A method and system for simulating stress of a variable cross-section bridge construction process

Abstract

The embodiment of the present disclosure provides a variable cross-section bridge construction process stress simulation method and system. Applied to the technical field of bridge engineering, comprising: obtaining bridge construction, constructing a spatial variable initial flexibility matrix, and outputting a multi-dimensional stress evolution vector; embedding the multi-dimensional stress evolution vector into a preset causal graph and performing dynamic reasoning to output a reasoning result; generating a plurality of candidate construction control strategies based on the reasoning result, simulating and deducing different candidate construction control strategies, selecting an optimal construction control strategy based on the deduced result; executing the optimal construction control strategy, generating an actual structure response trajectory, comparing the predicted linear evolution trajectory with the actual structure response trajectory to obtain a trajectory deviation, and adaptively correcting the parameters of the space-time graph convolution network and the parameters of the material time-varying constitutive model based on the deviation. In this way, the present application realizes high-fidelity stress simulation and intelligent control closed loop, significantly improving the accuracy and safety of variable cross-section bridge construction.

Description

Technical Field

[0001] This disclosure relates to the field of bridge engineering technology, and in particular to a method and system for simulating the stress during the construction process of a variable cross-section bridge. Background Technology

[0002] Variable cross-section bridges are widely used in urban interchanges, river crossings, and railway line crossings due to their lightweight structure, reasonable stress distribution, and good aesthetics. However, variable cross-section bridges undergo complex structural system transformations during construction, and the stress state at each stage is highly nonlinear. Traditional analysis methods are insufficient to accurately simulate the stress evolution throughout the entire construction process, especially the spatial stress behavior under the coupled action of axial force, shear force, bending moment, and torque. This can easily lead to deviations in the bridge alignment or local stress concentrations, affecting structural safety and durability.

[0003] The above problems indicate that existing technologies for simulating the stress during the construction of variable cross-section bridges have shortcomings such as oversimplification of models, insufficient consideration of coupling effects, limited applicability, and lack of dynamic and refined analysis capabilities.

[0004] Therefore, there is an urgent need for a method and system that can accurately simulate the stress state of a variable cross-section bridge throughout the entire construction process, so as to achieve dynamic prediction and safety control of the structural response during the construction stage. Summary of the Invention

[0005] This disclosure provides a method and system for simulating the stress during the construction process of a variable cross-section bridge. By constructing a spatial variable cross-section beam element based on the flexibility method, integrating the four-dimensional internal force field coupling analysis of axial force, shear force, bending moment, and torque, and combining digital twins, spatiotemporal graph convolutional networks, and adaptive parameter correction mechanisms, it solves the technical problems of distortion in stress prediction during the construction stage, lag in control strategies, and accumulation of alignment control deviations caused by insufficient modeling of structural geometric nonlinearity, material time-varying characteristics, and multi-dimensional internal force field coupling mechanisms in existing technologies.

[0006] According to a first aspect of this disclosure, a method for simulating the stress during the construction process of a variable cross-section bridge is provided, comprising the following steps: Parameters at each stage of bridge construction are obtained, an initial flexibility matrix of the spatial variable cross-section beam element is constructed, and based on the flexibility matrix, a multidimensional stress evolution vector characterizing the stress state of the structure is output. The multidimensional stress evolution vector is embedded into a pre-set causal graph, and dynamic reasoning is performed on the causal graph based on a spatiotemporal graph convolutional network to output the reasoning results. Based on the reasoning results, multiple candidate construction control strategies are generated, and different candidate construction control strategies are simulated and deduced. Based on the deduction results, the optimal construction control strategy is selected through a multi-objective Pareto optimization algorithm. The optimal construction control strategy is implemented, on-site monitoring data is continuously collected and the actual structural response trajectory is generated. The predicted linear evolution trajectory is compared with the actual structural response trajectory to obtain the trajectory deviation. Based on the trajectory deviation, the parameters of the spatiotemporal graph convolutional network and the parameters of the material time-varying constitutive model are adaptively corrected.

[0007] Preferably, the process of obtaining parameters at each stage of bridge construction, constructing the initial flexibility matrix of the spatial variable cross-section beam element, and outputting a multidimensional stress evolution vector characterizing the structural stress state based on the flexibility matrix is ​​as follows: Based on the construction stage division, obtain the structural geometric parameters, material properties and boundary conditions of each stage, and divide the unit integral segment according to the geometric parameters; Within each integration segment, the Gauss-Legendal numerical integration strategy is adopted, and the axial force-bending moment-shear force-torque coupling compliance coefficient is calculated by combining the cross-section fiber discrete model to construct the local compliance submatrix. Using the load increment step of the current construction stage as the weight, the flexibility submatrices of each integral segment are weighted and assembled to obtain the weighted flexibility matrix; By integrating geometric nonlinearity and material nonlinearity through a dual-scale coordination mapping mechanism, the nonlinear equilibrium equation is solved based on the weighted compliance matrix, and a multidimensional stress evolution vector characterizing the stress state of the structure is output.

[0008] Preferably, the process of using the Gauss-Legend de Gaulle numerical integration strategy within each integration segment, combined with the cross-sectional fiber discrete model to calculate the axial force-bending moment-shear force-torque coupled compliance coefficient, and constructing the local compliance sub-matrix is ​​as follows: Five Gaussian points are selected along the length of the integral segment, and local cross sections are defined. At each local cross section, a fiber discrete model is used for refined modeling to obtain the generalized strain vector. For any fiber, the strain and corresponding stress are calculated based on the generalized strain vector, and the internal force vector of the cross section is constructed. A nonlinear equilibrium equation is constructed and solved using a nonlinear iterative algorithm based on the compliance method, and the generalized displacement vector under unit internal force is calculated. The local compliance submatrix is ​​obtained by combining the internal force vector of the cross section with the generalized displacement vector to form an input-output pair. The local compliance submatrix is ​​then obtained by least squares fitting or direct differentiation.

