Method for evaluating construction scheme of main arch ring of stiff skeleton arch bridge based on comprehensive stability coefficient

Abstract

The invention discloses a stiff skeleton arch bridge main arch ring construction scheme evaluation method based on a comprehensive stability coefficient, and relates to the technical field of bridge construction, and the method comprises the steps: obtaining a non-dominated solution set of a construction scheme based on a multi-objective optimization algorithm; respectively determining evaluation indexes from the aspects of structural stability, objective function stability, solution robustness, dynamic adaptability and life cycle cost, and constructing a comprehensive stability coefficient evaluation system; performing standardization processing on each evaluation index, and determining the comprehensive weight of each evaluation index by combining subjective weighting and objective weighting methods; performing weighted summation on the comprehensive weight and the standardized score of each evaluation index to obtain a comprehensive stability coefficient; and selecting the non-dominated solution with the highest comprehensive stability coefficient as a final construction scheme, and performing dynamic adjustment according to a construction feedback result. According to the method, a perfect evaluation index system can be established, the optimal construction scheme is selected, and the construction safety and the structural stability of the large-span stiff skeleton concrete arch bridge are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge construction, and more particularly to a method for evaluating a construction plan of a main arch ring of a rigid skeleton arch bridge based on a comprehensive stability coefficient. Background Art

[0002] Long-span bridges are defined as those with a single span greater than 40 meters and multiple spans exceeding 100 meters. Their core characteristics are their large spans, complex structures, and high technical requirements. Through technological innovation, they have continuously pushed the limits of span, becoming a hallmark of modern transportation engineering. Among them, the rigid-frame concrete arch bridge is an advanced bridge technology that combines steel structure with concrete casting. Its core technology utilizes steel trusses as the skeleton support, with the arch rings cast in rings and encased in concrete. Thanks to technological innovation, these bridges have achieved breakthroughs in span, safety, and cost-effectiveness, becoming a representative achievement in Chinese bridge engineering and providing an important reference for the construction of long-span arch bridges worldwide.

[0003] The construction of the main arch ring of a rigid-frame arch bridge is a complex and technically demanding project. Its construction plan may face the following challenges: During the fabrication, transportation, and installation process, the rigid frame may deform due to factors such as welding stress, hoisting stress, and construction loads, resulting in the arch rib linear shape not meeting the design requirements and affecting the load-bearing performance of the main arch ring. Concrete shrinkage and creep can cause deformation and internal force redistribution in the main arch ring. If not properly controlled, this can lead to cracks in the arch ring, affecting the safety and service life of the structure. An unreasonable scheme for outsourcing concrete in rings and segments can lead to excessive transient tensile stress in the main arch ring during construction, causing concrete cracking, and excessive transient compressive stress, leading to concrete collapse. Large structural deformation can affect the main arch linear shape and thus the load-bearing performance, leading to partial or even complete structural instability and increasing construction risks. Therefore, a comprehensive evaluation of construction plans, providing a scientific basis for their selection, is of great engineering significance and application value.

[0004] In existing technologies, experts in related fields are typically assembled to conduct comprehensive assessments of construction plans based on their expertise and experience, including feasibility, safety, reliability, and construction difficulty. However, decision-makers' experience is often based on past similar projects, and each project varies in geological conditions, surrounding environment, and technical requirements. Experience alone may not fully account for all key factors of the current project, resulting in an incomplete and inaccurate evaluation. Furthermore, as the span of rigid-frame arch bridges continues to grow, the relevance of existing experience decreases. Different decision-makers lack objective, unified standards, which can easily lead to inconsistent and unfair evaluation results. Construction is a dynamic process, subject to various unexpected situations and changes. Relying on experience and subjective judgment may not be able to adapt to these changes in a timely manner, resulting in inaccurate and inadequate adjustments and optimizations to the plan.

[0005] Therefore, how to avoid the shortcomings of traditional methods that rely on the experience or subjective judgment of decision makers, establish a complete evaluation index system, select the optimal construction plan, and improve the construction safety and structural stability of large-span rigid skeleton concrete arch bridges is a technical problem that technical personnel in this field urgently need to solve. Summary of the Invention

[0006] In view of this, the present invention provides a method for evaluating the construction plan of the main arch ring of a rigid skeleton arch bridge based on a comprehensive stability coefficient, which solves the problems existing in the background technology.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A method for evaluating construction plans for a main arch ring of a rigid skeleton arch bridge based on a comprehensive stability coefficient comprises the following steps:

[0009] Based on the multi-objective optimization algorithm, the non-dominated solution set of the construction plan is obtained;

[0010] Determine the evaluation indicators from the perspectives of structural stability, objective function stability, solution robustness, dynamic adaptability, and life cycle cost, and construct a comprehensive stability coefficient evaluation system;

[0011] Standardize each evaluation indicator and determine the comprehensive weight of each evaluation indicator by combining subjective and objective weighting methods;

[0012] The comprehensive weight and standardized score of each evaluation indicator are weighted and summed to obtain the comprehensive stability coefficient;

[0013] The comprehensive stability coefficients of different construction schemes are sorted from large to small according to their values, and the non-dominated solution with the highest comprehensive stability coefficient is selected as the final construction scheme, and dynamically adjusted according to the construction feedback results.

