Bridge model design method and system based on static and dynamic information fusion

Abstract

The invention 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 reduced scale model of a bridge, and determining static dimensionless parameters based on the physical quantities and a dimensional analysis method; establishing a multi-degree-of-freedom motion equation, and determining a power dimensionless parameter based on the multi-degree-of-freedom motion equation and the physical quantity; and determining a similarity relationship between the prototype and the reduced-scale model based on the static dimensionless parameters and the dynamic dimensionless parameters, performing distortion analysis on the reduced-scale model based on the similarity relationship, determining an actual similarity relationship between the prototype and the reduced-scale model, and completing the design of the reduced-scale model based on the actual similarity relationship.

Description

Technical Field

[0001] The present invention relates to the technical field of bridges, and in particular to a bridge model design method and system based on static and dynamic information fusion. Background Art

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

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

[0004] Existing studies mostly focus on the static similarity or dynamic similarity of models, and rarely consider the fusion of static and dynamic similarity relationships. In addition, most of the models involved have simple structures and large scales. Small-scale models of complex structures are subject to dual restrictions of similarity relationships and processing and manufacturing in terms of cross-sectional design, node connection, boundary condition setting, etc. 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 scale models.

[0006] In order to solve the above problems, the present invention provides a bridge model design method based on static and dynamic information fusion, comprising: Obtaining physical quantities of a prototype and a scaled model of the bridge, and determining static dimensionless parameters based on the physical quantities and a dimensional analysis method; Establishing a multi-degree-of-freedom motion equation, and determining a dynamic dimensionless parameter based on the multi-degree-of-freedom motion equation and the physical quantity; The similarity relationship between the prototype and the scaled model is determined based on the static dimensionless parameters and the dynamic dimensionless parameters, distortion analysis is performed on the scaled model based on the similarity relationship, the actual similarity relationship between the prototype and the scaled model is determined, and the scaled model design is completed based on the actual similarity relationship.

[0007] In a possible implementation, determining the static dimensionless parameter based on the physical quantity according to a dimensional analysis method includes: Constructing a material mechanics model, and determining similarity constants between the prototype and the scaled model based on the material mechanics model and the physical quantities, wherein the physical quantities at least include length, mass, time, speed, 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; Based on the similarity constant, the static dimensionless parameters are determined according to the dimensional analysis method, wherein the 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.

[0008] In a possible implementation, the calculation formula of the static dimensionless parameter is: , , , , , , , , in, is the first static dimensionless parameter, is the second static dimensionless parameter, is the third static dimensionless parameter, is the third static dimensionless parameter, is the fifth static dimensionless parameter, is the sixth static dimensionless parameter, is the seventh static dimensionless parameter, is the eighth static dimensionless parameter, is the material Poisson’s ratio, is the linear displacement, is the material density, is the length of the component, is the acceleration due to gravity, is the load concentration on the distributed surface, For external force, is the elastic modulus of the material, is stress, For strain, is the bending moment on the cross section, is the distance from the desired point to the neutral axis, is the section moment of inertia.

[0009] In a possible implementation, determining the dynamic dimensionless parameter based on the multi-degree-of-freedom motion equation and the physical quantity includes: Constructing a dimensional matrix of multi-degree-of-freedom physical quantities based on the multi-degree-of-freedom motion equations and the physical quantities; According to the second similarity theory, the dynamic dimensionless parameters are determined based on the dimension matrix of the multi-degree-of-freedom physical quantity, 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.

[0010] In a possible implementation, the calculation formula of the dimensionless power parameter is: , , , , in, is the first dynamic dimensionless parameter, For external force, is the elastic modulus of the material, is the geometric scale ratio, is the dimensionless parameter of the second dynamic force, is the natural frequency, is the density, is the dimensionless parameter of the third dynamic force, In response to acceleration, is the linear displacement, is the fourth dynamic dimensionless parameter, For speed.

[0011] In a possible implementation, the calculation formula for the similarity relationship between the prototype and the scaled model is: , , , in, is the elastic modulus of the prototype, is the elastic modulus similarity ratio, is the elastic modulus of the scaled model, The geometric dimensions of the prototype, is the geometric size of the scaled model, is the geometric size similarity ratio, is the response acceleration similarity ratio, is the response acceleration of the prototype, Response acceleration of the scaled model.

[0012] In a possible implementation manner, 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: Obtaining a similarity constant of the scaled model based on the similarity relationship, and determining a material type of the scaled model based on the similarity constant; Determining a geometric scale ratio between the prototype and the scaled model, and determining a similarity coefficient between the prototype and the scaled model based on the similarity relationship, the material type, and the geometric scale ratio; The scaled model is subjected to distortion analysis based on the similarity relationship and the similarity coefficient to determine the actual similarity relationship between the prototype and the scaled model.

