High-pier multi-span continuous rigid frame bridge jacking force optimization method and system

Abstract

The application discloses a high-pier multi-span continuous rigid frame bridge jacking force optimization method and system, and is applied to the technical field of intelligent analysis, and the method comprises the steps of: constructing a finite element model and multiple groups of calculation working conditions; performing construction simulation calculation on the finite element model to obtain stress data of each pier; training a prediction model; outputting multiple groups of optimal solutions according to the prediction model; the optimal solution is a corresponding array of the jacking force of each closure section and the stress data of the pier; scoring each optimal solution, and taking the jacking force of each closure section corresponding to the optimal solution with the highest score as the final construction jacking force. The application solves the problem of explicit relationship between the closure jacking force and the pier stress, improves the pier stress acquisition efficiency under different working conditions, and requires fewer finite element calculations, so that the acquisition efficiency of the reasonable jacking force of the large-span high-pier continuous rigid frame bridge can be effectively improved, and the number of required finite element calculations is smaller.

Description

Technical Field

[0001] This invention relates to the field of intelligent analysis technology, specifically to a method and system for optimizing the thrust of a high-pier, multi-span continuous rigid frame bridge. Background Technology

[0002] In modern transportation systems, bridges serve as crucial infrastructure, spanning major rivers, canyons, and other structures. Available bridge types include continuous beam bridges, continuous rigid frame bridges, and cable-stayed bridges, with the continuous rigid frame bridge concept first proposed by German engineers in the early 20th century. With advancements in materials technology and bridge construction techniques, continuous rigid frame bridges have become highly competitive among medium- and long-span bridges due to their advantages such as strong structural integrity, good seismic performance, high driving comfort, and relatively low cost. With the development of highways and high-speed railways, continuous rigid frame bridges have become one of the most prevalent bridge types. Since continuous rigid frame bridges are generally constructed of concrete, the shrinkage and creep effects of concrete cause continuous deformation in large-span continuous rigid frame bridges during operation, leading to additional internal forces on the piers and impacting their operational safety. Therefore, a jacking force needs to be applied to the closure section during bridge closure to improve the stress on the piers during operation. Applying a jacking force to the closure section during mid-span closure and optimizing this force is crucial for the bridge's operational stress state.

[0003] In existing technologies, multi-objective linear programming is a mainstream method for studying the optimal jacking force of multi-span continuous rigid frame bridges. This method requires multiple calls to the finite element model (FEM) to calculate the internal forces at key sections, and then uses FEM to obtain the optimal jacking force. However, this method's efficiency is limited by the FEM's computational speed and the number of calls. To address the time-consuming nature of FEM models, researchers have established a relationship between jacking force and structural response based on mechanical principles, obtaining an explicit relationship between the two. Then, they use FEM to obtain the optimal jacking force for the bridge, improving both optimization accuracy and efficiency.

[0004] However, with the advancement of transportation infrastructure construction, mountain bridges are increasingly constrained by complex terrain conditions, leading to a trend towards larger spans, higher piers, and multi-span construction in continuous rigid frame bridges. This presents significant challenges to the optimization of closure and launching. Firstly, with increased pier height, the nonlinear effects of the bridge structure become more pronounced, rendering linear principles inapplicable. The relationship between launching force and pier stress is difficult to predict accurately using a linear approach. Secondly, the increased number of spans in continuous rigid frame bridges necessitates considering the stress of each pier simultaneously during optimization, increasing the number of optimization objectives and the difficulty of multi-objective optimization. Furthermore, the numerous closure segments in multi-span continuous rigid frame bridges significantly impact the final bridge condition due to the optimal construction closure sequence. These factors further complicate the prediction of pier stress under the applied launching force, while existing optimization methods suffer from significant shortcomings in both efficiency and accuracy.

[0005] In the prior art, Chinese patent application number CN202511214581.3 discloses a method and system for optimizing the jacking force of a multi-span continuous rigid frame bridge. First, the construction steps corresponding to the jacking sequence scheme are determined according to the jacking sequence scheme. Second, soil constraint degradation simulation is performed based on the jacking sequence scheme and the corresponding construction steps to establish a finite element model of the entire bridge. Then, based on the finite element model, the parameters corresponding to applying a unit jacking force and not applying a unit jacking force at each jacking joint are calculated, and a solution function is constructed based on the first and second parameters. Finally, fuzzy mathematics is used to transform the multi-objective optimization problem corresponding to the solution function into a single-objective linear programming problem to obtain the optimal solution for the jacking force. It can be seen that its main idea is to linearize the optimization solution before calculation, requiring a large number of finite element calculations. Summary of the Invention

[0006] In order to at least overcome the above-mentioned deficiencies in the prior art, the purpose of this application is to provide a method and system for optimizing the thrust of high-pier multi-span continuous rigid frame bridges.