[0009] Preferably, the parameters for each stage of beam construction include structural geometric parameters, material properties, and boundary conditions; The structural geometric parameters include cross-sectional height, web thickness, and flange width; The material properties include compressive strength, initial value of elastic modulus, and yield strength of steel reinforcement; The boundary conditions include temporary consolidation and constraints on the hanging basket support points.

[0010] Preferably, the process of embedding the multidimensional stress evolution vector into a pre-set causal graph, performing dynamic inference on the causal graph based on a spatiotemporal graph convolutional network, and outputting the inference result is as follows: The multidimensional stress evolution vector is decomposed into the cross-sectional state vector corresponding to the causal graph node and embedded into the node attribute. The coupling strength weight of the causal graph edge is dynamically updated based on the construction time sequence. Based on the coupling strength weights, the node attributes of the causal graph are inferred at the section level through a spatiotemporal graph convolutional network, and the local yield probability and deformation sensitivity of different key sections are output. Based on the local yield probability and deformation sensitivity, the internal force transmission disturbance coefficient of adjacent sections is quantified by combining the coupling strength weight, and the yield probability of the whole bridge and the risk of deviation of the bridge alignment are output. During the reasoning process, edges in the causal graph that satisfy the preset coupling significance threshold are activated to form a directional internal force redistribution path from the high stress source section to the linear sensitive area.

[0011] Preferably, the process of generating multiple candidate construction control strategies based on the inference results, simulating and deducing different candidate construction control strategies, and selecting the optimal construction control strategy based on the deduction results using a multi-objective Pareto optimization algorithm is as follows: Based on the deduction results of the stress evolution trajectory of key sections under the candidate construction control strategy, the evaluation dimensions of alignment control accuracy, material safety margin and construction efficiency are determined. Based on the risk level and remaining process complexity of the current construction stage, dynamic weights are assigned to different evaluation dimensions, and the sensitivity deviation rate of the simulation results of different candidate construction control strategies under ambient temperature and temporary load disturbances is calculated. The weighted evaluation results of different candidate construction control strategies are then corrected based on the sensitivity deviation rate. The corrected weighted evaluation results are input into a multi-objective Pareto optimization algorithm, and the optimal construction control strategy is selected based on the synergistic objectives of linear control accuracy and material safety margin.

[0012] Preferably, the process of implementing the optimal construction control strategy, continuously collecting on-site monitoring data, and generating the actual structural response trajectory is as follows: Before and after implementing the optimal construction control strategy, strain, deflection and rotation monitoring data of key sections are continuously collected, and fiber-level stress distribution, shear lag effect index and torsional warping displacement of the sections are extracted to form a reference response and real-time response sequence. Based on the importance score of the cross-sectional nodes in the causal graph, the real-time response sequence is divided into response sub-sequences corresponding to the key cross-sections, and the time decay weight of each response sub-sequence is dynamically adjusted as the construction stage progresses. The real-time response subsequence is compensated based on the ambient temperature gradient and concrete shrinkage and creep signals, and the weighted response subsequence is integrated according to the cross-sectional spatial location to generate the actual structural response trajectory that includes instantaneous construction disturbances and long-term time-varying effects.

[0013] Preferably, the process of adaptively correcting the parameters of the spatiotemporal graph convolutional network based on the trajectory deviation is as follows: Based on the coupling strength weight of the edges in the causal graph, the trajectory deviation is decomposed into cross-sectional sub-deviations, and it is determined that the cross-sectional sub-deviations originate from local state prediction deviations or cross-sectional propagation deviations. If the cross-section sub-bias originates from local state prediction bias, then the feature extraction weights of the corresponding cross-section nodes in the spatiotemporal graph convolutional network are corrected; if the cross-section sub-bias originates from cross-section propagation bias, then the normalized adjacency weights between adjacent cross-section nodes in the spatiotemporal graph convolutional network are corrected. Combining the mechanical importance of the cross section in the overall structure and the L2 norm of the cross section sub-deviation, a correction amplitude coefficient is set to correct the parameters of the spatiotemporal graph convolutional network, and an upper limit constraint on the correction step size is set based on the convergence rate of the historical corrected trajectory deviation. After correcting the parameters, verify the trajectory deviation between the inference result and the actual structural response trajectory. If the verification fails, backtrack the parameters of the spatiotemporal graph convolutional network and adjust the correction magnitude coefficient.

[0014] Preferably, the process of adaptively correcting the parameters of the time-varying constitutive model of the material based on the trajectory deviation is as follows: Based on the parameter intervention rules of the time-varying constitutive model of materials in the digital twin, the trajectory deviation is decomposed into constitutive prediction deviation of a single section and stiffness coordination deviation between multiple sections. If the deviation is constitutive prediction, the time-varying function of the elastic modulus of the concrete and the bond slip parameter of the steel reinforcement in the corresponding section are corrected in a directional manner; if the deviation is stiffness compatibility, the effective stiffness transfer coefficient between adjacent sections is corrected in a directional manner. By combining the cross-sectional material degradation sensitivity and the number of continuous construction steps of the deviation, a correction amplitude factor is set to correct the parameters of the time-varying constitutive model of the material, and the parameter correction results of the spatiotemporal graph convolutional network are synchronously associated. After correcting the parameters, the stress evolution trajectory is re-evaluated using a digital twin and the trajectory deviation is re-verified. If the verification fails, the correction amplitude factor is adjusted and the verification is repeated.