[0013] In a possible implementation manner, performing distortion analysis on the scaled model based on the similarity relationship and the similarity coefficient includes: Acquiring the volume of the scaled model, obtaining a density similarity ratio based on the similarity relationship, and determining an additional mass of the scaled model based on the density similarity ratio and the volume; Acquiring the actual mass of the scaled model, and determining the equivalent density of the scaled model based on the additional mass, the actual mass and the volume of the scaled model; Determine the theoretical density similarity ratio of the main beam and the theoretical density similarity ratio of the bridge tower based on the similarity coefficient and the equivalent density of the scaled model; Determine the density similarity ratio of the main beam and the density similarity ratio of the bridge tower based on the equivalent density of the scaled model; Determining the weight of the main beam and the weight of the bridge tower respectively based on the density similarity ratio of the main beam and the density similarity ratio of the bridge tower; Based on the weight of the main beam, the weight of the bridge tower and the similarity relationship, an equivalent density similarity ratio and an equivalent elastic modulus similarity ratio are determined, and based on the equivalent density similarity ratio and the equivalent elastic modulus similarity ratio, the dynamic dimensionless parameter is adjusted to determine the actual similarity relationship between the prototype and the scaled model.

[0014] In a possible implementation, completing the scaled model design based on the actual similarity relationship includes: Based on the actual similarity relationship and the geometric scale ratio, the truss section similarity coefficient, the main beam section parameters, and the bridge tower section similarity coefficient of the scaled model are determined, wherein the truss section includes the upper chord section, the flat cross-section, and the web section; the main beam section parameters include the axial stiffness, the transverse bending stiffness, and the torsional stiffness of the main beam; and the bridge tower section includes the bridge tower upper column section and the bridge tower middle column section; The parameters of the bridge are obtained, and the scaled model design is completed based on the parameters of the bridge, the truss section similarity coefficient, the main beam section parameters, and the bridge tower section similarity coefficient.

[0015] On the other hand, the present invention also provides a bridge model design system based on static and dynamic information fusion, comprising: A static dimensionless parameter determination module, used to obtain physical quantities of a prototype and a scaled model of the bridge, and determine static dimensionless parameters based on the physical quantities and a dimensional analysis method; A dynamic dimensionless parameter determination module, used for establishing a multi-degree-of-freedom motion equation, and determining the dynamic dimensionless parameter based on the multi-degree-of-freedom motion equation and the physical quantity; The scaled model design module is used to determine the similarity relationship between the prototype and the scaled model based on the static dimensionless parameters and the 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.

[0016] The invention has the following beneficial effects: static dimensionless parameters are determined according to the dimensional analysis method, various physical quantities in the prototype structure are converted into dimensionless forms, and complex physical relationships are converted into problems that are easier to understand and handle; on the basis of dimensionless transformation, key physical parameters that have a greater impact on system behavior are determined by analyzing the similarity of physical quantities; dynamic dimensionless parameters are determined based on multi-degree-of-freedom motion equations and physical quantities, and the relationship between various physical quantities in the prototype structure is described without any units, so the invention is more applicable; the similarity relationship between the prototype and the scaled model is determined based on static dimensionless parameters and dynamic dimensionless parameters; a similarity equation reflecting the relationship between the prototype structure and the scaled structure is established by integrating static similarity and dynamic similarity; various physical quantities in the prototype structure are associated with corresponding physical quantities in the scaled structure one by one, so as to ensure that the characteristics of the scaled structure are similar to those of the prototype structure; distortion analysis is performed on the scaled model based on the similarity relationship, and the problem of inconsistent additional mass of the tower beam of the bridge model is considered; the scaled model design is completed based on the actual similarity relationship, so as to ensure that the scaled model can indirectly reflect the stress state of the prototype structure, and prove the feasibility and correctness of the scaled model design idea. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A flow chart of an embodiment of a bridge model design method based on static and dynamic information fusion provided by the present invention; Figure 2 A schematic diagram of the overall structure of a scaled model of the bridge model design method based on static and dynamic information fusion provided by the present invention; Figure 3A schematic diagram showing a comparison of finite element analysis vibration modes of a prototype structure and a scaled structure of a bridge model design method based on static and dynamic information fusion provided by the present invention; Figure 4 A schematic diagram of the measured modal vibration shape of the bridge model design method based on static and dynamic information fusion provided by the present invention; Figure 5 A schematic structural diagram of an embodiment of a bridge model design system based on static and dynamic information fusion provided by the present invention. DETAILED DESCRIPTION

[0018] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a 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 used to limit the scope of the present invention.

