Structural system identification method and equipment during pouring construction of arch bridge cantilever

Abstract

The invention belongs to the related technical field of health detection, and discloses a structural system identification method and equipment during pouring construction of an arch bridge cantilever, and the method comprises the following steps: dividing the construction process of the arch bridge cantilever into a plurality of construction stages, and designing a measuring point position based on an observability state equation of the corresponding construction stage, and performing structural system identification on each construction stage by utilizing an observability technology one by one to obtain the bending rigidity and the axial rigidity of all arch rib beam units in the corresponding construction stage. According to the method, in each construction stage of arch bridge cantilever casting, the equivalent stiffness matrix equation is converted into the observable state equation, the observable state equation is solved through the null-space method, analytical solutions of the axial stiffness and the bending stiffness of arch rib beam section units in each construction stage are obtained, and the recognition precision is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to health detection, and more specifically, relates to a structural system identification method and equipment during cantilever casting construction of an arch bridge. Background Art

[0002] Due to the continuous advancement of construction technology, reinforced concrete arch bridges are becoming more and more common in the field of long-span bridges. In recent years, the cantilever casting method has been widely used in bridges with spans ranging from 150 meters to 300 meters. This method is widely used due to its advantages such as strong applicability, high safety, reasonable cost and advanced technology.

[0003] At present, the focus of stress research during the construction of the main arch ring is to ensure the safety of the main arch ring by optimizing the initial tension of the cable. However, the method of adjusting the stress of the arch ring section by the cable in practical applications has certain limitations. The adjustable range is limited. Due to the uncertainty of temporary loads and the control accuracy of on-site tensioning force, the actual stress of the arch ring is different from the theoretically calculated stress. Summary of the invention

[0004] In view of the above defects or improvement needs of the prior art, the present invention provides a structural system identification method and equipment during cantilever casting construction of an arch bridge, so as to realize parameter updating and state prediction of the arch rib segment stiffness as the construction progresses.

[0005] To achieve the above object, according to one aspect of the present invention, a method for identifying a structural system during cantilever casting construction of an arch bridge is provided, the method comprising the following steps:

[0006] The construction process of the arch bridge cantilever is divided into several construction stages. The measurement point locations are designed based on the observability state equations of the corresponding construction stages. Then, the observability technology is used to identify the structural system in each construction stage, and the bending stiffness and axial stiffness of all arch rib beam units in the corresponding construction stage are obtained.

[0007] The identification steps of the bending stiffness and axial stiffness of the beam unit in the first construction stage are as follows: first, the equilibrium equation of the first construction stage of the arch bridge cantilever is established based on the stiffness method, and then the equivalent stiffness matrix equation of the beam segment in the first construction stage is obtained;

[0008] Then, boundary conditions are introduced and observability techniques are used to separate the unknown and known quantities in the equivalent stiffness matrix equation of the beam segment in the first construction stage, and then the dynamic observability state equation is constructed, in which the known quantities include the rotation angles of the nodes.

[0009] Finally, the null space matrix of the coefficient matrix of the dynamic observability state equation is used to determine the solution of the dynamic observability state equation, and then the axial stiffness and bending stiffness of the arch rib beam unit in the first construction stage are obtained.

[0010] Furthermore, the matrix form of the equilibrium equation of the first construction stage is:

[0011]

[0012] Where: [K] is the stiffness matrix, corresponding to the characteristics of the two-dimensional beam element, including the element length L i , cross-sectional area A i 、Internal moment of inertia I zi and elastic modulus E i , i is the unit number; {δ} is the displacement column vector, including the horizontal displacement u j , vertical displacement v j and the rotation angle w j ; {f} is the force column vector, including the axial force H j , vertical force V j , bending moment M j , j is the node number.

[0013] Furthermore, the equivalent stiffness matrix equation of the beam segment in the first construction stage is:

[0014]

[0015] Where H, V and M are force vectors, u, v and w are the displacements and rotations of each node; E1A1 is the axial stiffness of the beam element in the first construction stage, and E1I1 is the bending stiffness of the beam element in the first construction stage.