[0015] According to a second aspect of this disclosure, a stress simulation system for the construction process of a variable cross-section bridge is provided, comprising: a data modeling module, an intelligent reasoning module, a construction control module, and a control feedback module; The data modeling module is used to obtain parameters at each stage of bridge construction, construct the initial flexibility matrix of the spatial variable cross-section beam element, and output a multidimensional stress evolution vector representing the stress state of the structure based on the flexibility matrix. The intelligent reasoning module is used to embed the multidimensional stress evolution vector into a pre-set causal graph, perform dynamic reasoning on the causal graph based on a spatiotemporal graph convolutional network, and output the reasoning results. The construction control module is used to generate multiple candidate construction control strategies based on the reasoning results, simulate and deduce different candidate construction control strategies, and select the optimal construction control strategy based on the deduction results using a multi-objective Pareto optimization algorithm. The control feedback module is used to execute the optimal control strategy for construction, continuously collect on-site monitoring data and generate the actual structural response trajectory, compare the predicted linear evolution trajectory with the actual structural response trajectory to obtain the trajectory deviation, and adaptively correct the parameters of the spatiotemporal graph convolutional network and the parameters of the material time-varying constitutive model based on the trajectory deviation.

[0016] Compared with the prior art, the present invention has the following technical effects: This invention constructs a spatial variable cross-section beam element model that integrates geometric nonlinearity, time-varying material properties, and a four-dimensional internal force field coupling mechanism. By combining the dynamic reasoning capabilities of the construction process-structural response causal spectrum and spatiotemporal graph convolutional network, it achieves high-fidelity simulation of the stress behavior of variable cross-section bridges throughout the construction process. Simultaneously, through the synergistic effect of digital twins and multi-objective Pareto optimization algorithms, it generates scientific and reasonable construction control strategies. Furthermore, by leveraging an adaptive correction mechanism driven by on-site monitoring data, it continuously improves the model's prediction accuracy and control effectiveness, thereby providing reliable technical support for the intelligent construction of variable cross-section bridges.

[0017] It should be understood that the description in the Summary of the Invention is not intended to limit the key or essential features of the embodiments of this disclosure, nor is it intended to restrict the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0018] The above and other features, advantages, and aspects of the embodiments of this disclosure will become more apparent from the accompanying drawings and the following detailed description. The drawings are provided for a better understanding of the invention and are not intended to limit the scope of this disclosure. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein: Figure 1 A schematic flowchart of a stress simulation method for the construction process of a variable cross-section bridge according to an embodiment of the present disclosure is shown. Figure 2 A schematic diagram of a stress simulation system for the construction process of a variable cross-section bridge according to an embodiment of the present disclosure is shown. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0020] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] like Figure 1 As shown in the figure, this embodiment provides a method for simulating the stress during the construction process of a variable cross-section bridge, including the following steps: S101. Obtain parameters for each stage of bridge construction, construct the initial flexibility matrix of the spatial variable cross-section beam element, and output a multidimensional stress evolution vector characterizing the stress state of the structure based on the flexibility matrix.

[0022] First, this embodiment obtains the structural geometric parameters (including section height h(x) and web thickness t) for the k-th stage (k=1,2,…,28) based on the construction stage division. w (x), flange width b f (x) and other spatial functions), material properties (such as the 28-day compressive strength f of concrete). ck =50MPa, initial value of elastic modulus E c0 =3.45×10 4 MPa, yield strength of steel reinforcement f y =400MPa) and boundary conditions (temporary consolidation, hanging basket support point constraints, etc.).

[0023] Based on the above parameters, the initial compliance matrix of the spatial variable cross-section beam element is constructed. The compliance matrix is ​​constructed using a nonlinear iterative algorithm based on the compliance method, coupling the four-dimensional internal force fields of axial force N, bending moment M, shear force V, and torque T. Through the above process, the corresponding internal force vector can be calculated under a given generalized strain.

[0024] To construct the compliance matrix, it is necessary to inversely calculate the generalized displacement under a unit internal force. Therefore, the core of this process lies in solving the following nonlinear equilibrium equations: (1) Where u is the generalized displacement vector at the end of the element, F ext Let F be the external load vector. int (u) is the internal force vector derived from the flexibility matrix f, satisfying u=f Fint .

[0025] To accurately reflect the characteristics of variable cross sections, based on the cross section height gradient With web thickness gradient Each beam element is divided into n integration segments, with the length of each segment satisfying that the gradient rate of change is less than a preset threshold (e.g., 0.05). Within each integration segment i, a five-point Gauss-Legendal numerical integration strategy is used to calculate the mechanical properties of the cross section. This strategy selects five Gaussian points along the length of the integration segment, defining a local cross section at each Gaussian point. For each local cross section, a fiber discretization model is further used for refined modeling: the cross section is divided into several rectangular or trapezoidal fiber elements, each fiber having independent coordinates (y, y). j ,z j Area A j And material properties. The generalized strain vector describes the overall deformation state of the cross section.

[0026] For any fiber j, its strain From the generalized strain vector (i.e., compliance coefficient) (Corresponding to axial strain, curvature, shear strain, and torsional rate, respectively) are determined through geometric relationships: (2) Among them, z j Let be the vertical distance from fiber j to the neutral axis. j This represents the warping function value.

[0027] The stress σ of each fiber is calculated based on the material constitutive relation. j =E(t)·ε j (E(t) is the elastic modulus of concrete considering age effects), from which the internal force vector of the section can be obtained: (3) Among them, s j ψ is the shear lag correction factor. j Let A be the torsional shear stress distribution function. j This represents the fiber area.

[0028] The internal force vector and the corresponding generalized displacement vector form an input-output pair of the local compliance submatrix. The local compliance submatrix f for this integral segment can be obtained by least-squares fitting or direct differentiation. i .

