Cable-stayed bridge cable force and linear collaborative control method and system based on finite element analysis

Abstract

The application relates to the technical field of cable-stayed bridge cable force control, in particular to a cable-stayed bridge cable force and linear collaborative control method and system based on finite element analysis, which comprises the following steps: by analyzing the cumulative degree of the vertical displacement of each measuring point when a unit cable force is applied to all cables, comparing the measured vertical displacement deviation of each measuring point with a preset displacement deviation threshold, and determining the bridge linear urgency; based on the measured vertical displacement deviation of all measuring points, using a generalized inverse matrix to solve the cable force adjustment amount of all cables in the finite element model of the cable-stayed bridge, determining the comprehensive cable force adjustment scale, combining the bridge linear urgency and the preset design cable force average value of all cables, determining the initial allowable dispersion value, and optimizing the constraint condition in the cable force and linear collaborative control process of the cable-stayed bridge. According to the application, the cable force uniformity constraint threshold is adaptively adjusted according to the actual risk and demand of the bridge, and the rationality and implementability of the cable force and linear collaborative control strategy are improved.

Description

Technical Field

[0001] This application relates to the field of cable-stayed bridge cable force control technology, specifically to a method and system for coordinated control of cable force and alignment of cable-stayed bridges based on finite element analysis. Background Technology

[0002] A cable-stayed bridge is a coordinated stress-bearing system composed of a main tower, a main girder, and stay cables. High-strength stay cables provide elastic support for the long-span main girder. Cable force, i.e., the axial tension of the stay cables, directly determines the stress distribution and geometric deformation of the main girder and main tower. The bridge's geometry, i.e., its actual geometric shape, must be consistent with the design objectives to ensure structural safety and performance. Given that traditional analytical methods struggle to accurately predict the coupling effect of cable force and geometry, finite element analysis, by establishing a structural model, can accurately calculate the cable force, geometry, and stress distribution of each component, providing high-precision data support for construction control.

[0003] Traditional methods aim to minimize cable force error and use alignment, stress, cable force limits, and uniformity as constraints to establish a nonlinear optimization model to solve for cable force adjustment. However, in the uniformity constraint, the maximum allowable value used to measure cable force dispersion relies on empirical settings. Since the requirements for cable force uniformity vary dynamically across different structures and construction stages, this static, empirical setting weakens the rationality and feasibility of the coordinated control strategy of cable force and alignment. Summary of the Invention

[0004] To address the aforementioned technical problems, the purpose of this application is to provide a method and system for the coordinated control of cable force and alignment of cable-stayed bridges based on finite element analysis. The specific technical solution adopted is as follows:

[0005] In a first aspect, embodiments of this application provide a method for the coordinated control of cable force and alignment of cable-stayed bridges based on finite element analysis. This method includes the following steps:

[0006] The measured vertical displacement deviation of each preset measuring point in the finite element model of the cable-stayed bridge is obtained, and the vertical displacement of each measuring point is obtained when a unit cable force is applied to each cable.

[0007] By analyzing the cumulative vertical displacement of each measuring point when a unit cable force is applied to all cables, the cable force sensitivity of each measuring point is determined; by comparing the measured vertical displacement deviation of each measuring point with the preset displacement deviation threshold, the displacement deviation limit value of each measuring point is determined, and combined with the cable force sensitivity, the sensitivity weight of each measuring point is determined; based on the displacement deviation limit value and the sensitivity weight, the bridge alignment urgency of the cable-stayed bridge is determined.

[0008] Based on the measured vertical displacement deviations at all measuring points, the cable force adjustment of all cables in the finite element model of the cable-stayed bridge is solved using a generalized inverse matrix to determine the comprehensive cable force adjustment scale of the cable-stayed bridge.

[0009] Based on the bridge alignment urgency and the comprehensive cable force adjustment scale, as well as the average value of the preset design cable force of all cables, the initial allowable discrete value of the cable-stayed bridge is determined in order to optimize the constraints in the cable force and linear coordinated control process of the cable-stayed bridge.

[0010] Preferably, the cable force sensitivity of each measuring point is the L1 norm of the vertical displacement of each measuring point when a unit cable force is applied to all cables.