[0007] In a first aspect, embodiments of this application provide a method for optimizing the thrust of a high-pier, multi-span continuous rigid frame bridge, including:

[0008] Obtain the design parameters of the target continuous rigid frame bridge, and construct a finite element model based on the design parameters;

[0009] Multiple sets of calculation conditions are constructed based on the closure segment and pier distribution of the target continuous rigid frame bridge; each set of calculation conditions corresponds to different jacking forces of different closure segments;

[0010] Based on the aforementioned calculation conditions, the finite element model is used to perform construction simulation calculations to obtain stress data for each bridge pier corresponding to different calculation conditions.

[0011] The prediction model is trained using the jacking force of each closure segment corresponding to the calculation condition as input data and the stress data of each pier as output data.

[0012] Based on the prediction model and intelligent optimization algorithm, multiple optimal solutions are output; the optimal solution is an array corresponding to the jacking force of each closure segment and the stress data of the pier.

[0013] Each optimal solution is scored, and the jacking force of each closure segment corresponding to the optimal solution with the highest score is taken as the final jacking force for construction.

[0014] In one possible implementation, the score for the optimal solution includes:

[0015] Obtain the maximum construction stress, minimum construction stress, maximum operational stress, and minimum operational stress from the stress data in the optimal solution;

[0016] The stress uniformity of the maximum stress during the operation phase is calculated based on the maximum operating stress, and the stress uniformity of the minimum stress during the operation phase is calculated based on the minimum operating stress.

[0017] A stress evaluation item is constructed based on the maximum stress during construction, the minimum stress during construction, the maximum stress during operation, and the minimum stress during operation. A stress uniformity evaluation item is constructed based on the stress uniformity of the maximum stress during operation and the stress uniformity of the minimum stress during operation.

[0018] The optimal solution is scored by weighting the stress evaluation item and the stress uniformity evaluation item.

[0019] In one possible implementation, the score for the optimal solution is calculated according to the following formula:

[0020]

[0021] In the formula, I opt For scoring, σ cs-max For the maximum stress during construction, σ cs-min For the minimum stress during construction, σ os-max For the maximum operational stress, σ os-min For minimum operational stress, SD(σ) os-max ) represents the stress uniformity of the maximum stress during the operation phase, SD(σ) os-min ) represents the stress uniformity of minimum stress during the operation phase, α is the weight of the stress evaluation item, and β is the weight of the stress uniformity evaluation item.

[0022] In one possible implementation, the construction of the computational working condition includes:

[0023] The jacking force of each of the aforementioned closure segments is divided into three loading levels: low jacking force, medium jacking force, and high jacking force.

[0024] Each closure segment is selected and combined under three loading levels to form multiple sets of training calculation conditions;

[0025] The thrust range is constructed with the low thrust as the minimum value and the high thrust as the maximum value.

[0026] Within the top thrust range, each closing segment is subjected to Latin hypercube sampling and combined to form multiple sets of verification calculation conditions.

[0027] In one possible implementation, performing construction simulation calculations on the finite element model according to the calculation conditions to obtain stress data for each bridge pier corresponding to different calculation conditions includes:

[0028] The finite element model is subjected to construction simulation calculations under the training calculation conditions to obtain multiple sets of maximum construction stress, minimum construction stress, maximum operation stress, and minimum operation stress as training stress data. The finite element model is then subjected to construction simulation calculations under the verification calculation conditions to obtain multiple sets of maximum construction stress, minimum construction stress, maximum operation stress, and minimum operation stress as verification stress data.

[0029] In one possible implementation, training the prediction model includes:

[0030] The SVR model is constructed using the Gaussian kernel function.

[0031] The SVR model is trained using the jacking force of each closure segment under the training calculation condition as input data and the corresponding training stress data as output data. The SVR model is then validated using the validation stress data to generate the prediction model.

[0032] In one possible implementation, the prediction model combined with an intelligent optimization algorithm outputs multiple sets of optimal solutions, including:

[0033] The constraints for constructing the optimal solution include minimizing the maximum operating stress, minimizing the absolute value of the minimum operating stress, ensuring that the maximum construction stress is within the allowable stress range, and ensuring that the minimum construction stress is within the allowable stress range.

[0034] Multiple sets of jacking forces for different closure sections are randomly generated within the jacking force range as initial jacking forces, and the initial stress data of each pier corresponding to each set of initial jacking forces are calculated through the prediction model.

[0035] Using the initial thrust and corresponding initial stress data as the initial population, multiple optimal solutions are obtained by performing multi-objective optimization calculations using NSGA-II based on the constraints.

[0036] Secondly, embodiments of this application also provide a thrust optimization system for high-pier multi-span continuous rigid frame bridges, including:

[0037] The modeling unit is configured to acquire the design parameters of the target continuous rigid frame bridge and construct a finite element model based on the design parameters;

[0038] The working condition unit is configured to construct multiple sets of calculation working conditions based on the distribution of the closure segment and piers of the target continuous rigid frame bridge; each set of calculation working conditions corresponds to different jacking forces of different closure segments;

[0039] The simulation unit is configured to perform construction simulation calculations on the finite element model according to the calculation conditions to obtain stress data of each pier corresponding to different calculation conditions;

[0040] The training unit is configured to train a prediction model using the jacking force of each closure segment corresponding to the calculation condition as input data and the stress data of each pier as output data.