[0019] A specific embodiment of the present invention discloses a bridge model design method based on static and dynamic information fusion. Figure 1 is a flow chart of a bridge model design method based on static and dynamic information fusion provided by an embodiment of the present invention. Figure 1 , the bridge model design method based on static and dynamic information fusion includes: S101, obtaining physical quantities of a prototype and a scaled model of the bridge, and determining static dimensionless parameters based on the physical quantities and dimensional analysis method; S102, establishing a multi-degree-of-freedom motion equation, and determining a dynamic dimensionless parameter based on the multi-degree-of-freedom motion equation and physical quantities; S103. Determine the similarity relationship between the prototype and the scaled model based on the static dimensionless parameters and the 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.

[0020] Among them, in order to ensure that the designed scaled model can accurately reflect the mechanical properties of the prototype structure, an appropriate similarity relationship must be established between the scaled model and the prototype structure. Similarity analysis includes two requirements. First, the similarity constant is determined, that is, the ratio of the same physical quantity of the scaled model and the prototype structure is a constant. Second, the relationship between the physical quantities in the scaled model should be consistent with the relationship between the corresponding physical quantities in the prototype structure. Based on dimensional analysis and The theorem derives the static and dynamic similarity relations of the structure.

[0021] Compared with the prior art, the bridge model design method based on static and dynamic information fusion provided in this embodiment obtains the physical quantities of the prototype and the scaled model of the bridge, determines the static dimensionless parameters based on the physical quantities and the dimensional analysis method, establishes a multi-degree-of-freedom motion equation, determines the dynamic dimensionless parameters based on the multi-degree-of-freedom motion equation and the physical quantities, determines the similarity relationship between the prototype and the scaled model based on the static dimensionless parameters and the dynamic dimensionless parameters, establishes a similarity equation reflecting the relationship between the prototype structure and the scaled structure by fusing static similarity and dynamic similarity, associates each physical quantity in the prototype structure with the corresponding physical quantity in the scaled structure one by one, ensures that the characteristics of the scaled structure are similar to those of the prototype structure, performs distortion analysis on the scaled model based on the similarity relationship, determines the actual similarity relationship between the prototype and the scaled model, completes the scaled model design based on the actual similarity relationship, takes into account the problem of inconsistent added mass of the tower and beam of the bridge model, ensures that the scaled model can indirectly reflect the stress state of the prototype structure, and proves the feasibility and correctness of the scaled model design idea.

[0022] In some embodiments, in step S101, physical quantities of the prototype and the scaled model of the bridge are obtained, and the physical quantities include at least length, mass, time, speed, and density. Based on the physical quantities, static dimensionless parameters are determined according to the dimensional analysis method. The specific steps are: constructing a material mechanics model, and determining similarity constants of the prototype and the scaled model based on the material mechanics model and the physical quantities. 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. Based on the similarity constants, static dimensionless parameters are determined according to the dimensional analysis method. The 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 of the material mechanics model is: , , in, is the elastic modulus of the material, is the external force on the cross section, is the cross-sectional area, is the bending moment on the cross section, is the distance from the desired point to the neutral axis, is the section moment of inertia, is stress, Strain is a dimensionless quantity. According to the dimensional analysis method, the static dimensionless parameter is obtained. The calculation formula is: , , , , , , , , in, is the first static dimensionless parameter, indicating that the strains of the scaled model and the prototype are equal. is the second static dimensionless parameter, is the third static dimensionless parameter, is the third static dimensionless parameter, It is the fifth static dimensionless parameter, indicating that the material Poisson's ratio of the scaled model and the prototype is equal. When the manufacturing material is selected, the material Poisson's ratio, elastic modulus, and mass density are also determined. is the sixth static dimensionless parameter, indicating that the displacement of the structural line is proportional to the geometric scale. It is the seventh static dimensionless parameter, indicating that when the elastic modulus of the material is the same, the density is inversely proportional to the geometric scale. This similar relationship is difficult to achieve and is usually achieved by the method of adding mass. is the eighth static dimensionless parameter, is the material Poisson's ratio, is the linear displacement, is the material density, is the length of the component, is the acceleration due to gravity, is the distributed surface load concentration.

[0023] In some embodiments, in step S102, a multi-degree-of-freedom motion equation is established, and the dynamic dimensionless parameters are determined based on the multi-degree-of-freedom motion equation and the physical quantity. First, a dimensional matrix of multi-degree-of-freedom physical quantities is constructed based on the multi-degree-of-freedom motion equation and the physical quantity. The dynamic similarity relationship is established on the basis of the motion equation, and the calculation formula of the multi-degree-of-freedom motion equation is: , in, , , are the acceleration, velocity and displacement of the system respectively, , , are the mass matrix, damping matrix and stiffness matrix of the system respectively, is the external stimulus to the system, Related to material density and component size, The above physical quantities and displacement transfer function jointly determine the dynamic characteristics of the system, which are related to the elastic modulus of the material and the size of the component. The dimensional matrix of the multi-degree-of-freedom physical quantities is shown in Table 1. Table 1

