A method, system, and medium for determining the failure mode of a cable-stayed arch composite bridge.

Abstract

This invention discloses a method, system, and medium for determining the failure mode of a cable-arch composite bridge. The method includes: calculating the initial and deformed configurations of planar curved elements to obtain the state of the cross-section; treating the cable-arch beam as a hybrid higher-order shear model, performing vibration analysis to obtain the distribution of transverse shear stress and deriving the finite element formulas required for training the model; constructing and training an adaptive surrogate model to obtain various failure modes; conducting numerical studies to analyze the failure probability of various overall instability modes; and, based on the above analysis and calculations, determining the failure risk of the cable-arch composite bridge under different conditions, drawing conclusions to guide design, construction, maintenance, and demolition work. This invention exhibits particularly excellent performance in calculating discontinuous and composite structures. Based on this method, the numerical values ​​and stability of the cable-arch composite bridge are calculated, and the failure mode of the cable-arch structure is accurately determined based on the results.

Description

Technical Field

[0001] This invention belongs to the technical field of bridge design and assessment in the discipline of mechanics, specifically relating to a method, system, and medium for determining the failure mode of a cable-stayed arch composite bridge. Background Technology

[0002] Cable-arch structures are a new type of structure that is gradually being accepted by the engineering community. In recent years, the application of cable-arch structures in practical engineering projects both domestically and internationally has become increasingly widespread. The basic form of a cable-arch structure, its core concept is to add cables to a conventional arch structure, thereby overcoming the shortcomings of arch structures such as large horizontal thrust at the bottom and susceptibility to instability and failure, thus significantly improving the overall stiffness and ultimate bearing capacity of the structure.

[0003] While the addition of cables can improve the ultimate bearing capacity of a structure, its equilibrium path shows that cable-arch structures often reach a critical point under conditions of relatively small deformation, and the bearing capacity decreases rapidly after crossing this point. In other words, when a cable-arch structure undergoes significant deformation, its bearing capacity may drop sharply, potentially leading to overall structural failure. From the perspective of structural stress characteristics and design, cables share the load that a typical arch structure would bear, reducing the internal forces of the arch and allowing for smaller cross-sectional dimensions and material properties. However, for arch structures primarily subjected to axial compression, the stability issues arising from reduced cross-sections and materials cannot be ignored. In particular, the complexity of cable construction increases structural uncertainty, and cable failure or breakage can trigger additional dynamic effects, all of which increase the structural risk.

[0004] First, existing research has shown that in some stability assessment scenarios, traditional linear buckling theory is insufficient to accurately predict the instability characteristics of cable-arch structures when large deformations occur. To more accurately simulate the nonlinear behavior of structures, the effects of large displacements, large rotations, and material nonlinearity must be considered, requiring research through full-process nonlinear simulation analysis. For the nonlinear stability analysis of cable-arch structures, theoretical methods for establishing governing equations and deriving analytical solutions are extremely complex, and sometimes infeasible. In contrast, the nonlinear finite element method is a feasible approach. In fact, most current research results are obtained using finite element simulation technology, and beam elements and cable elements are the two basic element models for finite element analysis of cable-arch structures.

[0005] For decades, mechanics researchers have done extensive work on developing high-performance beam elements and efficient solution algorithms. Research has progressed from elastic problems to elastoplastic problems, from planar problems to spatial problems, and from deterministic problems to uncertain problems. Element models have also evolved from straight beam models to curved beam models. However, most current research on the nonlinear stability behavior of cable-arch structures is based on deterministic theory and fails to reveal the intrinsic laws governing structural reliability. Summary of the Invention

[0006] The main objective of this invention is to overcome the shortcomings and deficiencies of the prior art and to provide a method, system, and medium for determining the failure mode of a cable-stayed arch composite bridge.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] One aspect of the present invention provides a method for determining the failure mode of a cable-stayed arch bridge, comprising the following steps:

[0009] Calculate the initial and deformed configurations of the planar curve element to obtain the state of the cross section;

[0010] The cable-stayed arch structure beam is treated as a hybrid high-order shear model, and vibration analysis is performed to obtain the distribution of transverse shear stress.

[0011] Based on the obtained distribution, the finite element formula required for training the model is derived by applying the principle of mixed energy variation.