[0041] The optimal solution unit is configured to output multiple sets of optimal solutions based on the prediction model and the intelligent optimization algorithm; the optimal solution is a corresponding array of the jacking force of each closure segment and the stress data of the pier.

[0042] The scoring unit is configured to score each of the optimal solutions and use the jacking force of each closure segment corresponding to the highest-scoring optimal solution as the final jacking force for construction.

[0043] In one possible implementation, the scoring unit is further configured as follows:

[0044] Obtain the maximum construction stress, minimum construction stress, maximum operational stress, and minimum operational stress from the stress data in the optimal solution;

[0045] The stress uniformity of the maximum stress during the operation phase is calculated based on the maximum operating stress, and the stress uniformity of the minimum stress during the operation phase is calculated based on the minimum operating stress.

[0046] A stress evaluation item is constructed based on the maximum stress during construction, the minimum stress during construction, the maximum stress during operation, and the minimum stress during operation. A stress uniformity evaluation item is constructed based on the stress uniformity of the maximum stress during operation and the stress uniformity of the minimum stress during operation.

[0047] The optimal solution is scored by weighting the stress evaluation item and the stress uniformity evaluation item.

[0048] In one possible implementation, the scoring unit is further configured as follows:

[0049] The score for the optimal solution is calculated using the following formula:

[0050]

[0051] In the formula, I opt For scoring, σ cs-max For the maximum stress during construction, σ cs-min For the minimum stress during construction, σ os-max For the maximum operational stress, σ os-min For minimum operational stress, SD(σ) os-max ) represents the stress uniformity of the maximum stress during the operation phase, SD(σ) os-min ) represents the stress uniformity of minimum stress during the operation phase, α is the weight of the stress evaluation item, and β is the weight of the stress uniformity evaluation item.

[0052] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0053] This invention relates to a method and system for optimizing the jacking thrust of a high-pier, multi-span continuous rigid frame bridge. It solves the problem of making the relationship between the closure jacking thrust and the pier stress explicit, improves the efficiency of obtaining the pier stress under different working conditions, and requires fewer finite element calculations. It can effectively improve the efficiency of obtaining the reasonable jacking thrust of a large-span, high-pier continuous rigid frame bridge, and requires fewer finite element calculations. Attached Figure Description

[0054] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0055] Figure 1 This is a schematic diagram of the method steps in an embodiment of this application;

[0056] Figure 2 This is a schematic diagram showing the distribution of the closure segment in an embodiment of this application;

[0057] Figure 3 This is a schematic diagram of the distribution of training sample points in an embodiment of this application;

[0058] Figure 4 This is a schematic diagram of the distribution of test sample points in an embodiment of this application;

[0059] Figure 5 This is a schematic diagram illustrating the minimum stress during the construction phase of an embodiment of this application;

[0060] Figure 6 This is a schematic diagram showing the maximum stress during the construction phase of an embodiment of this application;

[0061] Figure 7 This is a schematic diagram illustrating the minimum stress during the operation phase of an embodiment of this application;

[0062] Figure 8 This is a schematic diagram of the maximum stress during the operation phase of an embodiment of this application. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. It should be understood that the accompanying drawings in this application are for illustrative and descriptive purposes only and are not intended to limit the scope of protection of this application. Furthermore, it should be understood that the schematic drawings are not drawn to scale. The flowcharts used in this application illustrate operations implemented according to some embodiments of this application. It should be understood that the operations in the flowcharts may not be implemented in sequence, and steps without logical contextual relationships may be reversed or implemented simultaneously. In addition, those skilled in the art, guided by the content of this application, may add one or more other operations to the flowcharts, or remove one or more operations from the flowcharts.

[0064] Furthermore, the described embodiments are merely some, not all, of the embodiments of this application. The components of the embodiments of this application described and illustrated herein can typically be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0065] Please refer to the following: Figure 1 This is a flowchart illustrating the method for optimizing the thrust of a high-pier multi-span continuous rigid frame bridge provided in an embodiment of the present invention. Further, the method for optimizing the thrust of a high-pier multi-span continuous rigid frame bridge may specifically include the contents described in steps S1-S6.

[0066] S1: Obtain the design parameters of the target continuous rigid frame bridge, and construct a finite element model based on the design parameters;

[0067] S2: Construct multiple sets of calculation conditions based on the closure segment and pier distribution of the target continuous rigid frame bridge; each set of calculation conditions corresponds to different jacking forces of different closure segments;

[0068] S3: Perform construction simulation calculations on the finite element model according to the calculation conditions to obtain stress data for each pier corresponding to different calculation conditions;

[0069] S4: The prediction model is trained using the jacking force of each closure segment corresponding to the calculation condition as input data and the stress data of each pier as output data.