[0016] Furthermore, the dynamic observability state equation corresponding to the first construction stage is:

[0017]

[0018] Furthermore, the null space matrix V of the coefficient matrix B is solved. If V does not exist, that is, V is zero-dimensional, all variables in the equation have a unique solution; when V exists and is not 0, the variables corresponding to its rows that are all zero have a unique solution, and the corresponding unique special solution variables are obtained through B\D, and then the axial stiffness and bending stiffness of the arch rib beam unit in the first construction stage are obtained.

[0019] Furthermore, the stiffness parameters of the identified beam segment are compared with the corresponding original beam segment design stiffness parameters. When the obtained difference is greater than the set threshold, the dynamic observability state equation adopts the identified stiffness parameters.

[0020] Furthermore, the coefficient matrix B of the modified dynamic observability state equation is obtained, and the observability state equation of the structure is used to perform an inverse analysis to obtain the deflection and rotation angle at each node.

[0021] The present invention also provides a structural system identification system during cantilever casting construction of an arch bridge, the system comprising a memory and a processor, the memory storing a computer program, and the processor executing the structural system identification method during cantilever casting construction of an arch bridge as described above when executing the computer program.

[0022] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the structural system identification method during the cantilever casting construction of the arch bridge as described above.

[0023] In general, compared with the prior art, the above technical solution conceived by the present invention, the structural system identification method and device during the cantilever casting construction of the arch bridge provided by the present invention mainly have the following beneficial effects:

[0024] 1. In each construction stage of the cantilever casting of the arch bridge, the equivalent stiffness matrix equation is converted into an observable state equation, and the observable state equation is solved using the null space method. The analytical solutions of the axial stiffness and bending stiffness of the arch rib beam segment unit at each construction stage are obtained and verified with the finite element model. The results show that this method has a very high accuracy in identifying the axial and bending stiffness of the structure.

[0025] 2. As the number of segments increases, the axial stiffness (EA) is kept precisely controlled and within the calculation error range through observability techniques. However, the error of the bending stiffness (EI) is unacceptable. To solve this problem, the rotation angle of the corresponding node is also taken as a measurable parameter, and then the axial stiffness and bending stiffness calculated using observability techniques are in good agreement with the actual situation.

[0026] 3. During the construction process, the stiffness of the arch rib beam unit is not constant. If this factor is ignored, it will have an adverse effect on the response prediction of the arch rib beam unit. In order to solve this problem, the changes in the stiffness parameters are updated in real time to predict the actual displacement of each unit. Specifically, the observability technology is used to inversely analyze the structural equations in the construction phase: first, the errors corresponding to the stiffness parameters of the identified beam segment and the corresponding original beam segment design stiffness parameters are compared to select the one with the smaller error. The dynamic observability state equation uses the stiffness parameter corresponding to the smaller error, and then obtains the coefficient matrix B of the modified dynamic observability state equation. The dynamic observability state equation of the structure is used to perform an inverse analysis to obtain the deflection and rotation at each node. The results show that these observations are very close to the actual deflection and rotation obtained from the updated finite element model analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a schematic diagram of the first construction phase;

[0028] Figure 2 This is a schematic diagram of the second construction phase;

[0029] Figure 3 It is a schematic diagram of the modification of the bending stiffness of the arch rib part;

[0030] Figure 4 The present invention provides a flow chart of a structural system identification method during cantilever casting construction of an arch bridge. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0032] See also Figure 4 The present invention provides a structural system identification method during the casting construction of an arch bridge cantilever, the method comprising the following steps: dividing the construction process of the arch bridge cantilever into a plurality of construction stages, designing the measurement point positions based on the observability state equations of the corresponding construction stages, and then using the observability technology to identify the structural system for each construction stage one by one, and obtaining the bending stiffness and axial stiffness of all arch rib beam units in the corresponding construction stage;

[0033] See also Figure 1 , Figure 2 and Figure 3 , wherein the identification steps of the bending stiffness and axial stiffness of the beam unit in the first construction stage are: firstly, the equilibrium equation of the first construction stage of the arch bridge cantilever is established based on the stiffness method, and then the structural system of the first construction stage is identified using the observability technology to obtain the bending stiffness and axial stiffness of the corresponding arch rib beam unit.