[0014] Optional multi-objective optimization algorithms include: non-dominated sorting genetic algorithm II, decomposition-based multi-objective evolutionary algorithm, and multi-objective particle swarm optimization algorithm.

[0015] Optionally, obtain the non-dominated solution set of the construction plan, specifically:

[0016] Select the non-dominated sorting genetic algorithm II as the multi-objective optimization algorithm and initialize the parameters;

[0017] The non-dominated sorting genetic algorithm II is used to iteratively solve the construction optimization problem of the main arch ring of the rigid skeleton arch bridge. The solution sets obtained in each iterative solution are merged into one set as the optimal solution set for the construction optimization problem of the main arch ring of the rigid skeleton arch bridge.

[0018] The optimal solution set is sorted by non-dominated sorting, the dominated solutions are filtered out, and the non-dominated solution set is obtained.

[0019] Optionally, the evaluation index can be determined from the perspective of structural stability. Specifically, considering the risk of instability of rigid skeleton arch bridges during the construction process of external concrete, the structural stability coefficient λ is introduced. c and the stability coefficient variance σ1 2 To assess the overall stability of the structure during construction;

[0020] Structural stability coefficient λ c Defined as:

[0021]

[0022] Stability coefficient variance σ1 2 Defined as:

[0023]

[0024] Based on the structural stability coefficient λ c and the stability coefficient variance σ1 2 , construct the structural stability index I1:

[0025]

[0026] Where: min is the minimum value of the structural stability coefficient during the entire construction process, λ(t) is the structural stability coefficient at time t, Δt is the construction time, T is the total construction time, and n is the number of construction options. is the average structural stability coefficient, σ 1max is the maximum variance of all solutions; α1, α2, w1, w2 are weight coefficients, and α1+α2=1, w1+w2=1.

[0027] Optionally, determine the evaluation index from the perspective of objective function stability, specifically:

[0028] Divide different scenarios based on key variables in historical data and associate the characteristics of each scenario with the objective function of the non-dominated solution;

[0029] For each non-dominated solution, multiple sets of parameter perturbations are generated based on the historical data distribution, the target values under different scenarios are simulated, and multiple objective function values of the non-dominated solution under each scenario are recorded to construct the objective function stability index I2.

[0030] Optionally, determine the evaluation index from the perspective of the robustness of the solution, specifically:

[0031] Identify the key decision variables that affect the objective function and obtain the benchmark objective value f0 of the non-dominated solution;

[0032] Apply ±10% random perturbation to each parameter, generate the perturbed parameter combination, and obtain the objective function value f of the pth perturbation parameter combination (p) , construct the robustness index I3 of the solution.

[0033] Optionally, determine the evaluation indicators from the perspective of dynamic adaptability, specifically:

[0034] Based on historical data and risk database, define multiple emergency scenarios and provide parameterized descriptions for each scenario;

[0035] The construction plan is input into the discrete event simulation model, and emergency scenarios are randomly injected to trigger the preset adaptive strategy. The construction process is iteratively simulated and the changes in the objective function value are recorded.

[0036] The response time, cost increment and target deviation of each simulation are collected to calculate the dynamic adaptability index I4.

[0037] Optionally, confirm the comprehensive weight of each evaluation indicator, specifically:

[0038] Using the analytic hierarchy process, experts conduct pairwise comparisons of the importance of indicators, construct a judgment matrix, and calculate the subjective weight W1;

[0039] Through the entropy weight method, the degree of data dispersion is obtained and the objective weight W2 is calculated;

[0040] Based on the subjective weight W1 and the objective weight W2, the comprehensive weight W of each indicator is obtained:

[0041] W=δW1+(1-δ)W2

[0042] Where: δ is the balance coefficient.

[0043] Optionally, the comprehensive stability coefficient is calculated as:

[0044]

[0045] Where: W k is the comprehensive weight of the kth evaluation index, S k is the standardized score of the kth evaluation indicator.

[0046] It can be seen from the above technical solution that, compared with the prior art, the present invention discloses a method for evaluating the construction scheme of the main arch ring of a rigid skeleton arch bridge based on the comprehensive stability coefficient, which has the following beneficial effects:

[0047] The present invention determines evaluation indicators from multiple dimensions such as structural stability, objective function stability, solution robustness, dynamic adaptability, and life cycle cost, and constructs a comprehensive stability coefficient evaluation system. This can comprehensively consider construction plans and avoid the shortcomings of traditional methods that rely on the decision maker's experience or subjective judgment and only focus on one aspect of factors. In this way, the optimal construction plan can be selected, the accuracy of plan screening can be improved, the construction safety and structural stability of large-span rigid skeleton concrete arch bridges can be improved, the economic benefits of the project can be increased, problems arising during the construction process can be discovered and resolved in a timely manner, and the overall controllability of the project can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0049] Figure 1 The present invention provides a flowchart of a method for evaluating a construction plan for a main arch ring of a rigid skeleton arch bridge based on a comprehensive stability coefficient. DETAILED DESCRIPTION