[0070] S5: Based on the prediction model and the multi-objective intelligent optimization algorithm, output multiple sets of optimal solutions; the optimal solution is the corresponding array of the jacking force of each closure segment and the stress data of the pier.

[0071] S6: Score each of the optimal solutions and use the jacking force of each closure segment corresponding to the optimal solution with the highest score as the final jacking force for construction.

[0072] In implementing this embodiment, it is necessary to first construct a finite element model of the target continuous rigid frame bridge. This finite element model can be built using commercial finite element methods. During construction, design parameters such as the dimensions of various parts of the bridge and material-related parameters need to be obtained first. Simultaneously, the possible construction process needs to be considered when dividing the element mesh. This is a mature existing technology, and this embodiment does not impose any limitations. For continuous rigid frame bridges, the closure segment generally appears at the mid-span, and the distribution of the piers determines the position of the bridge span, which in turn determines the position of the closure segment. The main purpose of this embodiment is to determine the optimal solution for each closure segment, so multiple sets of calculation conditions need to be constructed first. For each calculation condition, the jacking force of each closure segment needs to be given, and then the pier stress is calculated using the finite element model.

[0073] In this embodiment of the application, in order to reduce the amount of finite element calculation, after calculating the results corresponding to multiple sets of calculation conditions through the finite element model, a prediction model is pre-trained using these results. The prediction model adopts a model that can perform data prediction, such as a neural network model or an SVR model. The input data of the prediction model needs to be the jacking force of each closure segment. It should be understood that the dimension of the jacking force as input data needs to be the same as the number of closure segments. That is, the jacking forces of all closure segments in a calculation condition need to be formed into a one-dimensional matrix as input data. The output data can be selected according to the requirements, such as selecting the maximum and minimum stresses during construction and operation, or selecting the stress values ​​and bending moment values ​​of multiple key parts.

[0074] In this embodiment, based on the trained prediction model, a multi-objective optimization algorithm can be used to find the optimal solution. Since the solution process generates data entirely from the prediction model, it does not require frequent calculations using the finite element model, thus effectively reducing computation time. The multi-objective optimization algorithm used can be MOEA / D, SPEA2, NSGA-II, etc., and this embodiment does not impose any limitations. A large number of optimal solutions can be obtained through the multi-objective optimization algorithm. Scoring these solutions accordingly yields the optimal solution, which is then used as the final jacking force for construction.

[0075] In one possible implementation, the score for the optimal solution includes:

[0076] Obtain the maximum construction stress, minimum construction stress, maximum operational stress, and minimum operational stress from the stress data in the optimal solution;

[0077] The stress uniformity of the maximum stress during the operation phase is calculated based on the maximum operating stress, and the stress uniformity of the minimum stress during the operation phase is calculated based on the minimum operating stress.

[0078] A stress evaluation item is constructed based on the maximum stress during construction, the minimum stress during construction, the maximum stress during operation, and the minimum stress during operation. A stress uniformity evaluation item is constructed based on the stress uniformity of the maximum stress during operation and the stress uniformity of the minimum stress during operation.

[0079] The optimal solution is scored by weighting the stress evaluation item and the stress uniformity evaluation item.

[0080] In the implementation of this application embodiment, for a set of optimal solutions, the stress data needs to include the maximum construction stress, minimum construction stress, maximum operational stress, and minimum operational stress; where the maximum stress is a positive value and belongs to tensile stress, and the minimum stress is a negative value and belongs to compressive stress. For the evaluation of an optimal solution, this application embodiment divides it into two parts: one part is used to characterize the safety during construction and operation, i.e., the stress evaluation item; the other part is used to characterize the bridge's economy, i.e., the stress uniformity evaluation item. The stress evaluation item is evaluated by assessing the maximum and minimum stresses, while the stress uniformity evaluation item is evaluated by assessing the stress uniformity of the maximum and minimum stresses. The reason for this is that, in the ideal situation, under operational conditions, the maximum stress and minimum stress of each pier are the same, indicating that the load can be completely and uniformly distributed to each pier. In this case, the stress uniformity is the best. It should be understood that the stress uniformity described in this application embodiment refers to the uniformity calculation after summing the maximum or minimum stress of each pier, and this calculation can be reflected through methods such as standard deviation.

[0081] In one possible implementation, the score for the optimal solution is calculated according to the following formula:

[0082]

[0083] In the formula, I opt For scoring, σ cs-max For the maximum stress during construction, σ cs-min For the minimum stress during construction, σ os-max For the maximum operational stress, σ os-min For minimum operational stress, SD(σ) os-max ) represents the stress uniformity of the maximum stress during the operation phase, SD(σ) os-min) represents the stress uniformity of minimum stress during the operation phase, α is the weight of the stress evaluation item, and β is the weight of the stress uniformity evaluation item.