[0011] Preferably, the displacement deviation exceeding the limit value of each measuring point is the ratio of the measured vertical displacement deviation of each measuring point to the preset displacement deviation threshold.

[0012] Preferably, the sensitivity weight of each measuring point is the normalized result of the product of the displacement deviation exceeding the limit value and the cable force sensitivity of each measuring point.

[0013] Preferably, the bridge alignment tightness of the cable-stayed bridge is the result of positive fusion of the displacement deviation exceeding the limit value of all measuring points on the finite element model of the cable-stayed bridge and the sensitive weight.

[0014] Preferably, the method of using a generalized inverse matrix to solve for the cable force adjustment of all cables in the finite element model of a cable-stayed bridge includes:

[0015] The vertical displacement of each measuring point when a unit cable force is applied to all cables is used to form the cable force vector of each measuring point. The matrix composed of the cable force vectors of all measuring points is denoted as the displacement-cable force matrix. The displacement-cable force matrix is ​​used as the input of the generalized inverse matrix algorithm, and the output is the pseudo-inverse matrix of the displacement-cable force matrix.

[0016] The measured vertical displacement deviations of all measuring points are used as inputs to the pseudo-inverse matrix of the displacement-cable force matrix, and the output is the cable force adjustment of all cables in the finite element model of the cable-stayed bridge.

[0017] Preferably, the overall cable force adjustment scale of the cable-stayed bridge is the average value of the cable force adjustment of all cables in the finite element model of the cable-stayed bridge.

[0018] Preferably, the expression for the initial allowable discrete value of the cable-stayed bridge is: In the formula, This represents the initial allowable discrete value for a cable-stayed bridge; This indicates the overall cable force adjustment scale for a cable-stayed bridge; Indicates the urgency of the bridge alignment of a cable-stayed bridge; This represents the lower bound of discrete values, where, , where n represents the number of all cables in the finite element model of the cable-stayed bridge; Denotes the upper limit of discrete values, where, , This indicates the preset relative cable force deviation. represents the average value of the preset design cable force of all cables in the finite element model of the cable-stayed bridge; exp() represents the exponential function with the natural constant as the base; clamp[] represents the truncation function.

[0019] Preferably, the constraints in the process of optimizing the cable force and linear coordinated control of the cable-stayed bridge include:

[0020] Based on the initial allowable discrete values, the Robbins–Monro algorithm is used to iteratively optimize the allowable discrete values ​​within the uniformity constraint during the cable force and linear coordinated control process of the cable-stayed bridge.

[0021] Secondly, embodiments of this application also provide a cable-stayed bridge cable force and alignment coordinated control system based on finite element analysis, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of any of the above-described cable force and alignment coordinated control methods based on finite element analysis.

[0022] This application has at least the following beneficial effects:

[0023] This application constructs a sensitivity weight that quantifies the comprehensive importance of key measuring points by integrating the cable force sensitivity and displacement deviation exceeding limits at measuring points. This weight is then aggregated into a bridge alignment urgency, ensuring that subsequent control strategies can accurately focus on critical areas that are both sensitive and exceed limits. This lays a solid data foundation for the adaptive updating of the uniformity constraint threshold. Furthermore, the cable force adjustment amount obtained by solving the generalized inverse matrix represents a scheme for correcting alignment deviations with minimal energy cost. This further quantifies the comprehensive cable force adjustment scale of the current correction requirement intensity. Working together with the bridge alignment urgency, this provides a crucial physical benchmark for generating an initial uniformity constraint threshold that accurately matches actual working conditions, ensuring the dimensional rationality and engineering feasibility of the control strategy. Finally, this application… Based on the urgency of bridge alignment and the comprehensive cable force adjustment scale, an initial permissible discrete value matching the current risks and adjustment needs is generated, and reasonable engineering and specification boundaries are set for it. Furthermore, by introducing the Robbins–Monro algorithm with the standard deviation of the optimized cable force adjustment as feedback, adaptive iterative updates of the permissible discrete value are achieved. This ensures that when optimization is feasible, it can be gradually tightened to the optimal uniformity, and when it is not feasible, it can be automatically relaxed to ensure the robustness of the solution. This dual guarantee mechanism ultimately enables the collaborative control strategy to converge to an optimal solution that satisfies both alignment and safety specifications and minimizes the cable force adjustment. Under the premise of ensuring structural safety and quality, construction costs and complexity are effectively reduced, and the rationality and operability of the collaborative control of cable-stayed bridges and alignment are improved. Attached Figure Description

[0024] To more clearly illustrate the technical solutions and advantages in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 A flowchart illustrating the steps of a method for coordinated control of cable force and alignment of a cable-stayed bridge based on finite element analysis, provided in one embodiment of this application.