[0029] Subsequently, the load increment step Δλ is taken at the current construction stage. k Assign weights to the compliance submatrices of each integral segment and assemble them accordingly: (4) Building upon this, a dual-scale coordinated mapping mechanism is employed to integrate geometric nonlinearity and material nonlinearity: at the macroscopic scale, an updated Lagrangian scheme is used to describe large displacement effects, i.e., the configuration coordinates are updated in each iteration; at the microscopic scale, a fiber model is used to capture material nonlinearity; the two are coupled through the force-displacement relationship within the cross-section. Finally, the nonlinear equilibrium equation u = f·F is solved. int , where F int From the external load vector F ext Through iterative approximation, a multidimensional stress evolution vector representing the stress state of the structure is output. Where d is the number of key sections, t is the time step dimension, and vector S (k) Each element S ij This vector represents the comprehensive stress index of the i-th critical section at the j-th time step. It includes the axial force, bending moment, shear force, and torque of each critical section (pier top, quarter span, mid span, three-quarter span, and support) along the construction time sequence t. k The evolutionary trajectory.

[0030] S102. Embed the multidimensional stress evolution vector into a preset causal graph, perform dynamic reasoning on the causal graph based on a spatiotemporal graph convolutional network, and output the reasoning result.

[0031] This embodiment pre-defines a construction procedure-structural response causal graph G=(V,E), where the node set V corresponds to key bridge sections (such as pier top, 1 / 4 span, and mid-span), and the edge set E represents the mechanical coupling relationship between sections. The construction method of the pre-define causal graph G is as follows: based on the bridge structural design drawings, select m sections (pier top, 1 / 4 span, mid-span, 3 / 4 span, and supports) as the initial node set V; based on structural mechanics theory, calculate the flexibility influence coefficient f between any two nodes u and v. uv If |f uv If |f is greater than a preset threshold τ, then an undirected edge is established between u and v, and |f| is set to f. uv | This serves as the initial coupling strength weight for that edge.

[0032] First, S (k) Decomposed into nodal state vectors by cross section It also embeds node attributes. Simultaneously, it dynamically updates the coupling strength weights of edges based on the construction sequence (e.g., forward movement of the formwork, prestressing tensioning). The calculation formula is as follows: (5) in, Let L be the spatial coordinate vector of section u in the k-th construction stage. uv I is the distance between sections u and v. con(u,v) is the connection indicator function (1 if the two sections belong to the same beam segment, 0 otherwise), and α=0.7 is the empirical coefficient.

[0033] Subsequently, dynamic reasoning of the causal graph is performed using a Spatiotemporal Graph Convolutional Network (ST-GCN). The node update rule of ST-GCN is as follows: (6) in, To normalize the adjacency weights, Here is the representation of node v at level l+1. Let u be a neighboring node of node v, du be the degree of node u, dv be the degree of node v, and W be a neighboring node of node v. (l) Let σ be the learnable weight matrix of the l-th layer, and σ be the ReLU activation function.

[0034] After multiple convolutions, the local yield probability p of each key section is output. y (v) and deformation sensitivity s d (v), the local yield probability is calculated by comparing the current stress with the material strength envelope; the deformation sensitivity is defined as the rate of change of deflection caused by a unit load increment.

[0035] Furthermore, the perturbation coefficient δ of internal force transmission between adjacent sections is quantified based on edge aggregation operation. uv Specifically, for each edge (u,v), the covariance of the state vectors of its two endpoints is calculated and combined with the weights. The disturbance coefficient is obtained.

[0036] By summing the disturbance coefficients across the entire map, the yield probability of the entire bridge and the risk of deviation in the bridge's alignment can be calculated, specifically: (7) (8) Among them, P Y R is the overall bridge yield probability. L To mitigate the risk of bridge alignment deviation, To predict the deflection residual.

[0037] At the same time, activation satisfies Edges with a coefficient of τ (τ=0.3 is the coupling significance threshold) form a high-stress source section (such as p) y (v)>0.6) points to a linear sensitive area (e.g. The directional internal force redistribution path is greater than 0.8.

[0038] S103. Based on the reasoning results, generate multiple candidate construction control strategies, simulate and deduce different candidate construction control strategies, and select the optimal construction control strategy based on the deduction results using a multi-objective Pareto optimization algorithm.

[0039] Based on the above reasoning results, this embodiment generates multiple candidate construction control strategies, such as: adjusting the prestressing tensioning sequence, changing the hanging basket loading rate, and adding temporary supports.

[0040] Each strategy is mapped to an intervention rule of the time-varying constitutive model of the material, such as adjusting the rate of decrease in the elastic modulus of concrete from the baseline value η0 = 0.02 / day to η = η0. (1 γ)η, where γ is the regulation intensity factor (0≤γ≤0.3); creep coefficient (t, t0) is corrected according to the CEB-FIP Model Code. ′(t,t0)= (t,t0)·(1 δ), where δ is the creep suppression coefficient. Simultaneously, environmental disturbance parameters (such as temperature change ΔT = ±15℃, wind pressure q = 1.2 kN / m²) are obtained from on-site temperature and humidity sensors and wind load monitoring equipment, and these are input as boundary conditions into the digital twin. The digital twin incorporates a geometry-material coupled nonlinear solver, based on the stiffness continuity constraint between sections (i.e., the rotation angle difference between adjacent sections |θ)... i θ i+1 ∣< , =0.001rad) to deduce the stress-strain-displacement evolution trajectory of key sections under each strategy.

[0041] Subsequently, this embodiment selects the optimal strategy based on the simulation results using a multi-objective Pareto optimization algorithm. The evaluation dimensions include linear control accuracy A. L =1 / (1+RMSE y ) (RMSE) y (For prediction of root mean square error of target line shape) and material safety margin (σ) v (Maximum stress of the cross section) and construction efficiency A E =1 / T c (T) c (For strategy execution time).

[0042] Based on the current risk level r (determined by P) Y With R L Based on the comprehensive judgment and the complexity c of the remaining processes, weights are dynamically allocated: (9) Simultaneously, the sensitivity deviation rate of each strategy under environmental disturbances is calculated. (y) nom For an undisturbed trajectory, y pert (For the perturbation trajectory), correct the weighted evaluation value Q: (10) Input the Q value into the NSGA-II multi-objective optimization algorithm, with A L With A M To optimize the objective, the optimal strategy is selected from the Pareto front.