[0012] An adaptive agent model was constructed and trained to derive various forms of destruction modes;

[0013] Numerical studies were conducted on the various failure modes obtained to analyze the failure probability of various overall instability modes;

[0014] Based on the above analysis and calculations, the risk of damage to cable-stayed arch bridges is determined according to different situations, and conclusions are drawn to guide the design, construction, maintenance and demolition work.

[0015] As a preferred technical solution, the state of the cross section includes the positional state of the cross section's center point and the rotational state of the cross section; the initial configuration and deformed configuration of the calculated planar curve element are used to obtain the state of the cross section, specifically as follows:

[0016] Calculate the tensile strain, shear strain, and curvature of the curve:

[0017] ε G (s)=r1(s)cosθ(s)+r2(s)sinθ(s)-1;

[0018] γ G(s)=r2(s)cosθ(s)-r1(s)sinθ(s);

[0019] K G (s)=θ(s)-θ0(s; (1)

[0020] Where, ε G (s) represents the tensile strain of the curve, γ G (s) represents the shear strain of the curve, K G (s) is the curvature of the curve, r1(s) and r2(s) are the positions of the curve axis, θ(s) is the azimuth angle of the cross section, and θ0(s) is the azimuth angle of the cross section of the initial configuration;

[0021] The position state of the cross-sectional element is calculated using the following expression:

[0022]

[0023] in, Here, s represents the initial position state quantity, and s represents the curve coordinate. Let ξ be the state variable at a certain position, and let ξ be the state at a certain position.

[0024] Using equation (1) and the relationship between the stress tensor and strain tensor of the curve, equation (2) is further expressed as follows:

[0025]

[0026] in, For rotational components, The vertical component is... and It is a function related to position and state variables;

[0027] Calculate the first-order constant-coefficient differential equations concerning the position state quantities based on the unit's compatibility conditions:

[0028]

[0029] in, This refers to the end position state quantity;

[0030] With the initial position and state already determined, the position and state quantities at any position can be obtained using numerical methods.

[0031] As a preferred technical solution, the cable-stayed arch structure beam is treated as a hybrid high-order shear model for vibration analysis, specifically as follows:

[0032] Under the hybrid higher-order shear model, the reasonable distribution of transverse shear stress is derived by using the stress balance equation, that is, the transverse shear stress that satisfies the stress balance equation.

[0033] The stress balance equation states that the sum of the derivative of the normal stress with respect to the axial coordinate and the derivative of the transverse shear stress with respect to the transverse coordinate is zero.

[0034] As a preferred technical solution, the principle of change based on mixed energy is specifically as follows: the displacement field and stress field inside the unit are represented by nodal displacement vectors and internal force vectors to obtain mixed changes;

[0035] The finite element formula required for deriving the training model is as follows:

[0036] By using the calculated initial and deformed configurations of the planar curve elements, a reasonable distribution of transverse shear stress is established for geometric nonlinear analysis with discontinuous stiffness.

[0037] In the proposed formula, the distribution of the resultant stress along the axial direction of the cable arch structure, including axial force, shear force and bending moment, is regarded as an unknown quantity. The solution of the equilibrium differential equation in the geometrically accurate cable arch theory is used to predetermine the specific form of these unknown quantities, perform incremental / iterative solutions, and derive the finite element nonlinear equation system and its linearization process.

[0038] In addition, numerical examples were used to examine the performance of the developed unit and the influence of cable distribution on the nonlinear stability of the circular arch.

[0039] As a preferred technical solution, the construction and training of the adaptive proxy model yields multiple forms of destruction modes, specifically:

[0040] S1. By changing the material properties and introducing geometric defects, considering cable failure, initial samples are randomly generated;

[0041] S2. Using the finite element formula, calculate the ultimate bearing capacity of the cable-arch structure under different conditions when the structure becomes unstable / fails through the nonlinear full-process analysis module of the cable-arch structure. Mark the initial sample with the ultimate bearing capacity calculated by this module and add it to the marked sample set.

[0042] S3. Construct an adaptive surrogate model based on SVM+Kriging, taking the state of the cable arch structure as input and the predicted value of the ultimate bearing capacity as output, and train it on the labeled sample set.

[0043] S4. Randomly generate an unlabeled sample set based on uncertain factors, and use an adaptive surrogate model to predict the function values ​​corresponding to the unlabeled sample set in order to determine whether the structure is safe.