[0084] In the implementation of this application embodiment, the score is calculated using the above formula. Since the minimum stress is a negative value, the absolute value needs to be taken. For the two weighting coefficients, different values ​​can be taken for different bridges, which can be obtained through the analysis of the corresponding data. Generally speaking, when safety is the primary consideration, the weight of the stress evaluation item is greater than the weight of the stress uniformity evaluation item, while when economic consideration is the primary consideration, the weight of the stress evaluation item is less than the weight of the stress uniformity evaluation item. When considering both safety and economy, a relatively close weight of the stress evaluation item and the stress uniformity evaluation item can be selected, such as a stress evaluation item weight of 0.6 and a stress uniformity evaluation item weight of 0.4.

[0085] In one possible implementation, the construction of the computational working condition includes:

[0086] The jacking force of each of the aforementioned closure segments is divided into three loading levels: low jacking force, medium jacking force, and high jacking force.

[0087] Each closure segment is selected and combined under three loading levels to form multiple sets of training calculation conditions;

[0088] The thrust range is constructed with the low thrust as the minimum value and the high thrust as the maximum value.

[0089] Within the top thrust range, each closing segment is subjected to Latin hypercube sampling and combined to form multiple sets of verification calculation conditions.

[0090] In the implementation of this application, the calculation of the load cases actually requires constructing multiple stress combinations for all closure segments. Different load case construction methods are used for the training load cases and the validation load cases. The training load cases employ the BBD sample construction method because it effectively handles nonlinear responses. It divides the stress level of the jacking force into three levels: low jacking force, medium jacking force, and high jacking force, and then selects and combines the stress level of each closure segment from these three levels to form a sample. For the validation load cases, Latin hypercube sampling can generate a richer variety of jacking force stress levels, thereby improving the model's predictive performance through more comprehensive validation calculations.

[0091] In one possible implementation, performing construction simulation calculations on the finite element model according to the calculation conditions to obtain stress data for each bridge pier corresponding to different calculation conditions includes:

[0092] The finite element model is subjected to construction simulation calculations under the training calculation conditions to obtain multiple sets of maximum construction stress, minimum construction stress, maximum operation stress, and minimum operation stress as training stress data. The finite element model is then subjected to construction simulation calculations under the verification calculation conditions to obtain multiple sets of maximum construction stress, minimum construction stress, maximum operation stress, and minimum operation stress as verification stress data.

[0093] In the implementation of this application embodiment, it is necessary to calculate the training stress data for training the model by using the generated training calculation conditions through the finite element model, and at the same time, calculate the verification stress data for verifying the model by using the generated verification calculation conditions through the finite element model.

[0094] In one possible implementation, training the prediction model includes:

[0095] The SVR model is constructed using the Gaussian kernel function.

[0096] The SVR model is trained using the jacking force of each closure segment under the training calculation condition as input data and the corresponding training stress data as output data. The SVR model is then validated using the validation stress data to generate the prediction model.

[0097] In the implementation of this application embodiment, an SVR model with a Gaussian kernel function is used. The SVR model requires less sample size and has high reliability and interpretability. In scientific practice, the number of training calculation cases can generally be reduced to less than 100, while the number of verification stress data can be reduced to less than 20. The number of calculations required by the finite element model is far less than the number of calculations in the prior art.

[0098] In one possible implementation, the prediction model combined with an intelligent optimization algorithm outputs multiple sets of optimal solutions, including:

[0099] The constraints for constructing the optimal solution include minimizing the maximum operating stress, minimizing the absolute value of the minimum operating stress, ensuring that the maximum construction stress is within the allowable stress range, and ensuring that the minimum construction stress is within the allowable stress range.

[0100] Multiple sets of jacking forces for different closure sections are randomly generated within the jacking force range as initial jacking forces, and the initial stress data of each pier corresponding to each set of initial jacking forces are calculated through the prediction model.

[0101] Using the initial thrust and corresponding initial stress data as the initial population, multiple optimal solutions are obtained by performing multi-objective optimization calculations using NSGA-II based on the constraints.

[0102] When implementing the embodiments of this application, the constraints need to meet four conditions: the maximum operating stress should be minimized, the absolute value of the minimum operating stress should be minimized, the maximum construction stress should be within the allowable stress range, and the minimum construction stress should be within the allowable stress range. This is a typical multi-objective optimization problem. Therefore, the embodiments of this application preferably use NSGA-II for multi-objective optimization processing. The initial population of NSGA-II needs to be constructed by combining within the thrust range. Since the thrust range is generated based on low thrust and high thrust, it can cover the thrust range of subsequent verification, the initial population, and the subsequent population, thereby ensuring the accuracy of the model output results.