[0043] S104. Implement the optimal construction control strategy, continuously collect on-site monitoring data and generate the actual structural response trajectory, compare the predicted linear evolution trajectory with the actual structural response trajectory to obtain the trajectory deviation, and adaptively correct the parameters of the spatiotemporal graph convolutional network and the parameters of the material time-varying constitutive model based on the trajectory deviation.

[0044] In this step, the optimal strategy is implemented. Before and after implementation, strain ε is continuously collected by fiber optic strain gauges, inclinometers, and total stations deployed at key cross-sections. m Deflection y m With the rotation angle θ m Data was collected, and the cross-sectional fiber-level stress distribution (through inverse analysis) and shear lag coefficient were extracted simultaneously. ( (mean stress) and torsional warping displacement w t This forms the baseline response y0 and the real-time response sequence y0. t .

[0045] Based on the importance score of cross-sectional nodes in the causal graph I v (Originally obtained by normalizing the L2 norm of the features of the last layer nodes in ST-GCN), the real-time response sequence is split into response subsequences. The time decay weight is dynamically adjusted as the construction phase progresses. ( The attenuation coefficient is... (where j is the most recent control moment of section j).

[0046] Furthermore, based on the measured temperature gradient T and shrinkage / creep signal ε sh (t) for the response subsequence Compensation is performed to obtain a weighted subsequence. : (11) Where, α T L is the coefficient of thermal expansion of concrete. v h is the characteristic length of the cross section. v For Liang Gao.

[0047] Finally, the weighted subsequences are integrated according to the spatial location of the cross-section to generate the actual structural response trajectory. : (12) Among them, W j This is the spatial weight matrix.

[0048] Predict the linear evolution trajectory Y pred With Y actual The trajectory deviation ΔY=Y is obtained by comparison. actual Y pred Based on this bias, the parameters of the spatiotemporal graph convolutional network and the time-varying constitutive model of the material are adaptively corrected.

[0049] For ST-GCN, ΔY is first decomposed into cross-sectional sub-biases Δy based on the causal graph edge weights. v And determine its source: if ( If the local bias threshold is used, it is determined to be a local state prediction bias, and the feature extraction weights W of ST-GCN node v are corrected. v Otherwise, it is determined to be a cross-section propagation deviation, and the normalized adjacency weight is corrected. Correction amplitude coefficient ( =0.01 is the learning rate, I v (For importance scoring), and the correction step size is limited by the historical convergence rate: if the deviation reduction rate after the past 3 corrections is <5%, then μ v Halved. Verified after correction. <ρ (ρ=0.95), otherwise backtrack the parameters and adjust μ. v .

[0050] For the time-varying constitutive model of the material, ΔY is decomposed into constitutive prediction bias (stress-strain mismatch at a single section) and stiffness compatibility bias (discontinuity in rotation angle between adjacent sections). If it is the former, then the time-varying function E of the concrete elastic modulus is corrected. c (t)=E c0 / (1+ (t,t0)) (t,t0) parameters and rebar bond slip parameter τ max If the latter, then adjust the effective stiffness transfer coefficient of adjacent sections. , where L uv Let u and v be the characteristic lengths of the cross sections. The correction amplitude factor ν = ζ S v n step (ζ=0.005, S) v For material degradation sensitivity, n stepThe deviation is continuously measured in construction steps and is synchronously linked with the ST-GCN parameter correction. After correction, the trajectory is re-enacted using a digital twin to verify the deviation. If it fails, ν is adjusted and the process is repeated until convergence.

[0051] like Figure 2 As shown, this embodiment also provides a stress simulation system for the construction process of a variable cross-section bridge, including: a data modeling module 1, an intelligent reasoning module 2, a construction control module 3, and a control feedback module 4; Data modeling module 1 is used to obtain parameters at each stage of bridge construction, construct the initial flexibility matrix of the spatial variable cross-section beam element, and output a multidimensional stress evolution vector representing the stress state of the structure based on the flexibility matrix. The intelligent reasoning module 2 is used to embed the multidimensional stress evolution vector into a preset causal graph, perform dynamic reasoning on the causal graph based on a spatiotemporal graph convolutional network, and output the reasoning results. Construction control module 3 is used to generate multiple candidate construction control strategies based on the reasoning results, simulate and deduce different candidate construction control strategies, and select the optimal construction control strategy based on the deduction results using a multi-objective Pareto optimization algorithm. The regulation and feedback module 4 is used to execute the optimal regulation and control strategy for construction, continuously collect on-site monitoring data and generate the actual structural response trajectory, compare the predicted linear evolution trajectory with the actual structural response trajectory to obtain the trajectory deviation, and adaptively correct the parameters of the spatiotemporal graph convolutional network and the parameters of the material time-varying constitutive model based on the trajectory deviation.

[0052] Through the aforementioned closed-loop process, this system achieves high-precision stress simulation and intelligent control of the entire construction process of variable cross-section bridges, significantly improving construction safety and the quality of the completed bridge.

[0053] To verify the technical effects of this disclosed technical solution compared to existing technologies, this embodiment uses a three-span variable cross-section prestressed concrete continuous rigid frame bridge as the simulation object. The method described in this embodiment and two existing technical solutions are used to conduct a comparative analysis of the stress simulation throughout the entire construction process. The simulation object has a span arrangement of 60m+100m+60m. The main girder is a single-box, single-cell variable cross-section box girder, with the girder height varying from 7.0m at the pier top along a quadratic parabola to 3.0m at the mid-span. The main girder uses C50 concrete (28-day compressive strength fck=50MPa, initial elastic modulus Ec0=3.45×10⁻⁶). 4 The entire bridge was divided into 28 cantilever casting construction stages (k=1,2,…,28), and the structural geometric parameters, material properties, and boundary conditions of each construction stage were consistent with those in the previous embodiment. The calculation results of a high-precision three-dimensional solid finite element model (ABAQUS, mesh size 0.25m, total number of elements approximately 128,000) were used as reference benchmarks.