[0044] S5. Select the samples predicted by the adaptive surrogate model according to the selection function, and send them to the nonlinear full-process analysis module of cable-arch structure to mark the selected samples;

[0045] S6. Add the labeled samples from step S5 to the labeled sample set, and repeat steps S3-S5 until the termination condition is met to obtain the trained adaptive surrogate model.

[0046] As a preferred technical solution, the construction principle of the selection function is as follows:

[0047] 1. Is the sample state close to the limit state?

[0048] 2. The positional relationship between the sample and the sample points in the labeled sample set;

[0049] 3. Select one or more.

[0050] As a preferred technical solution, the numerical study of the obtained various failure modes specifically includes:

[0051] Construct geometrically accurate cable arch element equations based on displacement;

[0052] For each unit, set its node position and number, and perform numerical integration;

[0053] The model was created using equal-length cable arch elements.

[0054] The nonlinearity is solved using an incremental / iterative scheme with load control, and the nonlinear displacement solution is solved using 10 equal incremental load steps.

[0055] Based on elements with different levels of refinement, displacements and rotations under different bending moments are obtained.

[0056] As a preferred technical solution, the following steps are also included: by comparing the reliability changes under whether the cables fail, the relationship between the failure characteristics and the cable arrangement is analyzed, and the relationship between the nonlinear equilibrium path of the structure and the failure risk is further determined.

[0057] Another aspect of the present invention provides a system for determining the failure mode of a cable-arch composite bridge, applied to the aforementioned method for determining the failure mode of a cable-arch composite bridge, comprising a cross-sectional state calculation module, a vibration analysis module, a finite element formula derivation module, a failure mode generation module, a numerical study module, and a result output module.

[0058] The cross-section state calculation module is used to calculate the initial configuration and deformed configuration of the planar curve element to obtain the state of the cross section;

[0059] The vibration analysis module is used to treat the cable arch structure beam as a hybrid high-order shear model, perform vibration analysis, and obtain the distribution of transverse shear stress.

[0060] The finite element formula derivation module is used to combine the obtained distribution and apply the principle of mixed energy change to derive the finite element formula required for training the model.

[0061] The destruction mode generation module is used to construct and train an adaptive proxy model to derive various destruction modes;

[0062] The numerical study module is used to conduct numerical studies on the various failure modes obtained and to analyze the failure probability of various overall instability modes.

[0063] The result output module is used to determine the risk of damage to cable-arch composite bridges under different circumstances, draw conclusions, and guide design, construction, maintenance, and demolition work.

[0064] In another aspect, the present invention provides a storage medium storing a program that, when executed by a processor, implements the above-described method for determining the failure mode of a cable-stayed arch composite bridge.

[0065] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0066] (1) This invention, based on nonlinear theory and reliability theory, and combined with a surrogate model-based structural uncertainty analysis method, studies the stochastic nonlinear behavior of cable-arch structures, explores the failure modes of cable-arch structures, and solves the problem of stability and reliability of (nonlinear) cable-arch structures. The research results of this invention provide a basis for engineering determination of the degree of failure of cable-arch structures, and the proposed determination method provides an effective basis for the reliability and stability assessment of cable-arch structures.

[0067] (2) Introduce the structural nonlinear full-process analysis method to analyze the cable-arch composite bridge and establish the instability / failure mode of the cable-arch composite bridge under different conditions.

[0068] (3) Introducing stress balance equations can significantly improve the accuracy of vibration analysis of shear deformation model elements.

[0069] (4) The proposed cable-arch composite bridge model achieves higher accuracy in vibration frequency calculation.

[0070] (5) For the model analysis constructed in this invention, the reasonable redistribution of transverse shear stress is of decisive significance for achieving a high-precision analytical solution.

[0071] (6) This invention has particularly excellent performance in the calculation of discontinuous and composite structures. Based on this method, the numerical values ​​and stability of cable-stayed arch composite bridges are calculated, and the failure modes of cable-stayed arch structures are accurately determined based on the results. Attached Figure Description

[0072] Figure 1 This is a flowchart of a method for determining the failure mode of a cable-stayed arch bridge according to an embodiment of the present invention;

[0073] Figure 2 These are schematic diagrams of the initial and deformed configurations of the planar curve unit according to an embodiment of the present invention;

[0074] Figure 3 This is a schematic diagram illustrating the training of the adaptive proxy model according to an embodiment of the present invention;

[0075] Figure 4 This is a schematic diagram of a system for determining the failure mode of a cable-stayed arch bridge according to an embodiment of the present invention;

[0076] Figure 5 This is a schematic diagram of the structure of the storage medium according to an embodiment of the present invention. Detailed Implementation

[0077] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without creative effort are within the scope of protection of the present application.