[0026] Figure 2 This is a schematic diagram of the bridge alignment urgency extraction process provided in one embodiment of this application. Detailed Implementation

[0027] To further illustrate the technical means and effects adopted by this application to achieve the intended purpose of the invention, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of the cable-stayed bridge cable force and alignment coordinated control method and system based on finite element analysis proposed in this application. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0028] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0029] The following, in conjunction with the accompanying drawings, details the specific scheme of the cable-stayed bridge cable force and alignment coordinated control method and system based on finite element analysis provided in this application.

[0030] Please see Figure 1 The diagram illustrates a flowchart of a method for coordinated control of cable force and alignment of a cable-stayed bridge based on finite element analysis, according to an embodiment of this application. The method includes the following steps:

[0031] Step S1: Obtain the measured vertical displacement deviation of each preset measuring point in the finite element model of the cable-stayed bridge, and obtain the vertical displacement of each measuring point when a unit cable force is applied to each cable.

[0032] The maximum allowable discrete value r is the core indicator for quantifying the uniformity of cable force distribution in a bridge. In the optimization model, it is set as a key constraint threshold, which directly defines the feasible solution space of the cable force adjustment scheme. The purpose of introducing this constraint is to prevent individual cable forces from exceeding the limit or the tensioning equipment capacity in order to unilaterally pursue the perfect alignment. Traditional methods usually use the standard deviation of the cable force adjustment amount to achieve this constraint.

[0033] To achieve adaptive maximum allowable discrete value, a quantitative bridge must be established between geometric displacement and internal force adjustment. The core steps of this embodiment are as follows: First, based on the finite element influence matrix and the measured alignment deviation, the key measurement points that are most sensitive to cable force uniformity and have the highest risk of exceeding limits are identified, and the urgency of the overall alignment problem is assessed. On this basis, the alignment deviation is inversely calculated into the cable force adjustment scale through the pseudo-inverse minimum norm solution, that is, the theoretical adjustment amount required for each cable on average. This dimensional mapping constitutes the physical basis for the coordinated control of cable force and alignment.

[0034] A finite element model of the cable-stayed bridge was established using Midas Civil finite element analysis software. Measuring points were set on the cross-section of the main beam of the bridge deck in the finite element model. The measuring points were fixed points of the cable stays closest to the bridge deck. In the completed bridge state, the three-dimensional coordinates of each measuring point were obtained using real-time dynamic positioning (GNSS-RTK) technology, and the measured vertical displacement of each measuring point was read, with the unit being mm. All cable stays were set as independent load conditions, and a unit cable force of 1 kN was applied to each cable individually. At this time, the vertical displacement of each measuring point was obtained.

[0035] Furthermore, intelligent sensors are used to record the temperature and load at each measuring point in real time under the completed bridge condition. The same conditions are applied in the finite element model of the cable-stayed bridge to obtain the design elevation of each measuring point in mm. The difference between the measured vertical displacement at each measuring point and the corresponding design elevation is recorded as the measured vertical displacement deviation at each measuring point.

[0036] Step S2: By analyzing the cumulative degree of vertical displacement at each measuring point when a unit cable force is applied to all cables, the cable force sensitivity of each measuring point is determined; by comparing the measured vertical displacement deviation of each measuring point with the preset displacement deviation threshold, the displacement deviation limit value of each measuring point is determined, and combined with the cable force sensitivity, the sensitivity weight of each measuring point is determined; based on the displacement deviation limit value and the sensitivity weight, the bridge alignment urgency of the cable-stayed bridge is determined.