[0103] For example, this application provides a specific implementation case, in which the target continuous rigid frame bridge is a continuous rigid frame beam in Southwest China; the superstructure of the main bridge adopts a prestressed concrete continuous rigid frame, the substructure adopts double-limb solid thin-walled piers, and the foundation adopts a pile cap foundation; the main beam material is C60 concrete, and the pier material is C50 concrete; the cantilevered cast beam segments of the main beam are divided into three segments of 3.0m, 4.0m, and 4.5m in length, and the mid-span closure segment of the bridge is designed to be 2m. Due to the influence of topography and landforms, the main piers of this bridge vary considerably in height, ranging from 66.4m to 192m. There are eight piers in total. Piers 1 and 8 are transition piers, while piers 2 and 7 are solid double-limb thin-walled piers with a diameter of 8.5m (transverse) × 2.5m (longitudinal). Piers 3 through 6 all have a top dimension of 8.5m (transverse) × 10m (longitudinal). Based on these design parameters, a finite element model can be constructed. The finite element model was built using the MIDAS commercial finite element method, dividing the entire bridge into 508 nodes and 502 elements, including 306 elements for the main beams and 196 elements for the piers, all using beam elements. The connection between the main beams and piers adopts a rigid connection within an elastic connection, while the bottom of piers 2 through 7 uses fixed constraints.

[0104] During construction, dead loads including self-weight, prestressing, formwork, and the wet weight of the main girder concrete were considered. The duration of the construction phase and nonlinear effects were also taken into account to accurately assess the impact of shrinkage and creep effects and nonlinear effects on the bridge. To minimize the impact of long-term creep on the bridge's internal condition, five closure sections were set at mid-span. A jacking force was applied to the already constructed main girder before the construction of each closure section. For the distribution of the closure sections, please refer to [link to relevant documentation]. Figure 2 JF A JF B JF C JF D and JF ETo characterize the jacking force of these five closure segments, in this example, the jacking force is first applied to closure segments A and E, and construction is carried out on the closure segments. After the concrete reaches the design strength, the jacking device is removed. The jacking force is then applied to closure segments B and D, and construction is carried out on the closure segments. After the concrete reaches the design strength, the jacking device is removed. Finally, the jacking force is applied to closure segment C, and construction is carried out on the closure segment. After the concrete reaches the design strength, the jacking device is removed.

[0105] After the finite element model was constructed, to improve the efficiency of training sample points and obtain a better prediction model with fewer sample points, 41 sets of top thrust training sample points were constructed, taking advantage of the BBD sample construction method's characteristics of requiring fewer samples and effectively handling nonlinear responses. For validation samples, 10 sets of thrust verification sample points were constructed using the LHS method. The low top thrust of the training sample points was selected as 1 kN, the medium top thrust as 6000.5 kN, and the high top thrust as 12000 kN. For the distribution of the training sample points, please refer to [link to relevant documentation]. Figure 3 Please refer to the sample point distribution test. Figure 4 ; Figure 3 and Figure 4 The vertical axis represents the thrust force (MN), and the horizontal axis represents the sample point number. After calculating the stresses of piers 2-7 using the constructed finite element model with the above training and test sample points, please refer to [reference needed]. Figures 5-8 In the figure, the horizontal axis represents the pier number, and the vertical axis represents the stress value in MPa. Figure 5 The minimum stress during the construction phase is shown. Figure 6 The maximum stress during the construction phase is shown. Figure 7 The minimum stress during the operation phase is shown. Figure 8 The maximum stress during the operation phase is shown.

[0106] In this example, the SVR model was trained using the aforementioned training sample points. The SVR model predicted the maximum and minimum stresses during the construction, operation, and maintenance phases of the training samples. Results showed that the vast majority of predicted values ​​were close to the experimental values ​​near the y=x line. Statistical analysis revealed that 4.5% of the data had prediction errors greater than ±5%, indicating high reliability. For continuous rigid frame bridges, the stress on the piers continuously changes during the subsequent operation phase due to shrinkage and creep effects, impacting the pier performance. To minimize the impact of shrinkage and creep, a reasonable jacking force needs to be applied at the mid-span closure section to improve the bridge's mechanical properties after completion. Therefore, constraints were constructed according to the "Design Specifications for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts," namely, minimizing the maximum operational stress, minimizing the absolute value of the minimum operational stress, ensuring the maximum construction stress is within the allowable stress range, and ensuring the minimum construction stress is within the allowable stress range. The solution was obtained using NSGA-II, yielding approximately 200 solutions. Further screening was required to select a unique final solution. When performing calculations based on the following formulas, it is necessary to select appropriate stress weighting coefficients and stress uniformity weighting coefficients. The inventors discovered that the stress weighting coefficients and stress uniformity weighting coefficients have the same unique optimal solution when they are (1,0), (0.2,0.8), and (0.6,0.4), respectively. After comprehensively considering safety and economy, (0.6,0.4) is chosen as the stress weighting coefficient and stress uniformity weighting coefficient, and the following optimal solution JF is finally obtained. A =4994.86kN, JF B =5680.62kN, JF C =9799.98kN, JF D =5645.07kN, JF E =5089.55kN.