[0054] Comparative Example 1 (Traditional Segmented Equal Section Beam Element Method): The entire bridge is divided into 56 equal section beam elements. The average section characteristics of each element are taken. The linear static step-by-step superposition method is used for calculation. The coupling effect of axial force-bending moment-shear force-torque is not considered, nor are the shear lag effect and torsional warping displacement.

[0055] Comparative Example 2 (Uncoupled Flexibility Method): The variable cross-section beam element flexibility method is adopted, but only the coupling relationship between axial force and bending moment is considered, ignoring the contribution of shear lag effect and torsional warping displacement, and does not include spatiotemporal graph convolutional network inference and digital twin adaptive correction.

[0056] This embodiment of the disclosure adopts the fully coupled flexibility method of the technical solution of this disclosure, integrates the four-dimensional internal force field of axial force, bending moment, shear force and torque, combines the cross-section fiber discrete model to perform five-point Gauss-Legendal numerical integration, and enables spatiotemporal graph convolutional network for dynamic inference and digital twin adaptive correction.

[0057] In stage 28 (the bridge completion stage), the comparison of the deflection prediction values ​​of the three methods at five key sections with the reference values ​​is shown in Table 1.

[0058] Table 1. Comparison of deflection prediction values ​​of the three methods in stage 28 (bridge completion stage) (unit: mm) As shown in Table 1, the average deflection prediction error of Comparative Example 1 is 37.7%, with errors exceeding 45% at the pier top and support sections. This indicates that the traditional segmented uniform cross-section beam element method cannot accurately simulate the stiffness distribution of variable cross-section beams due to neglecting the continuous variation of the cross-section. The average deflection prediction error of Comparative Example 2 is 15.3%, significantly lower than that of Comparative Example 1. This shows that the variable cross-section flexibility method can effectively improve the accuracy of stiffness simulation, but its prediction accuracy in thin-walled box girder sections remains insufficient due to neglecting shear lag effects and torsional warping displacement. The average deflection prediction error of the embodiments disclosed in this invention is only 2.4%, with errors at each section controlled within 3.1%, demonstrating that the full coupling of the four-dimensional internal force field and fiber discrete modeling can significantly improve the accuracy of stress simulation during the construction stage of variable cross-section bridges.

[0059] Furthermore, in the 14th construction stage (maximum cantilever state, highest structural risk), the comparison of the predicted values ​​of the top plate stress at five key sections using the three methods with the reference values ​​is shown in Table 2.

[0060] Table 2 Comparison of top plate stress prediction values ​​for the three methods in stage 14 (maximum cantilever state) (unit: MPa, negative values ​​indicate compressive stress). As shown in Table 2, Comparative Example 1, due to the use of the uniform cross-section approximation and the linear superposition of independent loads, has an average stress prediction error of 34.0%, and the redistribution effect of internal forces in each section under the maximum cantilever state is not reflected at all. Comparative Example 2, after introducing the variable cross-section flexibility method, reduces the average stress prediction error to 14.2%, but the local stress deviation in the flange-web interface area is still large because the shear lag effect is not considered. The embodiment of this disclosure, through the fine modeling of the fiber discrete model and the full coupling solution of the four-dimensional internal force field, controls the average stress prediction error to 2.2%, especially the error of the pier top section (maximum negative bending moment area) is only 2.2%, indicating that the method of this disclosure has a high-fidelity simulation capability for the stress state of key sections in the construction stage.

[0061] To verify the synergistic effect of the dual-channel adaptive correction mechanism of the spatiotemporal graph convolutional network and the material time-varying constitutive model in this technical solution, after introducing random fluctuations of ±8% in the elastic modulus and environmental disturbances of ±15℃ in the temperature gradient in stage 14, the convergence process of the trajectory deviation at the mid-span section (section C) was tracked. The changes in trajectory deviation with the number of construction steps were recorded under three modes: no correction, correction of only spatiotemporal graph convolutional network parameters, and dual-channel correction as disclosed in this solution, as shown in Table 3. The convergence threshold was set at a trajectory deviation of less than 0.5mm.

[0062] Table 3 Comparison of trajectory deviation convergence process at mid-span section (C section) (unit: mm) As shown in Table 3, the trajectory deviation in the uncorrected mode continuously increased from 8.74 mm to 9.88 mm (an increase of 13.0%), indicating that without parameter correction after perturbation, the prediction model will gradually deviate from the actual structural state. When only the spatiotemporal graph convolutional network parameters were corrected, the deviation gradually decreased from 8.74 mm, reaching 1.38 mm in step 5, but still did not reach the convergence threshold of 0.5 mm. In the dual-channel correction mode of this disclosure, the deviation decreased to 0.43 mm in step 4, reaching convergence, and further decreased to 0.21 mm in step 5. The convergence speed of dual-channel correction is about 37.5% higher than that of ST-GCN correction alone, proving that simultaneous correction of spatiotemporal graph convolutional network parameters and material time-varying constitutive model parameters can produce a synergistic acceleration effect: the correction of the material constitutive model makes the stress-strain relationship of the digital twin closer to the real time-varying characteristics, providing more accurate feature input for the spatiotemporal graph convolutional network; while the correction of network parameters improves the recognition accuracy of cross-section deviation propagation path, the two reinforce each other, forming a positive feedback loop.