[0037] To transform the maximum permissible discrete value from a static empirical parameter into an intelligent index that can dynamically influence the actual state of the bridge, this embodiment analyzes the cumulative vertical displacement of each measuring point when a unit cable force is applied to all cables to determine the cable force sensitivity of each measuring point, thereby accurately identifying the most vulnerable critical areas in the cable-stayed bridge structure to cable force adjustment. Furthermore, this embodiment compares the measured vertical displacement deviation of each measuring point with a preset displacement deviation threshold to determine the displacement deviation exceeding the limit value of each measuring point, thereby measuring the actual risk level of the current cable-stayed bridge alignment deviating from the design target. Further, the displacement deviation exceeding the limit value and cable force sensitivity are combined to obtain a sensitivity weight, ensuring that the cable force and alignment coordinated control strategy of the cable-stayed bridge can focus on unfavorable measuring points that are both sensitive and exceeding the limit, ultimately obtaining the bridge alignment urgency to achieve adaptive updating of the uniformity constraint threshold. This allows the coordinated control method to automatically and accurately adjust the control strategy according to the risk level of different structures. The specific process is as follows:

[0038] First, this embodiment determines the cable force sensitivity of each measuring point by analyzing the cumulative degree of vertical displacement at each measuring point when a unit cable force is applied to all cables. Specifically:

[0039] In this embodiment, the L1 norm of the vertical displacement of each measuring point when a unit cable force is applied to all cables is used as the cable force sensitivity of each measuring point. This is used to characterize the intrinsic sensitivity of the geometric alignment of the measuring point to changes in cable force. If the cable force sensitivity of the current measuring point is greater, it indicates that the current measuring point is at a lever position in the structure. Even a small change in cable force will trigger a significant displacement response at this point, indicating that the current measuring point is sensitive to cable force adjustments and that the linear deviation of the current measuring point must be given higher priority. Conversely, if the cable force sensitivity of the current measuring point is smaller, it indicates that the structural stiffness of the area where the measuring point is located is relatively large, and the response to cable force adjustments is relatively sluggish. Even if the cable force changes significantly, its geometric alignment remains relatively stable. This indicates that the location of the measuring point is not sensitive to cable force adjustments, and its alignment deviation has a low priority in the overall risk assessment, requiring no excessive control resources.

[0040] The method for calculating the L1 norm is a well-known technique, and its specific calculation process will not be elaborated here.

[0041] Furthermore, this embodiment determines the displacement deviation exceeding the limit for each measuring point by comparing the measured vertical displacement deviation at each measuring point with a preset displacement deviation threshold. Specifically:

[0042] In this embodiment, the ratio of the measured vertical displacement deviation of each measuring point to the preset displacement deviation threshold is used as the displacement deviation limit value for each measuring point, which characterizes the severity and urgency of the current linear deviation of the measuring point. If the displacement deviation limit value of the current measuring point is larger, it indicates that the measured displacement deviation of the current measuring point is closer to or even far exceeds the specification red line, indicating that the deviation between the current construction status and the design goal is very serious, and there are quality or safety hazards. Therefore, this high-risk signal will be amplified and transmitted to the subsequent scenario severity assessment to adopt a more stringent control strategy. Conversely, if the displacement deviation limit value of the current measuring point is smaller, it indicates that the measured displacement deviation of the measuring point is far within the specification allowable range, the current construction status matches the design goal well, the quality is under control, and the safety margin is sufficient. Therefore, this low-risk signal has a lower weight in the subsequent scenario severity assessment and will not trigger the system to adopt an overly strict control strategy, thereby allowing the optimization process to seek economical and efficient solutions more flexibly while ensuring safety.

[0043] It should be noted that the preset displacement deviation threshold is set manually, and the range of the preset displacement deviation threshold is usually 10~30mm. In this embodiment, the preset displacement deviation threshold is 20mm. In actual application, as other implementation methods, implementers can also set it according to specific circumstances. This embodiment does not impose any special restrictions.