[0107] Based on the same inventive concept, embodiments of this application also provide a thrust optimization system for high-pier multi-span continuous rigid frame bridges, including:

[0108] The modeling unit is configured to acquire the design parameters of the target continuous rigid frame bridge and construct a finite element model based on the design parameters;

[0109] The working condition unit is configured to construct multiple sets of calculation working conditions based on the distribution of the closure segment and piers of the target continuous rigid frame bridge; each set of calculation working conditions corresponds to different jacking forces of different closure segments;

[0110] The simulation unit is configured to perform construction simulation calculations on the finite element model according to the calculation conditions to obtain stress data of each pier corresponding to different calculation conditions;

[0111] The training unit is configured to train a prediction model using the jacking force of each closure segment corresponding to the calculation condition as input data and the stress data of each pier as output data.

[0112] The optimal solution unit is configured to output multiple sets of optimal solutions based on the prediction model and the intelligent optimization algorithm; the optimal solution is a corresponding array of the jacking force of each closure segment and the stress data of the pier.

[0113] The scoring unit is configured to score each of the optimal solutions and use the jacking force of each closure segment corresponding to the highest-scoring optimal solution as the final jacking force for construction.

[0114] In one possible implementation, the scoring unit is further configured as follows:

[0115] Obtain the maximum construction stress, minimum construction stress, maximum operational stress, and minimum operational stress from the stress data in the optimal solution;

[0116] The stress uniformity of the maximum stress during the operation phase is calculated based on the maximum operating stress, and the stress uniformity of the minimum stress during the operation phase is calculated based on the minimum operating stress.

[0117] A stress evaluation item is constructed based on the maximum stress during construction, the minimum stress during construction, the maximum stress during operation, and the minimum stress during operation. A stress uniformity evaluation item is constructed based on the stress uniformity of the maximum stress during operation and the stress uniformity of the minimum stress during operation.

[0118] The optimal solution is scored by weighting the stress evaluation item and the stress uniformity evaluation item.

[0119] In one possible implementation, the scoring unit is further configured as follows:

[0120] The score for the optimal solution is calculated using the following formula:

[0121]

[0122] In the formula, I opt For scoring, σ cs-max For the maximum stress during construction, σ cs-min For the minimum stress during construction, σ os-max For the maximum operational stress, σ os-min For minimum operational stress, SD(σ) os-max ) represents the stress uniformity of the maximum stress during the operation phase, SD(σ) os-min ) represents the stress uniformity of minimum stress during the operation phase, α is the weight of the stress evaluation item, and β is the weight of the stress uniformity evaluation item.

[0123] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0124] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices or units, or may be electrical, mechanical or other forms of connection.

[0125] The units described as separate components may or may not be physically separate. As will be apparent to those skilled in the art, the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0126] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0127] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or grid device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0128] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the thrust of a high-pier, multi-span continuous rigid frame bridge, characterized in that, include: Obtain the design parameters of the target continuous rigid frame bridge, and construct a finite element model based on the design parameters; Multiple sets of calculation conditions are constructed based on the closure segment and pier distribution of the target continuous rigid frame bridge; each set of calculation conditions corresponds to different jacking forces of different closure segments; Based on the aforementioned calculation conditions, the finite element model is used to perform construction simulation calculations to obtain stress data for each bridge pier corresponding to different calculation conditions. The prediction model is trained using the jacking force of each closure segment corresponding to the calculation condition as input data and the stress data of each pier as output data. Based on the prediction model and intelligent optimization algorithm, multiple optimal solutions are output; the optimal solution is an array corresponding to the jacking force of each closure segment and the stress data of the pier. Each optimal solution is scored, and the jacking force of each closure segment corresponding to the optimal solution with the highest score is taken as the final jacking force for construction. The score for the optimal solution includes: Obtain the maximum construction stress, minimum construction stress, maximum operational stress, and minimum operational stress from the stress data in the optimal solution; The stress uniformity of the maximum stress during the operation phase is calculated based on the maximum operating stress, and the stress uniformity of the minimum stress during the operation phase is calculated based on the minimum operating stress. A stress evaluation item is constructed based on the maximum stress during construction, the minimum stress during construction, the maximum stress during operation, and the minimum stress during operation. A stress uniformity evaluation item is constructed based on the stress uniformity of the maximum stress during operation and the stress uniformity of the minimum stress during operation. The optimal solution is scored by weighting the stress evaluation item and the stress uniformity evaluation item; The score for the optimal solution is calculated using the following formula: In the formula, I opt For scoring, σ cs-max For the maximum stress during construction, σ cs-min For the minimum stress during construction, σ os-max For the maximum operational stress, σ os-min For minimum operational stress, SD(σ) os-max ) represents the stress uniformity of the maximum stress during the operation phase, SD(σ) os-min ) represents the stress uniformity of minimum stress during the operation phase, α is the weight of the stress evaluation item, and β is the weight of the stress uniformity evaluation item.