[0078] Example

[0079] This invention, based on the definition of internal force fields, treats the cable-stayed arch structure beam as a hybrid higher-order shear model. Only the form of the internal force field needs to be predefined; the displacement field is obtained through integration, eliminating the need for rotational interpolation. This effectively ensures the objectivity of strain and thus exhibits excellent performance. This invention is achieved through the following methods:

[0080] 1. Research on nonlinear full-process analysis methods for cable-arch structures

[0081] This paper presents a nonlinear full-process analysis of cable-arch structures based on geometrically accurate beam theory, deriving the implementation and application of a geometrically accurate beam element model defined by internal force fields. Through theoretical derivation, fundamental unknown fields different from those of conventional elements are established, along with the definition of the degrees of freedom, nonlinear equilibrium equation system, and its linearized form for the new elements. The initial and deformed configurations of the planar curve elements are calculated. Based on the derived formulas, a computer program is used for implementation. Combined with nonlinear solution algorithms, necessary modifications and extensions are made to the geometrically accurate beam element model based on internal force field definitions, ultimately realizing a nonlinear analysis module for cable-arch structures.

[0082] 2. Stochastic nonlinear stability behavior of cable-arch structures and methods for determining the failure mode of this composite bridge

[0083] A stochastic nonlinear stability analysis platform for cable-arch structures is constructed by combining a nonlinear full-process analysis method with an adaptive surrogate model strategy. Using this platform, the stochastic nonlinear behavior of cable-arch structures is determined through numerical experiments, thereby establishing a method for determining the failure mode of cable-arch composite bridges.

[0084] like Figure 1 As shown in the figure, this embodiment provides a method for determining the failure mode of a cable-stayed arch composite bridge, including the following steps:

[0085] Step 1: Calculate the initial and deformed configurations of the planar curve elements to obtain the state of the cross-section, specifically:

[0086] like Figure 2 As shown, g1 = [1 0] T and g2 = [0 1] T These are the basis vectors of the global coordinate system. The two ends of the beam are represented by 'a' and 'b'. The total length of the curve is L, and s∈[0,L] are the curve coordinates.

[0087] The position of the curve axis is described by r1(s) and r2(s).

[0088] The azimuth angle of the cross section is represented by θ(s).

[0089] And r 01 (s), r 02 θ(s) and θ0(s) represent the axial position description and cross-sectional azimuth of the initial configuration.

[0090] G1(s) and G2(s) are the basis vectors representing the cross-sectional coordinate system.

[0091] According to geometrically precise beam theory, the tensile strain, shear strain, and curvature of a curve can be calculated using the following formula:

[0092] ε G (s)=r1(s)cosθ(s)+r2(s)sinθ(s)-1

[0093] γ G (s)=r2(s)cosθ(s)-r1(s)sinθ(s)

[0094] K G (s)=θ(s)-θ0(s) (1)

[0095] Where, ε G (s) represents the tensile strain of the curve, γ G (s) represents the shear strain of the curve, K Gr(s) is the curvature of the curve, r1(s) and r2(s) are the positions of the curve axis, and θ(s) is the azimuth angle of the cross section. 0，s (s) represents the cross-sectional azimuth angle of the initial configuration.

[0096] The position state is determined by r1(s), r2(s), and N, while the internal force state is determined by N. G (s), Q G (s) and M G (s) (representing axial force, shear force, and bending moment, respectively) are determined. N G (s), Q G (s) and M G The subscript 'G' in (s) indicates that it corresponds to the cross-sectional coordinate system. Correspondingly, the internal force state quantities corresponding to the global coordinate system are represented by N. g (s), Q g (s) and M g (s) indicates.

[0097] First, the expression for the position state of the cross-sectional element is as follows:

[0098]

[0099] in, Here, s represents the initial position state quantity, and s represents the curve coordinate. Let ξ be the state variable at a certain position, and let ξ be the state at a certain position.