[0044] Furthermore, in this embodiment, based on the displacement deviation exceeding the limit value of each measuring point and in combination with the cable force sensitivity, the sensitivity weight of each measuring point is determined, specifically as follows:

[0045] In this embodiment, the normalized product of the displacement deviation exceeding the limit value and the cable force sensitivity of each measuring point is used as the sensitivity weight of each measuring point. This weight is used to characterize the overall importance that the measuring point should be assigned when determining the overall cable force uniformity strategy. If the sensitivity weight of the current measuring point is larger, it indicates that the current measuring point is the point that needs the most priority for attention and control under the current working condition. This reflects that the alignment state of the current measuring point has a decisive impact on the overall structural safety and final control effect of the cable-stayed bridge. Therefore, when calculating the severity of the scenario, the current measuring point should be given a larger weight. Conversely, if the sensitivity weight of the current measuring point is smaller, it indicates that the measuring point is either not sensitive to structural response or the current deviation is not significant. It belongs to the secondary concern, reflecting that its alignment state has a limited impact on the overall structural safety and final control effect. Therefore, when calculating the severity of the scenario, the measuring point will be assigned a smaller weight, thereby avoiding interference from local secondary problems in the accurate judgment of the global risk level and ensuring that the control strategy can focus on the real key contradictions.

[0046] Furthermore, this embodiment determines the bridge alignment urgency of the cable-stayed bridge based on the displacement deviation exceeding the limit value and the sensitivity weight, specifically:

[0047] In this embodiment, the result of positively fusing the displacement deviation exceeding the limit values ​​of all measuring points on the finite element model of the cable-stayed bridge with the sensitive weight is used as the bridge alignment urgency of the cable-stayed bridge.

[0048] Preferably, the schematic diagram of the bridge alignment urgency extraction process provided in this embodiment is as follows: Figure 2 As shown.

[0049] It should be understood that positive fusion refers to combining two or more indicators through addition or multiplication to obtain a comprehensive indicator, thereby more comprehensively and accurately assessing a phenomenon or problem. This fusion method is not limited to simple arithmetic operations, but can also include more complex statistical models and analytical methods. Implementers can choose according to specific circumstances, and this embodiment does not impose any special restrictions.

[0050] Preferably, as one implementation method, in this embodiment, the result of multiplying the displacement deviation exceeding the limit value of each measuring point on the finite element model of the cable-stayed bridge with the sensitive weight is calculated, and the mean of the multiplication result of all measuring points is normalized as the bridge alignment tightness of the cable-stayed bridge. In actual application, as other implementation methods, implementers may also adopt other positive fusion methods according to specific circumstances. This embodiment does not impose any special restrictions.

[0051] Based on the bridge alignment urgency of cable-stayed bridges, it can be understood that the bridge alignment urgency is used to comprehensively characterize the overall urgency of the bridge's linear deviation from the design target. If the bridge alignment urgency is greater, it means that there are widespread or near-exceeding limits in the entire bridge, especially at those sensitive and critical measuring points, and strong corrective measures must be taken.

[0052] Conversely, if the bridge alignment is less urgent, it indicates that the overall bridge alignment is generally good, the measured deviations at each key measuring point are within a safe and controllable range, the current construction status is highly consistent with the design goals, and the overall structure is healthy with sufficient safety margin. Therefore, there is no need to take radical corrective measures, and the strict requirements for cable force uniformity can be appropriately relaxed to provide greater freedom for optimization solutions. This allows for seeking more economical and easier-to-implement cable force adjustment schemes while ensuring structural safety.

[0053] Thus, this embodiment constructs a sensitive weight that can quantify the comprehensive importance of key measuring points by integrating the cable force sensitivity and displacement deviation exceeding the limit value of the measuring points, and finally aggregates them into the bridge alignment urgency, ensuring that the subsequent control strategy can accurately focus on the key areas that are both sensitive and exceed the limit, laying a solid data foundation for the final adaptive update of the uniformity constraint threshold.

[0054] Step S3: Based on the measured vertical displacement deviation of all measuring points, the cable force adjustment of all cables in the finite element model of the cable-stayed bridge is solved by using a generalized inverse matrix to determine the comprehensive cable force adjustment scale of the cable-stayed bridge.

[0055] Furthermore, in this embodiment, the vertical displacement of each measuring point when a unit cable force is applied to all cables is used to form the cable force vector of each measuring point. The matrix composed of the cable force vectors of all measuring points is denoted as the displacement-cable force matrix. The displacement-cable force matrix is ​​used as the input of the generalized inverse matrix algorithm, and the output is the pseudo-inverse matrix of the displacement-cable force matrix.

