prototype, Aprototypeis the response acceleration of the prototype, Aprototypeis the response acceleration of the prototype, Amodelis the response acceleration of the scaled model, The performing distortion analysis on the scale model based on the similarity relationship and determining the actual similarity relationship between the prototype and the scale model comprise: Obtain a similarity constant of the scale model based on the similarity relationship, and determine a material type of the scale model based on the similarity constant; Determine a geometric scale ratio between the prototype and the scale model, and determine similarity coefficients between the prototype and the scale model based on the similarity relationship, the material type and the geometric scale ratio; The performing distortion analysis on the scale model based on the similarity relationship and the similarity coefficients and determining the actual similarity relationship between the prototype and the scale model comprise: obtaining a volume of the scale model, obtaining a density similarity ratio based on the similarity relationship, determining an additional mass of the scale model based on the density similarity ratio and the volume; obtaining an actual mass of the scale model, determining an equivalent density of the scale model based on the additional mass, the actual mass of the scale model and the volume; determining a theoretical density similarity ratio of the main girder and a theoretical density similarity ratio of the bridge tower based on the similarity coefficient and the equivalent density of the scale model; determining a density similarity ratio of the main girder and a density similarity ratio of the bridge tower based on the equivalent density of the scale model; determining a weight of the main girder and a weight of the bridge tower based on the density similarity ratio of the main girder and the density similarity ratio of the bridge tower respectively; determining an equivalent density similarity ratio and an equivalent elastic modulus similarity ratio based on the weight of the main girder, the weight of the bridge tower and the similarity relationship, and adjusting the dynamic dimensionless parameter based on the equivalent density similarity ratio and the equivalent elastic modulus similarity ratio to determine an actual similarity relationship between the prototype and the scale model.

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