[0063] To verify the engineering value of this disclosed technical solution in construction control decision-making, when a 12.0mm alignment deviation was detected in stage 14, three candidate construction control strategies were generated based on the reasoning results: Strategy 1 was to adjust only the subsequent prestressing tensioning sequence; Strategy 2 was to add only temporary supports; and Strategy 3 was the combined control strategy output by the method of this disclosure (fine-tuning of tensioning sequence + local counterweight + adjustment of hanging basket loading rate). The alignment control accuracy (AL), material safety margin (AM), and construction efficiency (AE) were used as evaluation dimensions, and the NSGA-II multi-objective Pareto optimization algorithm was used for evaluation. The results are shown in Table 4.

[0064] Table 4. Multi-objective evaluation results of three candidate construction control strategies As shown in Table 4, Strategy 1, by only adjusting the tensioning sequence, has limited improvement in alignment control accuracy (AL=0.82), with a comprehensive score of 0.76. Strategy 2, by adding temporary supports, can improve the safety margin (AM=1.35) and alignment accuracy (AL=0.88) to some extent, but significantly reduces construction efficiency (AE=0.71), with a comprehensive score of 0.73. Strategy 3, output by the method of this disclosure, achieves synergistic optimization of the three objectives through combined regulation. The alignment accuracy is improved by 14.6% compared to Strategy 1, the safety margin is improved by 10.9% compared to Strategy 1, while maintaining a construction efficiency of 0.88, with a comprehensive score of 0.91, outperforming the single strategy on the Pareto front. These results demonstrate that the causal graph dynamic reasoning and multi-objective Pareto optimization algorithm in the technical solution of this disclosure can effectively balance the multi-dimensional constraints of construction accuracy, safety, and efficiency, providing scientific and reliable decision support for the construction process of variable cross-section bridges.

[0065] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this disclosure is not limited to the described order of actions, because according to this disclosure, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are all optional embodiments, and the actions and modules involved are not necessarily essential to this disclosure.

[0066] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this disclosure can be achieved, and this is not limited herein.

[0067] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for simulating the stress during the construction process of a variable cross-section bridge, characterized in that, Includes the following steps: The specific process of obtaining parameters at each stage of bridge construction, constructing the initial flexibility matrix of the spatial variable cross-section beam element, and outputting the multidimensional stress evolution vector representing the stress state of the structure based on the flexibility matrix is ​​as follows: obtaining the structural geometric parameters, material properties and boundary conditions of each stage based on the construction stage division, and dividing the element integration segment according to the geometric parameters; Within each integration segment, the Gauss-Legendal numerical integration strategy is adopted, and the axial force-bending moment-shear force-torque coupling compliance coefficient is calculated by combining the cross-section fiber discrete model to construct the local compliance submatrix. Using the load increment step of the current construction stage as the weight, the flexibility sub-matrices of each integral segment are weighted and assembled to obtain the weighted flexibility matrix; the geometric nonlinearity and material nonlinearity effects are fused through a dual-scale coordination mapping mechanism, and the nonlinear equilibrium equation is solved based on the weighted flexibility matrix to output a multidimensional stress evolution vector characterizing the stress state of the structure. The process of constructing a local compliance submatrix by employing a Gauss-Legendal numerical integration strategy within each integration segment, combined with a cross-sectional fiber discrete model to calculate the axial force-bending moment-shear force-torque coupling compliance coefficient, is as follows: Five Gaussian points are selected along the length of the integration segment, and local cross-sections are defined. At each local cross-section, a fiber discrete model is used for refined modeling to obtain a generalized strain vector. For any fiber, the strain and corresponding stress are calculated based on the generalized strain vector to construct the cross-sectional internal force vector. A nonlinear equilibrium equation is constructed and solved using a nonlinear iterative algorithm based on the compliance method to calculate the generalized displacement vector under unit internal force. The cross-sectional internal force vector and the generalized displacement vector form an input-output pair for the local compliance submatrix, and the local compliance submatrix is ​​obtained by least squares fitting or direct differentiation. The multidimensional stress evolution vector is embedded into a pre-set causal graph, and dynamic reasoning is performed on the causal graph based on a spatiotemporal graph convolutional network to output the reasoning results. Based on the reasoning results, multiple candidate construction control strategies are generated, and different candidate construction control strategies are simulated and deduced. Based on the deduction results, the optimal construction control strategy is selected through a multi-objective Pareto optimization algorithm. The optimal construction control strategy is implemented, on-site monitoring data is continuously collected and the actual structural response trajectory is generated. The predicted linear evolution trajectory is compared with the actual structural response trajectory to obtain the trajectory deviation. Based on the trajectory deviation, the parameters of the spatiotemporal graph convolutional network and the parameters of the material time-varying constitutive model are adaptively corrected.

2. The method for simulating the stress during the construction process of a variable cross-section bridge according to claim 1, characterized in that, The parameters for each stage of beam construction include structural geometric parameters, material properties, and boundary conditions. The structural geometric parameters include cross-sectional height, web thickness, and flange width; The material properties include compressive strength, initial value of elastic modulus, and yield strength of steel reinforcement; The boundary conditions include temporary consolidation and constraints on the hanging basket support points.

3. The method for simulating the stress during the construction process of a variable cross-section bridge according to claim 1, characterized in that, The process of embedding the multidimensional stress evolution vector into a pre-set causal graph, performing dynamic inference on the causal graph based on a spatiotemporal graph convolutional network, and outputting the inference result is as follows: The multidimensional stress evolution vector is decomposed into the cross-sectional state vector corresponding to the causal graph node and embedded into the node attribute. The coupling strength weight of the causal graph edge is dynamically updated based on the construction time sequence. Based on the coupling strength weights, the node attributes of the causal graph are inferred at the section level through a spatiotemporal graph convolutional network, and the local yield probability and deformation sensitivity of different key sections are output. Based on the local yield probability and deformation sensitivity, the internal force transmission disturbance coefficient of adjacent sections is quantified by combining the coupling strength weight, and the yield probability of the whole bridge and the risk of deviation of the bridge alignment are output. During the reasoning process, edges in the causal graph that satisfy the preset coupling significance threshold are activated to form a directional internal force redistribution path from the high stress source section to the linear sensitive area.