[0056] The measured vertical displacement deviations of all measuring points are used as inputs to the pseudo-inverse matrix of the displacement-cable force matrix, and the output is the cable force adjustment amount of all cables in the finite element model of the cable-stayed bridge, denoted as the cable force adjustment amount.

[0057] The generalized inverse matrix algorithm is a well-known technique, and the specific solution process will not be described in detail here.

[0058] Furthermore, the average value of the cable force adjustment of all cables in the finite element model of the cable-stayed bridge is used as the comprehensive cable force adjustment scale of the cable-stayed bridge, which is used to adjust the setting of the allowable discrete value of the cable force adjustment.

[0059] Thus, the cable force adjustment amount obtained by solving the generalized inverse matrix in this embodiment represents a scheme to correct alignment deviations with minimal energy cost. This further quantifies the comprehensive cable force adjustment scale of the current correction demand intensity. Together with the urgency of bridge alignment, it provides a crucial physical benchmark for the subsequent generation of an initial uniformity constraint threshold that accurately matches the actual working conditions, ensuring the rationality of the control strategy in terms of dimensions and its feasibility in engineering.

[0060] Step S4: Based on the bridge alignment urgency and the comprehensive cable force adjustment scale, as well as the preset design cable force average value of all cables, determine the initial allowable discrete value of the cable-stayed bridge to optimize the constraints in the cable force and linear coordinated control process of the cable-stayed bridge.

[0061] To generate an initial uniformity upper limit, this embodiment combines scale parameters and scenario severity to construct a threshold that can adaptively scale with the urgency of the bridge alignment. Specifically, based on the bridge alignment urgency, the comprehensive cable force adjustment scale, and the average value of the preset design cable forces of all cables, the initial allowable discrete value of the cable-stayed bridge is determined to optimize the constraints in the cable force and linear coordinated control process of the cable-stayed bridge. The specific process is as follows:

[0062] As one implementation method, in this embodiment, the initial allowable discrete value of the cable-stayed bridge The expression is: In the formula, This indicates the overall cable force adjustment scale for a cable-stayed bridge; Indicates the urgency of the bridge alignment of a cable-stayed bridge; This represents the lower bound of discrete values, where, , where n represents the number of all cables in the finite element model of the cable-stayed bridge; Denotes the upper limit of discrete values, where, , This indicates the preset relative cable force deviation. represents the average value of the preset design cable force of all cables in the finite element model of the cable-stayed bridge; exp() represents the exponential function with the natural constant as the base; clamp[] represents the truncation function.

[0063] The calculation principle of the truncation function is a well-known technique and will not be elaborated further.

[0064] It should be noted that the preset relative cable force deviation value is set manually. In this embodiment, the preset relative cable force deviation value is 0.1. In actual application, as other implementation methods, implementers can also set it according to specific circumstances. This embodiment does not impose any special restrictions.

[0065] It should be noted that the method for obtaining the pre-designed cable force is manually set in the finite element model of the cable-stayed bridge.

[0066] Among them, the initial allowable dispersion value is used to characterize the initial cable force dispersion tolerance standard that satisfies both engineering feasibility and risk level.

[0067] Furthermore, due to the existence of measurement noise, model errors, and multi-objective coupling in actual practice, the allowable discrete values ​​in the uniformity constraints obtained in one go cannot guarantee the feasibility of optimization. Therefore, the Robbins-Monro algorithm is used to decrease the step size and update the allowable discrete values ​​with the observation standard deviation during the optimization process as feedback. This enables automatic relaxation when the constraints are too tight, gradual tightening when they are too loose, and retreat to the standard deviation of the unconstrained solution when the constraints are not feasible. This ensures that the iterative process of optimization is within the range of construction feasibility and standard safety, and finally converges to the optimal uniformity constraint control value that can reflect the real structural response and minimize the tensioning work.

[0068] The iterative optimization of the permissible discrete values ​​is performed as follows:

[0069] Step 1: Perform optimization and determine feasibility.