[0100] Using equation (1) and the constitutive relation of the beam (i.e., the relationship between its stress tensor and strain tensor), the above equation can be further expressed as follows:

[0101]

[0102] in, For rotational components, The vertical component is... and It is a function related to position and state quantities, and its specific form can be derived theoretically.

[0103] Calculate the first-order constant-coefficient differential equations concerning the position state quantities based on the unit's compatibility conditions:

[0104] Based on the coordination conditions of the units, the following can be derived:

[0105]

[0106] Equation (4) illustrates that the distribution of the element's positional state can be determined by the internal force parameters and the positional state at the element's initial position. Combined with the determined initial positional state, numerical methods such as the Runge-Kutta method, Euler's method, linear multistep methods, and numerical solutions to differential equations can be used to solve for the positional state variables at any location. This invention employs the Runge-Kutta method to solve for the positional state variables at any location.

[0107] Step 2: Treat the cable-stayed arch structure beam as a hybrid higher-order shear model and perform vibration analysis on the model, specifically:

[0108] Under the hybrid higher-order shear model, the reasonable distribution of transverse shear stress is derived using the stress balance equation; that is, the transverse shear stress that satisfies the stress balance equation.

[0109] The stress balance equation states that the sum of the derivative of the normal stress with respect to the axial coordinate and the derivative of the transverse shear stress with respect to the transverse coordinate is zero.

[0110] Step 3: Combining the distribution obtained in Step 2, and applying the principle of mixed energy variation, derive the finite element formula for vibration analysis orientation, as follows:

[0111] The principle of change based on mixed energy is specifically as follows: the displacement field and stress field inside the unit are represented by nodal displacement vectors and internal force vectors to obtain mixed changes;

[0112] Using the initial and deformed configurations of the planar curve elements calculated in Step 1, a force-based cable arch element formulation is established in Step 2 (i.e., establishing a reasonable distribution of transverse shear stress in Step 2) for geometric nonlinear analysis with discontinuous stiffness. In the proposed formula, the distribution of the resultant stress along the axial direction of the cable arch structure, including axial force, shear force, and bending moment, is considered an unknown. The solutions to the equilibrium differential equations in the geometrically accurate cable arch theory are used to predetermine the specific forms of these unknowns. In Step 3, incremental / iterative solutions are used to derive the finite element nonlinear equations and their linearization process. Furthermore, numerical examples are used to examine the performance of the developed element and the influence of cable distribution on the nonlinear stability of the circular arch.

[0113] Step 4: Using the finite element formula from Step 3, by changing material properties and introducing geometric defects, and considering cable failure, training samples are constructed based on common modes of structural instability / failure of cable-stayed arch bridges under different conditions. Through active learning under computer simulation, an adaptive surrogate model is constructed and trained to derive various failure modes, i.e., possible extreme cases under different conditions.

[0114] like Figure 3As shown, a sample selection function is established based on different sample importance principles, and valuable samples are selected using this function. The selected high-value samples are then labeled using an adaptive surrogate model (by calling the structural nonlinear full-process analysis module). In this process, the cable-arch structure nonlinear full-process analysis module acts as the supervisor, primarily responsible for labeling the samples. In each iteration, the adaptive surrogate model predicts the function values ​​corresponding to unlabeled samples, including the structure's ultimate bearing capacity and ultimate displacement. After selecting one or more unlabeled samples according to given criteria, the supervisor labels the selected samples and adds them to the labeled sample set. Finally, the adaptive surrogate model is trained using the updated labeled sample set.

[0115] Furthermore, the constructed and trained adaptive agent model yields multiple forms of disruption modes, specifically:

[0116] S1. Randomly generate initial samples;

[0117] S2. Calculate the ultimate bearing capacity of the cable-arch structure using the nonlinear full-process analysis module. Mark the initial sample with the ultimate bearing capacity calculated by this module and add it to the marked sample set.

[0118] S3. Construct an adaptive surrogate model based on SVM+Kriging, taking the state of the cable arch structure as input and the predicted ultimate bearing capacity as output, and train it on the labeled sample set.

[0119] S4. Randomly generate an unlabeled sample set based on uncertain factors, and use an adaptive surrogate model to predict the function values ​​corresponding to the unlabeled sample set in order to determine whether the structure is safe.

[0120] S5. Select the samples predicted by the adaptive surrogate model according to the selection function, and send them to the nonlinear full-process analysis module of cable-arch structure to mark the selected samples;

[0121] S6. Add the labeled samples from step S5 to the labeled sample set, and repeat steps S3-S5 until the termination condition is met to obtain the trained adaptive surrogate model.