[0024] Secondly, according to the second similarity theory, the dimensionless parameters of the dynamics are determined based on the dimension 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: , in, It is a dimensionless term composed of the physical quantity of the dynamic parameter, and the calculation formula of its dynamic dimensionless parameter is: , , , , in, is the first dimensionless dynamic parameter, indicating that when the elastic modulus of the material is the same, the external force is proportional to the square of the geometric scale ratio. For external force, is the elastic modulus of the material, is the geometric scale ratio, is the second dynamic dimensionless parameter, indicating that the natural frequency of the scaled model and the prototype is inversely proportional to the product of the geometric scale ratio and the square root of the density scale ratio. is the natural frequency, is the density, is the third dimensionless parameter of dynamics, indicating that when the acceleration of the scaled model and the prototype is the same, the linear displacement similarity ratio is equal to the square of the frequency ratio. In response to acceleration, is the linear displacement, is the fourth dimensionless parameter of dynamics, indicating that when the speed of the scaled model and the prototype is the same, the linear displacement similarity ratio is equal to the frequency comparison. For speed.

[0025] In some embodiments, in step S103, the similarity relationship between the prototype and the scaled model is determined based on the static dimensionless parameters and the dynamic dimensionless parameters. The scaled model of the bridge is designed according to the similarity criteria of the static dimensionless parameters and the dynamic dimensionless parameters, wherein the similarity constants of the elastic modulus, the system response acceleration and the geometric dimensions are used as basic variables, and other similarity constants are derived quantities. The similarity relationship between the various physical quantities of the prototype and the scaled model is shown in Table 2. Table 2

[0026] The distortion analysis of the scaled model is carried out based on the similarity relationship. First, based on the similarity relationship between the prototype and the scaled model, the similarity constant of the scaled model is obtained. Based on the similarity constant, the material type of the scaled model is determined, and the geometric scale ratio between the prototype and the scaled model is determined. Considering the factors such as the size of the laboratory site, model production and assembly, and the purpose of the test, the geometric scale ratio is determined to be 1:100. Secondly, based on the similarity relationship, material type, and geometric scale ratio, the similarity coefficient between the prototype and the scaled model is determined. The similarity coefficient between the prototype and the scaled model is shown in Table 3. Table 3

[0027] Finally, the scaled model is subjected to distortion analysis based on the similarity relationship and similarity coefficient to determine the actual similarity relationship 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 of the model needs to be obtained through distortion analysis. The process of distortion analysis of the scaled model is as follows: first, the volume of the scaled model is obtained, the density similarity ratio is obtained based on the similarity relationship, and the additional mass of the scaled model is determined based on the density similarity ratio and the volume. The calculation formula for the density similarity ratio is: , in, is the density similarity ratio, is the elastic modulus similarity ratio, is the response acceleration similarity ratio, is the geometric size similarity ratio; for models with small scale ratios, the density similarity constant is very large, and it is difficult for general model materials to meet this similarity constant requirement. Usually, the method of adding mass to the model is used to compensate for the density difference caused by the material. The additional mass is the difference between the theoretical mass and the actual mass of the scaled model. The calculation formula for the additional mass is: , in, is the theoretical additional mass that should be imposed on the model, is the density of the prototype, is the density of the model, is the theoretical density similarity ratio, is the volume of the scaled model; Due to the limitations of model size, bearing capacity, and the location of added weights, the small-scale scale model actually produced cannot add weights according to the calculated theoretical additional mass to obtain the actual mass of the scale model. The equivalent density of the scale model is determined based on the additional mass, the actual mass of the scale model, and the volume. The calculation formula for the equivalent density is: , in, is the equivalent density of the scaled model; Based on the similarity coefficient and the equivalent density of the scaled model, the theoretical density similarity ratio of the main beam and the theoretical density similarity ratio of the bridge tower are determined. Based on the density similarity ratio of the main beam and the density similarity ratio of the bridge tower, the weight of the main beam and the weight of the bridge tower are determined respectively. The calculation formula is: , in, is the actual density similarity ratio of the main beam, is the actual density similarity ratio of the bridge tower; Based on the weight of the main beam, the weight of the bridge tower and the similarity relationship, the equivalent density similarity ratio and the equivalent elastic modulus similarity ratio are determined. The calculation formula of the equivalent density similarity ratio is: , The calculation formula of the similarity ratio of equivalent elastic modulus is: , in, is the equivalent density similarity ratio, is the similarity ratio of equivalent elastic modulus, is the similarity ratio of elastic modulus of the main beam, is the similarity ratio of elastic modulus of the bridge tower; 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 model. The second dynamic dimensionless parameter is mainly adjusted. .