4. The method for simulating the stress during the construction process of a variable cross-section bridge according to claim 1, characterized in that, The process of generating multiple candidate construction control strategies based on the inference results, simulating and deducing different candidate construction control strategies, and selecting the optimal construction control strategy based on the deduction results using a multi-objective Pareto optimization algorithm is as follows: Based on the deduction results of the stress evolution trajectory of key sections under the candidate construction control strategy, the evaluation dimensions of alignment control accuracy, material safety margin and construction efficiency are determined. Based on the risk level and remaining process complexity of the current construction stage, dynamic weights are assigned to different evaluation dimensions, and the sensitivity deviation rate of the simulation results of different candidate construction control strategies under ambient temperature and temporary load disturbances is calculated. The weighted evaluation results of different candidate construction control strategies are then corrected based on the sensitivity deviation rate. The corrected weighted evaluation results are input into a multi-objective Pareto optimization algorithm, and the optimal construction control strategy is selected based on the synergistic objectives of linear control accuracy and material safety margin.

5. The method for simulating the stress during the construction process of a variable cross-section bridge according to claim 1, characterized in that, The process of executing the optimal construction control strategy, continuously collecting on-site monitoring data, and generating the actual structural response trajectory is as follows: The optimal construction control strategy is implemented, and strain, deflection and rotation monitoring data of key sections are continuously collected. The fiber-level stress distribution, shear lag effect index and torsional warping displacement of the sections are extracted to form the reference response and real-time response sequences. Based on the importance score of the cross-sectional nodes in the causal graph, the real-time response sequence is divided into response sub-sequences corresponding to the key cross-sections, and the time decay weight of each response sub-sequence is dynamically adjusted as the construction stage progresses. The response subsequence is compensated based on the ambient temperature gradient and concrete shrinkage and creep signals, and the weighted response subsequence is integrated according to the cross-sectional spatial location to generate the actual structural response trajectory that includes instantaneous construction disturbance and long-term time-varying effects.

6. The method for simulating the stress during the construction process of a variable cross-section bridge according to claim 1, characterized in that, The process of adaptively correcting the parameters of the spatiotemporal graph convolutional network based on the trajectory deviation is as follows: Based on the coupling strength weight of the edges in the causal graph, the trajectory deviation is decomposed into cross-sectional sub-deviations, and it is determined that the cross-sectional sub-deviations originate from local state prediction deviations or cross-sectional propagation deviations. If the cross-section sub-bias originates from local state prediction bias, then the feature extraction weights of the corresponding cross-section nodes in the spatiotemporal graph convolutional network are corrected. If the cross-section sub-bias originates from the cross-section propagation bias, then the normalized adjacency weights between adjacent cross-section nodes in the spatiotemporal graph convolutional network are corrected. Combining the mechanical importance of the cross section in the overall structure and the L2 norm of the cross section sub-deviation, a correction amplitude coefficient is set to correct the parameters of the spatiotemporal graph convolutional network, and an upper limit constraint on the correction step size is set based on the convergence rate of the historical corrected trajectory deviation. After correcting the parameters, verify the trajectory deviation between the inference result and the actual structural response trajectory. If the verification fails, backtrack the parameters of the spatiotemporal graph convolutional network and adjust the correction magnitude coefficient.

7. The method for simulating the stress during the construction process of a variable cross-section bridge according to claim 1, characterized in that, The process of adaptively correcting the parameters of the time-varying constitutive model of the material based on the trajectory deviation is as follows: Based on the parameter intervention rules of the time-varying constitutive model of materials in the digital twin, the trajectory deviation is decomposed into constitutive prediction deviation of a single section and stiffness coordination deviation between multiple sections. If it is a constitutive prediction deviation, then the time-varying function of the elastic modulus of the concrete and the bond slip parameter of the steel reinforcement in the corresponding section are corrected in a directional manner. If it is a stiffness compatibility deviation, then the effective stiffness transfer coefficient between adjacent sections is corrected in a directional manner; By combining the cross-sectional material degradation sensitivity and the number of continuous construction steps of the deviation, a correction amplitude factor is set to correct the parameters of the time-varying constitutive model of the material, and the parameter correction results of the spatiotemporal graph convolutional network are synchronously associated. After correcting the parameters, the stress evolution trajectory is re-evaluated using a digital twin and the trajectory deviation is re-verified. If the verification fails, the correction amplitude factor is adjusted and the verification is repeated.

8. A stress simulation system for the construction process of a variable cross-section bridge, used to implement the stress simulation method for the construction process of a variable cross-section bridge as described in any one of claims 1-7, characterized in that, include: Data modeling module (1), intelligent reasoning module (2), construction control module (3), and control feedback module (4); The data modeling module (1) is used to obtain parameters at each stage during bridge construction, construct the initial flexibility matrix of the spatial variable cross-section beam element, and output a multidimensional stress evolution vector representing the stress state of the structure based on the flexibility matrix. The intelligent reasoning module (2) is used to embed the multidimensional stress evolution vector into a preset causal graph, perform dynamic reasoning on the causal graph based on a spatiotemporal graph convolutional network, and output the reasoning results. The construction control module (3) is used to generate multiple candidate construction control strategies based on the reasoning results, simulate and deduce different candidate construction control strategies, and select the optimal construction control strategy based on the deduction results using a multi-objective Pareto optimization algorithm. The regulation feedback module (4) is used to execute the optimal regulation strategy for construction, continuously collect on-site monitoring data and generate the actual structural response trajectory, compare the predicted linear evolution trajectory with the actual structural response trajectory to obtain the trajectory deviation, and adaptively correct the parameters of the spatiotemporal graph convolutional network and the parameters of the material time-varying constitutive model based on the trajectory deviation.

Images