[0034] From the stiffness method, we know that for N N The two-dimensional structure of the node has a matrix form of equilibrium equation:

[0035]

[0036] Where: [K] is the stiffness matrix, corresponding to the characteristics of the two-dimensional beam element, including the element length L i , cross-sectional area A i 、Internal moment of inertia I zi and elastic modulus E i (i is the unit number); {δ} is the displacement column vector, including the horizontal displacement uj , vertical displacement v j and the rotation angle w j (j is the node number); {f} is the force column vector, including the axial force H j , vertical force V j , bending moment M j , j is the node number.

[0037] The beam element in the first construction stage has 2 nodes, and the external loads of the nodes include the weight of the hanging basket and the deadweight of the newly cast section. Assume that the weight of the hanging basket is 900kN, the weight of the newly cast section is 2150kN, and the characteristics of the beam element are known. Therefore, the equivalent stiffness matrix equation of the beam segment in the first construction stage can be obtained as follows:

[0038]

[0039] Where H, V and M are force vectors, u, v and w are displacements and rotations of each node; E1A1 is the axial stiffness of the beam element in the first construction stage, and E1I1 is the bending stiffness of the beam element in the first construction stage. The subscripts represent the node numbers of the beam segments in the first construction stage.

[0040] From the boundary conditions, we can see that in the above formula u1, v1, w1 = 0, and u2 and v2 can be measured, so the above quantities are all known quantities.

[0041] The observability technology is used to separate the unknown and known quantities in the equivalent stiffness matrix equation of the beam segment during the construction phase, and then the dynamic observability state equation is constructed, where the known quantities include the rotation angle of the node. The dynamic observability state equation is:

[0042]

[0043] Finally, the null space matrix of the coefficient matrix of the dynamic observability state equation is used to determine the solution of the dynamic observability state equation, and then the axial stiffness and bending stiffness of the arch rib beam unit in the first construction stage are obtained.

[0044] Specifically, observability analysis is performed based on the null space matrix. Solve the null space matrix V of the coefficient matrix B. If V does not exist, that is, when V is zero-dimensional, all variables in the equation have a unique solution; when V exists and is not 0, the variables corresponding to its rows that are all zero have a unique solution, and the corresponding unique solution variables are obtained through B\D. Thus, the bending stiffness and axial stiffness of the first section of the beam can be obtained as follows:

[0045]

[0046] The identification method of the first construction stage is used to identify the bending stiffness and axial stiffness of the beam unit in the second construction stage to obtain the bending stiffness and axial stiffness of the corresponding arch rib beam unit.

[0047] The beam element in the second construction stage has 3 nodes, and the external loads of the nodes include the weight of the hanging basket and the deadweight of the newly cast section. The weight of the hanging basket is 900kN, and the weight of the newly cast section is 2150kN.

[0048] The equivalent stiffness matrix equation of the first two beams is obtained as follows:

[0049]

[0050] Where H, V and M are force vectors, u, v and w are the displacement and rotation of each node and the symbols in the formula need to correspond, K a , K c , and K b is the stiffness matrix of the first beam segment, K d , K e , and K f is the stiffness matrix of the second beam segment.

[0051] From the boundary conditions, we can see that in the above formula u1, v1, w1 = 0, and u2, v2 and u3, v3 can be measured, so the above quantities are all known quantities.