[0028] Based on the actual similarity relationship and the geometric scale ratio, the truss section similarity coefficient, the main beam section parameters, and the bridge tower section similarity coefficient of the scaled model are determined, wherein the truss section includes the upper chord section, the flat cross-section, and the web section, the main beam section parameters include the axial stiffness, the transverse bending stiffness, and the torsional stiffness of the main beam, and the bridge tower section includes the bridge tower upper column section and the bridge tower middle column section, and the parameters of the bridge are obtained. Based on the parameters of the bridge, the truss section similarity coefficient, the main beam section parameters, the bridge tower section similarity coefficient, and the parameters of the bridge, the scaled model design is completed; The parameters of the bridge prototype are as follows: the track form is CRTS-Ⅲ type ballastless track, which is 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 length of the bridge is 684 m, and the bridge span arrangement scheme is: the first side span is 60 m, the first middle span is 120 m, the main span is 324 m, the second middle span is 120 m, and the second side span is 60 m. The main beam is composed of a lower chord steel box beam and an upper chord steel truss beam. 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, and the truss height is 12 m. The cable tower is a reinforced concrete structure with a concrete strength grade of C60. The tower top elevation is 130.9143 m and the tower bottom elevation is 9.9130 m. The cable-stayed cable is a spatial double cable plane. There are 13 pairs of cables on both sides of each bridge tower on the facade. There are a total of 104 cables in the whole bridge, and their standard values ​​of tensile strength are all 1670 MPa; the geometric scale ratio is 1:100, The total length of the scaled model bridge is determined to be 6.84 m, that is, the bridge span is arranged to be 6.84 m, with a total of 52 pairs of cables. The entire bridge is designed as a symmetrical structure with the middle span as the symmetry axis. For the overall structural diagram of the scaled model, please refer to Figure 2 Based on the similarity relationship, the similarity constant of the scaled model is obtained, and the material type of the scaled model is determined based on the similarity constant. The material properties considered also need to consider the influence of temperature and humidity, loading rate and strain rate, size and shape on the material properties. The material properties include elastic modulus, stress characteristics, shrinkage creep. Therefore, the beams, bridge towers and piers of the scaled model are made of stainless steel, and the inclined cables are made of steel wire ropes. The beams are connected by a combination of bolts and welding. The cables are connected to the beams and bridge towers with cable bolts. The beams are connected to the piers and bridge towers with hinged supports, and the bottoms of the piers and bridge towers are fixed to the workbench with bolts.

[0029] Based on the geometric scale ratio, the truss design parameters are calculated according to the prototype parameters and the actual similarity relationship. The model truss does not contain vertical bars, the lateral spacing of the upper chord center is 14.0 cm, the lateral spacing of the lower chord is 14.0 cm, the height difference between the upper and lower chords is 12.0 cm, the segment length is 12.0 cm, the vertical inclination of the diagonal bar is 63.43°, and the truss structure is connected by 57 segments. According to the similarity coefficient requirements and actual processing needs, the truss cross-sectional dimensions of the final proposed model are: the upper chord cross-sectional dimensions are 5.5 mm*6.5 mm rectangular cross-sectional dimensions, the flat cross-sectional dimensions are 2 mm*4 mm rectangular cross-sectional dimensions, and the web cross-sectional dimensions are 5.5 mm*5.5 mm rectangular cross-sectional dimensions. The cross-sectional similarity coefficients of the scaled model truss are shown in Table 4. Table 4

[0030] in, is the axial stiffness, is the lateral bending stiffness, For torsional stiffness.

[0031] The complex structure of the prototype section is designed according to the similarity ratio. The cross-sectional size of the scaled model will be less than 1 mm, which is difficult to process in practice. Therefore, the longitudinal rib effect of the main beam section is equivalent to the thickness, and the cross-sectional thickness of the main beam is set to 1 mm. The cross-sectional design of the main beam of the scaled model needs to meet the similarity coefficients of axial stiffness, transverse bending stiffness, and torsional stiffness. The cross-sectional parameters of the main beam of the scaled model are shown in Table 5. Table 5

[0032] Since the cross-sectional inertia moment of the bridge cable has no significant effect on the stress of the scaled structure, the similarity of the cross-sectional inertia moment of the cable is ignored, and the focus is on the similarity relationship of the cross-sectional area of ​​the cable. A single steel wire rope with a diameter of 3 mm is selected to simulate the inclined cable. There are a total of 104 steel wires in the whole bridge. The tower end is connected to the tower column of the bridge tower through a cable sleeve, and the main beam end is anchored by cable bolts.

[0033] The shape of the bridge tower is designed to be the same H-shaped as the prototype bridge, the cross-sectional shape is the same rectangular as the prototype, and the axial stiffness is , bending stiffness along the bridge direction , transverse bending stiffness According to the similarity relationship between the scaled model and the prototype, the cross-sectional dimensions of the bridge tower are finally determined. The length of the upper column is 40 mm, the height is 40 mm, and the middle hollow dimension is 30 mm*24 mm; the length of the middle column is 40 mm, the height is 69 mm, and the middle hollow dimension is 39 mm*24 mm. For the cross-sectional similarity coefficient of the bridge tower, please refer to Table 6. Table 6

[0034] in, The unit is N, , The unit is .