[0122] Furthermore, in step S5, the specific construction principle of the selection function is as follows:

[0123] 1. Is the sample state close to the limit state?

[0124] 2. The positional relationship between the sample and the sample points in the labeled sample set;

[0125] 3. Select one or more.

[0126] Step 5: The data obtained after training the adaptive surrogate model, i.e., the values ​​of the function, including the ultimate bearing capacity and ultimate displacement of the structure, are fed back into the self-built analysis platform for analysis. The analysis includes numerical studies on the stochastic behavior and reliability of cable-arch structures, using interval models for partitioning and combination, and analyzing the failure probability of various overall instability modes through numerical experiments;

[0127] Furthermore, to demonstrate the performance of the proposed method, numerical examples are provided.

[0128] For the geometrically accurate cable arch element equations based on displacement, r1(s), r2(s), and θ(s) are considered as unknowns. For a cable arch element with 4 nodes, its unknowns are approximately:

[0129]

[0130]

[0131]

[0132] Where, N i (s), (i = 1, 2, 3, 4) represents the relationship with the i-th node, and θ i The Lagrange interpolation functions associated with (i = 1, 2, 3, 4) send the position vector component and direction angle component at the i-th node, respectively.

[0133] For each element, the node locations are set to match the Gauss-Lobatto integration points. The number of nodes in each element is set to 4. Numerical integration is performed using Gauss-Lobatto integration for both elements.

[0134] The geometric and material properties considered are detailed below: E = 2.1 × 10 4 G = 1.05 × 10 4 , L0=100, A=20, I=1.6667, k s =5 / 6, considering three different bending moment values ​​(M=100, M=1000, M=4000), and modeling with equal-length cable arch elements. An incremental / iterative scheme with load control is used to solve the nonlinearity, and 10 equal-increment load steps are used to solve the nonlinear displacement solution. Based on two elements with different refinement levels, displacement and rotation under different bending moments are obtained. Results show that for M=100 and M=1000, one element described in this method is sufficient to obtain an exact solution. For M=4000, four elements are sufficient. It is worth noting that when using four cable arch elements, the computation time is 0.23 s, while the computation time using the traditional method is 42.28 s.

[0135] Step 6: By comparing the reliability changes under cable failure conditions, analyze the relationship between failure characteristics and cable arrangement, and further determine the relationship between the nonlinear equilibrium path of the structure and the failure risk.

[0136] Step 7: Based on the above analysis and calculations, determine the risk of damage to the cable-arch composite bridge under different circumstances, draw conclusions, and guide the design, construction, maintenance, and demolition work.

[0137] This invention primarily employs numerical experiments, divided into two phases. The first phase verifies the effectiveness of the structural nonlinear full-process analysis method and the failure modes of cable-arch composite bridges. The second phase clarifies the probability of failure and the risk of structural failure in cable-arch composite bridges. By comparing reliability changes under conditions of structural failure, the relationship between failure characteristics and cable arrangement is analyzed, and the connection between the nonlinear equilibrium path of the structure and the failure risk is further derived. Based on the results, a precise judgment is made on the failure mode of the cable-arch structure.

[0138] like Figure 4 As shown, in another embodiment of this application, a system for determining the failure mode of a cable-stayed arch bridge is provided. The system includes a cross-sectional state calculation module, a vibration analysis module, a finite element formula derivation module, a failure mode generation module, a numerical study module, and a result output module.

[0139] The cross-section state calculation module is used to calculate the initial configuration and deformed configuration of the planar curve element to obtain the state of the cross section;

[0140] The vibration analysis module is used to treat the cable arch structure beam as a hybrid high-order shear model for vibration analysis.

[0141] The finite element formula derivation module is used to combine the distribution obtained in step two and apply the principle of mixed energy change to derive the finite element formula required for training the model.

[0142] The failure mode generation module is used to apply the finite element formula in step three, by changing material properties, introducing geometric defects, and considering cable failure, to construct training samples based on common modes of structural instability / failure of cable-arch composite bridges under different conditions, construct and train an adaptive surrogate model, and derive various forms of failure modes.

[0143] The numerical study module is used to conduct numerical studies on the various failure modes obtained and to analyze the failure probability of various overall instability modes.