[0052] Similarly, according to the observability method, the variables are separated and transformed into the standard form of the observability equation:

[0053]

[0054] Finally, observability analysis is performed based on the null space matrix. Solve the null space matrix V of the coefficient matrix B. If V does not exist, that is, when V is zero-dimensional, all variables in the equation have a unique solution; when V exists and is not 0, the variables corresponding to its rows that are all zero have a unique solution, and the corresponding unique special solution variables are obtained through B\D. The solution to the observability state equation of this construction stage is as follows:

[0055]

[0056] Observability techniques are used to identify the bending and axial stiffness of the arch rib beam elements corresponding to the subsequent construction stages.

[0057] Based on the above observability techniques, the axial stiffness and bending stiffness of each construction stage can be identified. However, as the number of segments increases, the axial stiffness (EA) is kept precisely controlled and within the calculation error range through the observability technique. However, the error of the bending stiffness (EI) is unacceptable. To solve this problem, the rotation angle of the corresponding node is also taken as a measurable parameter, and then the axial stiffness and bending stiffness calculated by the observability technique are consistent with the actual situation. During the construction process, the stiffness of the arch rib beam unit is not constant. If this factor is ignored, it will have an adverse effect on the response prediction of the arch rib beam unit. To solve this problem, the changes in the stiffness parameters are updated in real time to predict the actual displacement of each unit. Specifically, the observability technique was used to perform an inverse analysis of the structural equations during the construction phase: the stiffness parameters of the identified beam segments were compared with the corresponding original beam segment design stiffness parameters. When the difference was greater than the set threshold, the dynamic observability state equation adopted the identified stiffness parameters, and then the coefficient matrix B of the modified dynamic observability state equation was obtained. The dynamic observability state equation of the structure was used to perform an inverse analysis to obtain the deflections and rotations at each node. The results showed that these observations were very close to the actual deflections and rotations obtained from the updated finite element model analysis.

[0058] This approach ensures that the model remains dynamically consistent with the changing physical conditions on site, providing more accurate and realistic predictions of structural response during construction.

[0059] The present invention is further described in detail below with specific implementation modes.

[0060] This specific embodiment includes the following steps:

[0061] 1) The construction process of the arch bridge is divided into several construction stages, and the measurement point locations are designed based on the observability state equations in the corresponding construction stages. The observability technology is used to identify the structural system in each stage, and the bending stiffness and axial stiffness of all arch rib beam units in the corresponding construction stage are obtained.

[0062] S1: First, the equilibrium equation of the structure is established based on the stiffness method. Then, the observability technology is used to identify the structural system of the first construction stage to obtain the bending stiffness and axial stiffness of the corresponding arch rib beam unit.

[0063] From the stiffness method, we know that for N N The two-dimensional structure of the node has a matrix form of equilibrium equation:

[0064]

[0065] Where: [K] is the stiffness matrix, corresponding to the characteristics of the two-dimensional beam element, including the element length L i, cross-sectional area A i 、Internal moment of inertia I zi and elastic modulus E i (i is the unit number); {δ} is the displacement column vector, including the horizontal displacement u j , vertical displacement v j and the rotation angle w j (j is the node number); {f} is the force column vector, including the axial force H j , vertical force V j , bending moment M j (j is the node number).

[0066] The beam element in the first construction stage has two nodes, and the external loads of the nodes include the weight of the hanging basket and the deadweight of the newly cast section. Assume that the weight of the hanging basket is 900kN, the weight of the newly cast section is 2150kN, and the characteristics of the beam element are known. The equivalent stiffness matrix equation of the first beam section can be obtained as follows:

[0067]

[0068] Where H, V and M are force vectors, u, v and w are displacements and rotations of each node. EA is the axial stiffness of the beam element, EI is the bending stiffness of the beam element, and the subscript 1 of EA and EI indicates the beam segment in the first construction stage.

[0069] From the boundary conditions, we can see that in the above formula u1, v1, w1 = 0, and u2 and v2 can be measured, so the above quantities are all known quantities.