[0035] In some embodiments, the similarity ratio values ​​are analyzed, and finite element models of the prototype structure and the scaled model structure are established respectively. The prototype structure has 1353 units and 1186 nodes, and the scaled structure has 1279 units and 1137 nodes. The establishment methods are: the cables are simulated by tension-only truss units, and the rest are simulated by beam units; the side piers, auxiliary piers and the bottom of the bridge tower are consolidated, the main beam and the pier are connected by elastic connection, and the cables are connected to the main beam and the upper tower column of the bridge tower by rigid connection; the mass of iron sand in the hollow part of the box beam and the bridge tower is equivalent to the mass of the corresponding components, and the calculation formula of the bulk density of the box beam and the bridge tower is: , , in, is the mass of iron sand added, is the volume of the corresponding component; through the distortion analysis of the scaled model, it can be known that the theoretical density similarity ratio of the main beam is , the total volume of the main beam , theoretical counterweight of main beam kg, the actual scale model is to fill the hollow space of the box beam with iron sand, the mass of the iron sand used kg, 57 pieces of 8 cm in size are evenly suspended on the bottom plate of the box beam. 8 cm A solid iron block of 15 cm in diameter with a total mass kg, the actual additional mass of the main beam only reaches 13.7% of the theoretical value, and the equivalent density of the main beam , density similarity ratio , bridge tower volume , theoretical weight kg, the actual filling of the hollow part of the bridge tower with iron sand, the mass of iron sand used kg, the actual additional mass of the bridge tower is only 0.3% of the theoretical value. , density similarity ratio , determine the modal frequency similarity ratio, which is calculated as: , The actual frequency similarity ratio between the model and the prototype is calculated based on the equivalent elastic modulus similarity ratio, equivalent density similarity ratio and geometric scale ratio. According to the actual frequency similarity ratio, the box girder density is calculated as The bridge tower density is ,The mass block suspended at the bottom of the main beam acts on the finite element model in the form of vertical node loads, with a single size of 74 N. The unit type and connection method are consistent with the prototype structure.

[0036] The modal analysis of the finite element models of the scaled structure and the prototype structure is performed separately. For the comparison diagram of the finite element analysis vibration mode of the prototype structure and the scaled structure, please refer to Figure 3 , select the above six modes (third-order horizontal, third-order vertical) to verify whether the designed scaled model meets the frequency similarity ratio between the model and the prototype derived above, the error Defined as: , in, is the frequency similarity ratio of the finite element model, To derive the frequency similarity ratio, modal frequency results, please refer to Table 7, Table 7

[0037] As shown in Table 7, the finite element analysis modal frequency errors of the prototype structure and the scaled structure are less than 7%, the maximum error is 6.99%, the minimum error is only 0.38%, and the average error is 3.74%. The reason for this error is that the distortion analysis considers the additional mass and elastic modulus that play a dominant role in the modal frequency, and other minor distortion items are not considered for the time being. For example, the cross-sectional size and shape of the scaled structure are rounded off in combination with the actual processing conditions under the premise of ensuring similar stiffness, and the cross-sectional design does not achieve complete similarity. The actual similarity ratio of the model is in good agreement with the theoretical calculation similarity ratio, which proves the correctness of the above similarity analysis and distortion analysis. At the same time, it shows that the established finite element scaled model can better predict the working state of the actual bridge, providing reference data for the monitoring and analysis of the actual bridge.

[0038] In the modal test analysis of the scaled model, the modal order can be determined by the vibration mode of the main beam, so only the vibration mode of the main beam is measured. Due to the symmetry of the model, only the vibration mode of 1 / 2 structure needs to be measured, and the modal order can be deduced according to the structural symmetry. In order to measure the complete vibration mode of the main beam and then compare it with the vibration mode of the finite element scaled model, the six-order (third-order horizontal, third-order vertical) finite element analysis mode of the scaled model is selected for comparison with the measured mode to verify whether the dynamic characteristics of the model are consistent with those of the actual scaled model, and define the modal frequency error. , , in, is the analytical modal frequency of the finite element scaled model, The measured modal frequencies of the laboratory scale model are averaged after multiple measurements. For the modal test analysis results, please refer to Table 8. For the schematic diagram of the measured modal vibration type, please refer to Figure 4 , Figure 4 In the figure, the horizontal vibration shape diagram is the top view of the steel box, and the vertical vibration shape diagram is the front view of the steel box. Table 8

[0039] As shown in Table 8, the modal frequencies of the finite element analysis are in good agreement with the first three lateral modes and the first three vertical modes of the measured modal frequencies. The modal frequency errors corresponding to the same vibration mode are within 8%, the maximum error is 7.85%, the minimum error is 0.97%, and the average error is 3.92%. The reasons for the errors are: it is difficult for the finite element analysis to accurately simulate the boundary conditions of the actual structure, and the connection stiffness of the rods in the actual structure, the physical properties of the materials, etc. cannot be accurately calculated; the noise interference and human operation errors in the modal test have a certain impact on the test results; on the other hand, the modal analysis method used in the test software itself will also produce errors. Based on the above results, the dynamic characteristics of the laboratory scale model and the finite element scale model are in good consistency.