[0144] The result output module is used to determine the risk of damage to cable-arch composite bridges under different circumstances, draw conclusions, and guide design, construction, maintenance, and demolition work.

[0145] It should be noted that the system provided in the above embodiments is only an example of the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure can be divided into different functional modules to complete all or part of the functions described above. This system is a method for determining the failure mode of a cable-stayed arch composite bridge applied to the above embodiments.

[0146] like Figure 5 As shown, in another embodiment of this application, a storage medium is also provided, storing a program. When the program is executed by a processor, it implements a method for determining the failure mode of a cable-stayed arch composite bridge as described in the above embodiment, specifically:

[0147] Step 1: Calculate the initial configuration and deformed configuration of the planar curve element to obtain the state of the cross section;

[0148] Step 2: Treat the cable-stayed arch structure beam as a hybrid higher-order shear model and perform vibration analysis;

[0149] Step 3: Based on the distribution obtained in Step 2, apply the principle of mixed energy variation to derive the finite element formula required for training the model.

[0150] Step 4: Using the finite element formula from Step 3, by changing material properties, introducing geometric defects, and considering cable failure, training samples are constructed based on common modes of structural instability / failure of cable-arch composite bridges under different conditions. An adaptive surrogate model is constructed and trained to derive various forms of diverse failure modes.

[0151] Step 5: Conduct numerical studies on the various failure modes obtained, and analyze the failure probability of various overall instability modes;

[0152] Step 6: By comparing the reliability changes under cable failure conditions, analyze the relationship between failure characteristics and cable arrangement, and further determine the relationship between the nonlinear equilibrium path of the structure and the failure risk.

[0153] Step 7: Based on the above analysis and calculations, determine the risk of damage to the cable-arch composite bridge under different circumstances, draw conclusions, and guide the design, construction, maintenance, and demolition work.

[0154] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0155] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for determining the failure mode of a cable-stayed arch composite bridge, characterized in that, Includes the following steps: Calculate the initial and deformed configurations of the planar curve element to obtain the state of the cross section; The cable-stayed arch structure beam is treated as a hybrid high-order shear model, and vibration analysis is performed to obtain the distribution of transverse shear stress. Based on the obtained distribution, the finite element formula required for training the model is derived by applying the principle of mixed energy variation. An adaptive agent model was constructed and trained, resulting in various forms of disruption modes, specifically: S1. By changing the material properties and introducing geometric defects, considering cable failure, initial samples are randomly generated; S2. Using the finite element formula, calculate the ultimate bearing capacity of the cable-arch structure under different conditions when the structure becomes unstable / fails through the nonlinear full-process analysis module of the cable-arch structure. Mark the initial sample with the ultimate bearing capacity calculated by this module and add it to the marked sample set. S3. Construct an adaptive surrogate model based on SVM+Kriging, taking the state of the cable arch structure as input and the predicted value of the ultimate bearing capacity as output, and train it based on the labeled sample set. S4. Based on uncertain factors, an unlabeled sample set is randomly generated, and an adaptive surrogate model is used to predict the function values ​​corresponding to the unlabeled sample set in order to determine whether the structure is safe. S5. Select the samples predicted by the adaptive surrogate model according to the selection function, and send them to the nonlinear full-process analysis module of cable-arch structure to mark the selected samples; S6. Add the labeled samples from step S5 to the labeled sample set, and repeat steps S3-S5 until the termination condition is met to obtain the trained adaptive surrogate model. Numerical studies were conducted on the various failure modes obtained to analyze the failure probability of various overall instability modes; Based on the above analysis and calculations, the risk of damage to cable-arch composite bridges is determined according to different situations, and conclusions are drawn to guide the design, construction, maintenance and demolition work.

2. The method for determining the failure mode of a cable-stayed arch composite bridge according to claim 1, characterized in that, The state of the cross section includes the positional state of the cross section's center point and the rotational state of the cross section; the initial and deformed configurations of the calculated planar curve elements are used to derive the state of the cross section, specifically as follows: Calculate the tensile strain, shear strain, and curvature of the curve: ； ； ； （1）； in, Let be the tensile strain of the curve. The shear strain of the curve is given. Let be the curvature of the curve. , The position of the curve axis. The azimuth angle of the cross section. The azimuth angle of the section of the initial configuration; The position state of the cross-sectional element is calculated using the following expression: ；（2）； in, This is the initial position state quantity. For curve coordinates, For a state variable at a certain position, The state at a certain location; Using equation (1) and the relationship between the stress tensor and strain tensor of the curve, equation (2) is further expressed as: ； in, For rotational components, The vertical component is... and A function relating to position and state variables; Calculate the first-order constant-coefficient differential equations concerning the position state quantities based on the unit's compatibility conditions: ； in, This refers to the end position state quantity; With the initial position and state already determined, the position and state quantities at any position can be obtained using numerical methods.