2. The method for optimizing the thrust of a high-pier, multi-span continuous rigid frame bridge according to claim 1, characterized in that, The construction of the calculation conditions includes: The jacking force of each of the aforementioned closure segments is divided into three loading levels: low jacking force, medium jacking force, and high jacking force. Each closure segment is selected and combined under three loading levels to form multiple sets of training calculation conditions; The thrust range is constructed with the low thrust as the minimum value and the high thrust as the maximum value. Within the top thrust range, each closing segment is subjected to Latin hypercube sampling and combined to form multiple sets of verification calculation conditions.

3. The method for optimizing the thrust of a high-pier, multi-span continuous rigid frame bridge according to claim 2, characterized in that, Based on the aforementioned calculation conditions, the finite element model is used to perform construction simulation calculations to obtain stress data for each bridge pier corresponding to different calculation conditions, including: The finite element model is subjected to construction simulation calculations under the training calculation conditions to obtain multiple sets of maximum construction stress, minimum construction stress, maximum operation stress, and minimum operation stress as training stress data. The finite element model is then subjected to construction simulation calculations under the verification calculation conditions to obtain multiple sets of maximum construction stress, minimum construction stress, maximum operation stress, and minimum operation stress as verification stress data.

4. The method for optimizing the thrust of a high-pier, multi-span continuous rigid frame bridge according to claim 3, characterized in that, The training of the prediction model includes: The SVR model is constructed using the Gaussian kernel function. The SVR model is trained using the jacking force of each closure segment under the training calculation condition as input data and the corresponding training stress data as output data. The SVR model is then validated using the validation stress data to generate the prediction model.

5. The method for optimizing the thrust of a high-pier, multi-span continuous rigid frame bridge according to claim 3, characterized in that, Based on the prediction model and intelligent optimization algorithm, multiple sets of optimal solutions are output, including: The constraints for constructing the optimal solution include minimizing the maximum operating stress, minimizing the absolute value of the minimum operating stress, ensuring that the maximum construction stress is within the allowable stress range, and ensuring that the minimum construction stress is within the allowable stress range. Multiple sets of jacking forces for different closure sections are randomly generated within the jacking force range as initial jacking forces, and the initial stress data of each pier corresponding to each set of initial jacking forces are calculated through the prediction model. Using the initial thrust and corresponding initial stress data as the initial population, multiple optimal solutions are obtained by performing multi-objective optimization calculations using NSGA-II based on the constraints.

6. A thrust optimization system for high-pier multi-span continuous rigid frame bridges, characterized in that, include: The modeling unit is configured to acquire the design parameters of the target continuous rigid frame bridge and construct a finite element model based on the design parameters; The working condition unit is configured to construct multiple sets of calculation working conditions based on the distribution of the closure segment and piers of the target continuous rigid frame bridge; each set of calculation working conditions corresponds to different jacking forces of different closure segments; The simulation unit is configured to perform construction simulation calculations on the finite element model according to the calculation conditions to obtain stress data of each pier corresponding to different calculation conditions; The training unit is configured to train a prediction model using the jacking force of each closure segment corresponding to the calculation condition as input data and the stress data of each pier as output data. The optimal solution unit is configured to output multiple sets of optimal solutions based on the prediction model; the optimal solution is a corresponding array of the jacking force of each closure segment and the stress data of the pier. The scoring unit is configured to score each of the optimal solutions and use the jacking force of each closure segment corresponding to the optimal solution with the highest score as the final jacking force for construction. The scoring unit is also configured to: Obtain the maximum construction stress, minimum construction stress, maximum operational stress, and minimum operational stress from the stress data in the optimal solution; The stress uniformity of the maximum stress during the operation phase is calculated based on the maximum operating stress, and the stress uniformity of the minimum stress during the operation phase is calculated based on the minimum operating stress. A stress evaluation item is constructed based on the maximum stress during construction, the minimum stress during construction, the maximum stress during operation, and the minimum stress during operation. A stress uniformity evaluation item is constructed based on the stress uniformity of the maximum stress during operation and the stress uniformity of the minimum stress during operation. The optimal solution is scored by weighting the stress evaluation item and the stress uniformity evaluation item; The scoring unit is also configured to: The score for the optimal solution is calculated using the following formula: In the formula, I opt For scoring, σ cs-max For the maximum stress during construction, σ cs-min For the minimum stress during construction, σ os-max For the maximum operational stress, σ os-min For minimum operational stress, SD(σ) os-max ) represents the stress uniformity of the maximum stress during the operation phase, SD(σ) os-min ) represents the stress uniformity of minimum stress during the operation phase, α is the weight of the stress evaluation item, and β is the weight of the stress uniformity evaluation item.

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