[0040] Finite element models of the prototype structure and the scaled model were established. The modal frequency similarity ratio of the scaled model and the prototype structure was calculated based on the actual added mass of the scaled model. Finite element analysis verified that the analytical modal frequency similarity ratio was highly consistent with the derived modal frequency similarity ratio, proving the feasibility and correctness of the scaled model design idea. Modal tests were carried out on the designed scaled models, and the first three-order lateral vibration modes and the first three-order vertical vibration modes of the experimental modes and the finite element modes of the scaled structure were matched. The experimental modes of the scaled model were close to the same-order modal frequencies of the established finite element modes of the scaled structure, indicating that the experimental modes of the scaled model were in good agreement with the analytical modes of the scaled finite element model. The relevant characteristics of the laboratory scaled structure were analyzed through simple and convenient model tests, and the similarity ratio was used to deduce the prototype structure, thereby obtaining the relevant characteristics of the prototype structure, providing a reference for research on damage identification and reliability assessment of the prototype structure.

[0041] In order to better implement the bridge model design method based on static and dynamic information fusion in the embodiment of the present invention, on the basis of the bridge model design method based on static and dynamic information fusion, correspondingly, Figure 5 As shown, the embodiment of the present invention further provides a bridge model design system 500 based on static and dynamic information fusion, including: The static dimensionless parameter determination module 501 is used to obtain the physical quantities of the prototype and the scaled model of the bridge, and determine the static dimensionless parameters based on the physical quantities and the dimensional analysis method; A dynamic dimensionless parameter determination module 502 is used to establish a multi-degree-of-freedom motion equation and determine the dynamic dimensionless parameters based on the multi-degree-of-freedom motion equation and physical quantities; The scaled model design module 503 is used to determine the similarity relationship between the prototype and the scaled model based on the static dimensionless parameters and the 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.

[0042] In summary, the bridge model design method and system based on static and dynamic information fusion provided by the present invention obtain the physical quantities of the prototype and scale model of the bridge, determine the static dimensionless parameters based on the physical quantities and dimensional analysis method; establish a multi-degree-of-freedom motion equation, and determine the dynamic dimensionless parameters based on the multi-degree-of-freedom motion equation and the physical quantities; determine the 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 the actual similarity relationship between the prototype and the scale model, and complete the scale model design based on the actual similarity relationship, thereby ensuring that the scale model can indirectly reflect the stress state of the prototype structure, and proving the feasibility and correctness of the scale model design idea.

[0043] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A bridge model design method based on static and dynamic information fusion, characterized in that: include: Obtaining physical quantities of a prototype and a scaled model of the bridge, and determining static dimensionless parameters based on the physical quantities and a dimensional analysis method; Establishing a multi-degree-of-freedom motion equation, and determining a dynamic dimensionless parameter based on the multi-degree-of-freedom motion equation and the physical quantity; The similarity relationship between the prototype and the scaled model is determined based on the static dimensionless parameters and the dynamic dimensionless parameters, distortion analysis is performed on the scaled model based on the similarity relationship, the actual similarity relationship between the prototype and the scaled model is determined, and the scaled model design is completed based on the actual similarity relationship.

2. The bridge model design method based on static and dynamic information fusion according to claim 1 is characterized in that: The step of determining the static dimensionless parameter based on the physical quantity according to the dimensional analysis method includes: Constructing a material mechanics model, and determining similarity constants between the prototype and the scaled model based on the material mechanics model and the physical quantities, wherein the physical quantities at least include length, mass, time, speed, 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; Based on the similarity constant, the static dimensionless parameters are determined according to the dimensional analysis method, wherein the 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.

3. The bridge model design method based on static and dynamic information fusion according to claim 2 is characterized in that: The calculation formula of the static dimensionless parameter is: ， ， ， ， ， ， ， ， in, is the first static dimensionless parameter, is the second static dimensionless parameter, is the third static dimensionless parameter, is the third static dimensionless parameter, is the fifth static dimensionless parameter, is the sixth static dimensionless parameter, is the seventh static dimensionless parameter, is the eighth static dimensionless parameter, is the material Poisson’s ratio, is the linear displacement, is the material density, is the length of the component, is the acceleration due to gravity, is the load concentration on the distributed surface, For external force, is the elastic modulus of the material, is stress, For strain, is the bending moment on the cross section, is the distance from the desired point to the neutral axis, is the section moment of inertia.