3. The method for determining the failure mode of a cable-stayed arch composite bridge according to claim 1, characterized in that, The cable-stayed arch structure beam is treated as a hybrid higher-order shear model for vibration analysis, specifically: Under the hybrid higher-order shear model, the reasonable distribution of transverse shear stress is derived by using the stress balance equation, that is, the transverse shear stress that satisfies the stress balance equation. The stress balance equation states that the sum of the derivative of the normal stress with respect to the axial coordinate and the derivative of the transverse shear stress with respect to the transverse coordinate is zero.

4. The method for determining the failure mode of a cable-stayed arch composite bridge according to claim 1, characterized in that, The principle of change based on mixed energy is specifically as follows: the displacement field and stress field inside the unit are represented by nodal displacement vectors and internal force vectors to obtain mixed changes; The finite element formula required for deriving the training model is as follows: By using the calculated initial and deformed configurations of the planar curve elements, a reasonable distribution of transverse shear stress is established for geometric nonlinear analysis with discontinuous stiffness. In the proposed formula, the distribution of the resultant stress along the axial direction of the cable arch structure, including axial force, shear force and bending moment, is regarded as an unknown quantity. The solution of the equilibrium differential equation in the geometrically accurate cable arch theory is used to predetermine the specific form of these unknown quantities, perform incremental / iterative solutions, and derive the finite element nonlinear equation system and its linearization process. In addition, numerical examples were used to examine the performance of the developed unit and the influence of cable distribution on the nonlinear stability of the circular arch.

5. The method for determining the failure mode of a cable-stayed arch composite bridge according to claim 1, characterized in that, The specific principles for constructing the selection function are as follows: Is the sample state close to the limit state? The positional relationship between the sample and the sample points in the labeled sample set; Select one or more.

6. The method for determining the failure mode of a cable-stayed arch composite bridge according to claim 1, characterized in that, The numerical study of the various damage modes obtained is as follows: Construct geometrically accurate cable arch element equations based on displacement; For each unit, set its node position and number, and perform numerical integration; The model was created using equal-length cable arch elements. The nonlinearity is solved using an incremental / iterative scheme with load control, and the nonlinear displacement solution is solved using 10 equal incremental load steps. Based on elements with different levels of refinement, displacements and rotations under different bending moments are obtained.

7. The method for determining the failure mode of a cable-stayed arch composite bridge according to claim 1, characterized in that, It also includes the following steps: By comparing the reliability changes under cable failure conditions, the relationship between failure characteristics and cable arrangement is analyzed, and the relationship between the nonlinear equilibrium path of the structure and failure risk is further determined.

8. A system for determining the failure mode of a cable-stayed arch composite bridge, characterized in that, A method for determining the failure mode of a cable-arch composite bridge according to any one of claims 1-7 includes a cross-section state calculation module, a vibration analysis module, a finite element formula derivation module, a failure mode generation module, a numerical study module, and a result output module. The cross-section state calculation module is used to calculate the initial configuration and deformed configuration of the planar curve element to obtain the state of the cross section; The vibration analysis module is used to treat the cable arch structure beam as a hybrid high-order shear model, perform vibration analysis, and obtain the distribution of transverse shear stress. The finite element formula derivation module is used to combine the obtained distribution and apply the principle of mixed energy change to derive the finite element formula required for training the model. The destruction mode generation module is used to construct and train an adaptive proxy model to derive various destruction modes; The numerical study module is used to conduct numerical studies on the various failure modes obtained and to analyze the failure probability of various overall instability modes. The result output module is used to determine the risk of damage to cable-arch composite bridges under different circumstances, draw conclusions, and guide design, construction, maintenance, and demolition work.

9. A storage medium storing a program, characterized in that: When the program is executed by the processor, it implements the method for determining the failure mode of a cable-stayed arch composite bridge as described in any one of claims 1-7.

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