[0070] By using observability technology to separate the unknown and known quantities in the equation, the standard form of the dynamic observability state equation B·z=D is constructed as follows:

[0071]

[0072] Finally, observability analysis is performed based on the null space matrix. Solve the null space matrix V of the coefficient matrix B. If V does not exist, that is, when V is zero-dimensional, all variables in the equation have a unique solution; when V exists and is not 0, the variables corresponding to its rows that are all zero have a unique solution, and the corresponding unique solution variables are obtained through B\D. The bending stiffness and axial stiffness of the first beam section can be obtained as follows:

[0073]

[0074] S2: Then, the structural system of the second construction stage is identified according to the method in step S1 to obtain the corresponding bending stiffness and axial stiffness of the arch rib beam unit.

[0075] The beam element in the second construction stage has 3 nodes, and the external loads of the nodes include the weight of the hanging basket and the deadweight of the newly cast section. The weight of the hanging basket is 900kN, and the weight of the newly cast section is 2150kN.

[0076] The equivalent stiffness matrix equations of the first two beams are as follows:

[0077]

[0078] Where H, V and M are force vectors, u, v and w are the displacement and rotation of each node, and K a , K c , and K b is the stiffness matrix of the first beam segment, K d , K e , and K f is the stiffness matrix of the second beam segment.

[0079] From the boundary conditions, we can see that in the above formula u1, v1, w1 = 0, and u2, v2 and u3, v3 can be measured, so the above quantities are all known quantities.

[0080] Similarly, according to the observability method, the variables are separated and transformed into the standard form of the observability equation:

[0081]

[0082] Finally, observability analysis is performed based on the null space matrix. Solve the null space matrix V of the coefficient matrix B. If V does not exist, that is, when V is zero-dimensional, all variables in the equation have a unique solution; when V exists and is not 0, the variables corresponding to its rows that are all zero have a unique solution, and the corresponding unique special solution variables are obtained through B\D. The solution to the observability state equation of this construction stage is as follows:

[0083]

[0084] S3: Use observability techniques to identify the flexural and axial stiffness of the arch rib beam elements corresponding to the subsequent construction stages.

[0085] As described in sub-steps S1 and S2, the axial and bending stiffnesses at each construction stage can be identified based on the above observability techniques. However, as the number of segments increases, the axial stiffness (EA) is kept precisely controlled by the observability technique and within the calculation error range. However, the error of the bending stiffness (EI) is unacceptable. To solve this problem, we also take the rotation angle of the corresponding node as a measurable parameter, and then the axial stiffness and bending stiffness calculated by the observability technique are in good agreement with the actual situation.

[0086] 2) Structural response prediction

[0087] During the construction process, the stiffness of the arch rib beam unit is not static, and if this factor is ignored, it will have an adverse effect on the response prediction of the arch rib beam unit. To address this issue, the changes in the stiffness parameters in the finite element model are updated in real time to predict the actual displacement of each unit. Using observability techniques, the system identification process will first evaluate the updated bending stiffness parameters within the design parameters. Subsequently, using the updated stiffness parameters, the vertical deflection of each new segment will be predicted at each construction stage. This approach ensures that the model remains dynamically consistent with the changing physical conditions on site, providing more accurate and realistic structural response predictions during the construction process.

[0088] During the construction of the arch bridge, monitoring data such as displacement and rotation were used in the structural system identification technology. This technology is used to identify, update and establish the physical parameters of the structure in the current construction stage. The updated structural state inverse equation predicts the actual displacement and rotation of the structure in the next construction stage. The results were compared with the actual monitoring results to verify the reliability of the structural system identification algorithm during the construction of the cantilever arch bridge.

[0089] The main difference between this step and the traditional method is that the application of structural system identification and observability technology to the construction analysis of cantilever cast arch bridges can more accurately identify the axial stiffness and bending stiffness of the beam section during the cantilever casting construction of the arch bridge, and can predict the structural displacement in the next construction stage.