4. The bridge model design method based on static and dynamic information fusion according to claim 2 is characterized in that: The determining of the dynamic dimensionless parameter based on the multi-degree-of-freedom motion equation and the physical quantity comprises: Constructing a dimensional matrix of multi-degree-of-freedom physical quantities based on the multi-degree-of-freedom motion equations and the physical quantities; According to the second similarity theory, the dynamic dimensionless parameters are determined based on the dimension matrix of the multi-degree-of-freedom physical quantity, 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.

5. The bridge model design method based on static and dynamic information fusion according to claim 4 is characterized in that: The calculation formula of the dimensionless parameters of the power is: ， ， ， ， in, is the first dynamic dimensionless parameter, For external force, is the elastic modulus of the material, is the geometric scale ratio, is the second dynamic dimensionless parameter, is the natural frequency, is the density, is the dimensionless parameter of the third dynamic force, In response to acceleration, is the linear displacement, is the fourth dynamic dimensionless parameter, For speed.

6. The bridge model design method based on static and dynamic information fusion according to claim 5 is characterized in that: The calculation formula for the similarity relationship between the prototype and the scaled model is: ， ， ， in, is the elastic modulus of the prototype, is the elastic modulus similarity ratio, is the elastic modulus of the scaled model, The geometric dimensions of the prototype, is the geometric size of the scaled model, is the geometric size similarity ratio, is the response acceleration similarity ratio, is the response acceleration of the prototype, Response acceleration of the scaled model.

7. The bridge model design method based on static and dynamic information fusion according to claim 5 is characterized in that: The 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: Obtaining a similarity constant of the scaled model based on the similarity relationship, and determining a material type of the scaled model based on the similarity constant; Determining a geometric scale ratio between the prototype and the scaled model, and determining a similarity coefficient between the prototype and the scaled model based on the similarity relationship, the material type, and the geometric scale ratio; The scaled model is subjected to distortion analysis based on the similarity relationship and the similarity coefficient to determine the actual similarity relationship between the prototype and the scaled model.

8. The bridge model design method based on static and dynamic information fusion according to claim 7 is characterized in that: The performing distortion analysis on the scaled model based on the similarity relationship and the similarity coefficient includes: Acquiring the volume of the scaled model, obtaining a density similarity ratio based on the similarity relationship, and determining an additional mass of the scaled model based on the density similarity ratio and the volume; Acquiring the actual mass of the scaled model, and determining the equivalent density of the scaled model based on the additional mass, the actual mass and the volume of the scaled model; Determine the theoretical density similarity ratio of the main beam and the theoretical density similarity ratio of the bridge tower based on the similarity coefficient and the equivalent density of the scaled model; Determine the density similarity ratio of the main beam and the density similarity ratio of the bridge tower based on the equivalent density of the scaled model; Determining the weight of the main beam and the weight of the bridge tower respectively based on the density similarity ratio of the main beam and the density similarity ratio of the bridge tower; Based on the weight of the main beam, the weight of the bridge tower and the similarity relationship, an equivalent density similarity ratio and an equivalent elastic modulus similarity ratio are determined, and based on the equivalent density similarity ratio and the equivalent elastic modulus similarity ratio, the dynamic dimensionless parameter is adjusted to determine the actual similarity relationship between the prototype and the scaled model.

9. The bridge model design method based on static and dynamic information fusion according to claim 8 is characterized in that: The step of completing the scale model design based on the actual similarity relationship includes: Based on the actual similarity relationship and the geometric scale ratio, the truss section similarity coefficient, the main beam section parameters, and the bridge tower section similarity coefficient of the scaled model are determined, wherein the truss section includes the upper chord section, the flat cross-section, and the web section; the main beam section parameters include the axial stiffness, the transverse bending stiffness, and the torsional stiffness of the main beam; and the bridge tower section includes the bridge tower upper column section and the bridge tower middle column section; The parameters of the bridge are obtained, and the scaled model design is completed based on the parameters of the bridge, the truss section similarity coefficient, the main beam section parameters, and the bridge tower section similarity coefficient.

10. A bridge model design system based on static and dynamic information fusion, characterized in that: include: A static dimensionless parameter determination module, used to obtain physical quantities of a prototype and a scaled model of the bridge, and determine static dimensionless parameters based on the physical quantities and a dimensional analysis method; A dynamic dimensionless parameter determination module, used for establishing a multi-degree-of-freedom motion equation, and determining the dynamic dimensionless parameter based on the multi-degree-of-freedom motion equation and the physical quantity; The scaled model design module is used to determine the similarity relationship between the prototype and the scaled model based on the static dimensionless parameters and the 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.

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