[0070] Input: The allowable discrete value for the current iteration, where the initial value of the allowable discrete value is the initial allowable discrete value;

[0071] Action: Call Sequential Quadratic Programming (SQP) to solve the following objective function, specifically:

[0072] objective function : In the formula, This represents the tension adjustment amount of the i-th cable; represents the number of all cables in the finite element model of the cable-stayed bridge; min() represents the minimum value function.

[0073] Constraints: (1) Linear constraint: The displacement deviation of each measuring point is less than or equal to 1;

[0074] (2) Cable force safety constraints: In the formula, , These are the preset lower limit and preset upper limit of cable force, respectively, both of which can be obtained from the design specifications for highway cable-stayed bridges. This represents the tension in the i-th cable. The current tension adjustment of the i-th cable.

[0075] (3) Homogeneity constraint: In the formula, This represents the standard deviation of the cable force adjustment for all cables in the finite element model of a cable-stayed bridge. This indicates that discrete values ​​are allowed.

[0076] like If all the above constraints are met, the optimization is feasible, proceed to Step 2;

[0077] like If any of the above constraints are not met, optimization is not feasible, proceed to Step 3;

[0078] Step 2:

[0079] Objective: When When feasible but potentially too large, the Robbins–Monro step-size update algorithm is used. Gradually moving towards a realistic and achievable minimum standard By approximating, we can find a better uniformity.

[0080] Updated formula: In the formula, , These represent the allowable discrete values ​​at the (j+1)th and jth iterations, respectively; This represents the standard deviation of the cable force adjustment of all cables in the finite element model of the cable-stayed bridge at the j-th iteration.

[0081] The purpose of this update and iteration is to make the step size automatically decrease with the number of iterations. The difference between the standard deviation of the current cable force adjustment and the allowable discrete value is used as a correction signal. That is, when the cable force adjustment is uneven in the early stage, the standard deviation is large, resulting in a larger step size. This is gradually superimposed on the allowable discrete value to achieve rapid correction with large steps in the early stage and gradual convergence with small steps in the later stage, so that the threshold approaches the lowest uniformity level that the real structure can achieve.

[0082] Step 3:

[0083] Objective: When If overly strict requirements lead to no solution, the requirements are automatically relaxed to ensure that the next iteration is at least theoretically feasible.

[0084] Updated formula: ,in, In the formula, This represents the machine tolerance at the j-th iteration; represents a preset value, which is 10e-9 in this embodiment to ensure that the next iteration has at least the theoretical minimum dispersion. max() represents the maximum value function.

[0085] Finally, when the difference between the allowable discrete values ​​in three consecutive iterations is less than Furthermore, when the linear constraint condition is always true, the iteration stops, and the final cable force adjustment and allowable discrete value are output.

[0086] Thus, this embodiment generates an initial permissible discrete value that matches the current risks and adjustment needs based on the urgency of bridge alignment and the comprehensive cable force adjustment scale, and sets reasonable engineering and specification boundaries for it. Furthermore, by introducing the Robbins–Monro algorithm with the standard deviation of the optimized cable force adjustment as feedback, adaptive iterative updates of the permissible discrete value are achieved. This ensures that when optimization is feasible, it can be gradually tightened to the optimal uniformity, and when it is not feasible, it can be automatically relaxed to ensure the robustness of the solution. This dual guarantee mechanism ultimately enables the collaborative control strategy to converge to an optimal solution that satisfies both alignment and safety specifications and minimizes the cable force adjustment. Under the premise of ensuring structural safety and quality, it effectively reduces construction costs and complexity, and improves the rationality and operability of the collaborative control of cable-stayed bridges and alignment.

[0087] Based on the same inventive concept as the above methods, this application also provides a cable-stayed bridge cable force and alignment coordinated control system based on finite element analysis, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of any one of the above-described cable-stayed bridge cable force and alignment coordinated control methods based on finite element analysis.

[0088] It should be noted that the order of the embodiments described above is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. Furthermore, specific embodiments of this specification have been described above. Additionally, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired results. In some implementations, multitasking and parallel processing are possible or may be advantageous.

[0089] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0090] The above description is only a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the principles of this application should be included within the protection scope of this application.