[0090] The present invention also provides a structural system identification system during cantilever casting construction of an arch bridge, the system comprising a memory and a processor, the memory storing a computer program, and the processor executing the structural system identification method during cantilever casting construction of an arch bridge as described above when executing the computer program.

[0091] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the structural system identification method during the cantilever casting construction of the arch bridge as described above.

[0092] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for identifying a structural system during cantilever casting construction of an arch bridge, characterized in that: The method comprises the following steps: The construction process of the arch bridge cantilever is divided into several construction stages. The measurement point locations are designed based on the observability state equations of the corresponding construction stages. Then, the observability technology is used to identify the structural system in each construction stage, and the bending stiffness and axial stiffness of all arch rib beam units in the corresponding construction stage are obtained. The identification steps of the bending stiffness and axial stiffness of the beam unit in the first construction stage are as follows: first, the equilibrium equation of the arch bridge cantilever in the first construction stage is established based on the stiffness method, and then the equivalent stiffness matrix equation of the beam segment in the first construction stage is obtained; Then, boundary conditions are introduced and observability techniques are used to separate the unknown and known quantities in the equivalent stiffness matrix equation of the beam segment in the first construction stage, and then the dynamic observability state equation is constructed, in which the known quantities include the rotation angles of the nodes. Finally, the null space matrix of the coefficient matrix of the dynamic observability state equation is used to determine the solution of the dynamic observability state equation, and then the axial stiffness and bending stiffness of the arch rib beam unit in the first construction stage are obtained.

2. The structural system identification method during cantilever casting construction of an arch bridge according to claim 1, characterized in that: The matrix form of the equilibrium equation for the first construction stage is: Where: [K] is the stiffness matrix, corresponding to the characteristics of the two-dimensional beam element, including the element length L i , cross-sectional area A i 、Internal moment of inertia I zi and elastic modulus E i , i is the unit number; {δ} is the displacement column vector, including the horizontal displacement u j , vertical displacement v j and the rotation angle w j ; {f} is the force column vector, including the axial force H j , vertical force V j , bending moment M j , j is the node number.

3. The structural system identification method during cantilever casting construction of an arch bridge according to claim 2, characterized in that: The equivalent stiffness matrix equation of the beam segment in the first construction stage is: Where H, V and M are force vectors, u, v and w are the displacements and rotations of each node; E1A1 is the axial stiffness of the beam element in the first construction stage, and E1I1 is the bending stiffness of the beam element in the first construction stage.

4. The structural system identification method during cantilever casting construction of an arch bridge according to claim 3, characterized in that: The dynamic observability state equation corresponding to the first construction stage is:

5. The structural system identification method during cantilever casting construction of an arch bridge according to claim 4, characterized in that: Solve the null space matrix V of the coefficient matrix B. If V does not exist, that is, V is zero-dimensional, all variables in the equation have a unique solution; when V exists and is not 0, the variables corresponding to its rows that are all zero have a unique solution. The corresponding unique solution variables are obtained through B\D, and then the axial stiffness and bending stiffness of the arch rib beam unit in the first construction stage are obtained.

6. The structural system identification method during cantilever casting construction of an arch bridge according to any one of claims 1 to 5, characterized in that: The stiffness parameters of the identified beam segment are compared with the corresponding original beam segment design stiffness parameters. When the difference is greater than the set threshold, the dynamic observability state equation adopts the identified stiffness parameters.

7. The structural system identification method during cantilever casting construction of an arch bridge according to claim 6, characterized in that: The coefficient matrix B of the modified dynamic observability state equation is obtained, and the observability state equation of the structure is used to perform inverse analysis to predict the deflection and rotation at the corresponding nodes in the next construction stage.

8. A structural system identification system during cantilever casting construction of an arch bridge, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the method for identifying the structural system during the cantilever casting construction of an arch bridge as described in any one of claims 1 to 7 is executed.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the structural system identification method during the cantilever casting construction of an arch bridge as described in any one of claims 1-7.

Images