Claims

1. A method for coordinated control of cable force and alignment of cable-stayed bridges based on finite element analysis, characterized in that, The method includes the following steps: The measured vertical displacement deviation of each preset measuring point in the finite element model of the cable-stayed bridge is obtained, and the vertical displacement of each measuring point is obtained when a unit cable force is applied to each cable. By analyzing the cumulative vertical displacement of each measuring point when a unit cable force is applied to all cables, the cable force sensitivity of each measuring point is determined; by comparing the measured vertical displacement deviation of each measuring point with the preset displacement deviation threshold, the displacement deviation limit value of each measuring point is determined, and combined with the cable force sensitivity, the sensitivity weight of each measuring point is determined; based on the displacement deviation limit value and the sensitivity weight, the bridge alignment urgency of the cable-stayed bridge is determined. Based on the measured vertical displacement deviations at all measuring points, the cable force adjustment of all cables in the finite element model of the cable-stayed bridge is solved using a generalized inverse matrix to determine the comprehensive cable force adjustment scale of the cable-stayed bridge. Based on the bridge alignment urgency and the comprehensive cable force adjustment scale, as well as the average value of the preset design cable force of all cables, the initial allowable discrete value of the cable-stayed bridge is determined in order to optimize the constraints in the cable force and linear coordinated control process of the cable-stayed bridge. The cable force sensitivity of each measuring point is the L1 norm of the vertical displacement of each measuring point when a unit cable force is applied to all cables; The displacement deviation exceeding the limit value of each measuring point is the ratio of the measured vertical displacement deviation of each measuring point to the preset displacement deviation threshold. The sensitivity weight of each measuring point is the normalized result of the product of the displacement deviation exceeding the limit value and the cable force sensitivity of each measuring point. The bridge alignment tightness of the cable-stayed bridge is the result of positive fusion of the displacement deviation exceeding the limit value of all measuring points on the finite element model of the cable-stayed bridge and the sensitive weight; The expression for the initial allowable discrete value of the cable-stayed bridge is: In the formula, This represents the initial allowable discrete value for a cable-stayed bridge; This indicates the overall cable force adjustment scale for a cable-stayed bridge; Indicates the urgency of the bridge alignment of a cable-stayed bridge; This represents the lower bound of discrete values, where, , where n represents the number of all cables in the finite element model of the cable-stayed bridge; Denotes the upper limit of discrete values, where, , This indicates the preset relative cable force deviation. represents the average value of the preset design cable force of all cables in the finite element model of the cable-stayed bridge; exp() represents the exponential function with the natural constant as the base; clamp[] represents the truncation function.

2. The method for coordinated control of cable force and alignment of cable-stayed bridges based on finite element analysis as described in claim 1, characterized in that, The method of using a generalized inverse matrix to solve for the cable force adjustment of all cables in the finite element model of a cable-stayed bridge includes: The vertical displacement of each measuring point when a unit cable force is applied to all cables is used to form the cable force vector of each measuring point. The matrix composed of the cable force vectors of all measuring points is denoted as the displacement-cable force matrix. The displacement-cable force matrix is ​​used as the input of the generalized inverse matrix algorithm, and the output is the pseudo-inverse matrix of the displacement-cable force matrix. The measured vertical displacement deviations of all measuring points are used as inputs to the pseudo-inverse matrix of the displacement-cable force matrix, and the output is the cable force adjustment of all cables in the finite element model of the cable-stayed bridge.

3. The method for coordinated control of cable force and alignment of cable-stayed bridges based on finite element analysis as described in claim 1, characterized in that, The overall cable force adjustment scale of the cable-stayed bridge is the average of the cable force adjustment amounts of all cables in the finite element model of the cable-stayed bridge.

4. The method for coordinated control of cable force and alignment of cable-stayed bridges based on finite element analysis as described in claim 1, characterized in that, The constraints in the optimized cable force and linear coordinated control process of the cable-stayed bridge include: Based on the initial allowable discrete values, the Robbins–Monro algorithm is used to iteratively optimize the allowable discrete values ​​within the uniformity constraint during the cable force and linear coordinated control process of the cable-stayed bridge.

5. A cable-stayed bridge cable force and alignment coordinated control system based on finite element analysis, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the cable force and alignment coordination control method for cable-stayed bridges based on finite element analysis as described in any one of claims 1-4.

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