[0050] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0051] In order to select a final solution from a large number of non-dominated solutions of the construction plan to guide engineering practice, while avoiding the uncertainty and arbitrariness caused by relying solely on the subjective judgment of the decision maker, the embodiment of the present invention discloses a construction plan evaluation method for the main arch ring of a rigid skeleton arch bridge based on the comprehensive stability coefficient, such as Figure 1 As shown, the following steps are included:

[0052] Based on the multi-objective optimization algorithm, the non-dominated solution set of the construction plan is obtained;

[0053] Determine evaluation indicators from the perspectives of structural stability, objective function stability, solution robustness, dynamic adaptability, and life cycle cost, and construct a comprehensive stability coefficient evaluation system to avoid the one-sidedness of a single indicator;

[0054] Standardize each evaluation indicator, combine subjective and objective weighting methods to determine the comprehensive weight of each evaluation indicator, and improve the scientific nature of decision-making;

[0055] The comprehensive weight and standardized score of each evaluation indicator are weighted and summed to obtain the comprehensive stability coefficient;

[0056] The comprehensive stability coefficients of different construction schemes are sorted from large to small according to their values, and the non-dominated solution with the highest comprehensive stability coefficient is selected as the final construction scheme (if multiple solutions are screened out, a second screening can be performed based on the actual project needs), and dynamic adjustments are made based on the construction feedback results to significantly reduce the randomness of subjective judgment.

[0057] Reference Figure 1 According to the process shown in the figure, after obtaining the non-dominated solution set of the construction scheme, this embodiment first determines that the stability of the solution can be evaluated through the structural stability index, the objective function stability index, the solution robustness index, the dynamic adaptability index and the life cycle cost index; the data is standardized to facilitate the subsequent comparison and integration of various indicators; the weight of each indicator is determined, and the advantages and disadvantages of each construction scheme are quantified based on the comprehensive stability coefficient, thereby improving the accuracy and efficiency of scheme screening.

[0058] Furthermore, multi-objective optimization algorithms include: non-dominated sorting genetic algorithm II, decomposition-based multi-objective evolutionary algorithm, and multi-objective particle swarm optimization algorithm. Among them, non-dominated sorting genetic algorithm II (NSGA-II) is a widely used multi-objective optimization algorithm that combines fast non-dominated sorting (stratifying individuals in a population according to non-domination relationships, with individuals in the first layer being non-dominated individuals in the entire population, not dominated by any other individuals) with crowding distance calculation (measuring the density of individuals around each individual) to improve the algorithm's convergence speed and diversity. Decomposition-based multi-objective evolutionary algorithm (MOEA / D) decomposes multi-objective optimization problems into multiple single-objective optimization sub-problems and simultaneously optimizes these sub-problems through evolutionary algorithms. Multi-objective particle swarm optimization algorithm (MOPSO) is a multi-objective optimization method based on particle swarm optimization algorithm that finds the optimal solution by simulating the group behavior of flocks of birds or schools of fish.

[0059] Furthermore, the non-dominated solution set of the construction plan is obtained, specifically:

[0060] A non-dominated sorting genetic algorithm II was selected as the multi-objective optimization algorithm. Parameters such as population size, maximum number of iterations, crossover probability, and mutation probability were initialized. An initial population was randomly generated, and each individual in the population represented a construction plan for the main arch ring of a rigid skeleton arch bridge, represented by a set of decision variables.

[0061] The non-dominated sorting genetic algorithm II is used to iteratively solve the construction optimization problem of the main arch ring of the rigid skeleton arch bridge. The solution sets obtained in each iterative solution are merged into one set as the optimal solution set for the construction optimization problem of the main arch ring of the rigid skeleton arch bridge.

[0062] The optimal solution set is sorted by non-dominated sorting, the dominated solutions are filtered out, and the non-dominated solution set is obtained.

[0063] Furthermore, in order to ensure structural safety, this embodiment determines the evaluation index from the perspective of structural stability. Specifically, considering the risk of instability of the rigid skeleton arch bridge during the construction process of the outer concrete, the structural stability coefficient λ is introduced. c and the stability coefficient variance σ1 2 To assess the overall stability of the structure during construction;

[0064] Structural stability coefficient λ c Defined as:

[0065]

[0066] Stability coefficient variance σ1 2 Defined as:

[0067]

[0068] Based on the structural stability coefficient λ c and the stability coefficient variance σ1 2 , construct the structural stability index I1:

[0069]

[0070] Where: min is the minimum value of the structural stability coefficient during the entire construction process, λ(t) is the structural stability coefficient at time t, Δt is the construction time, T is the total construction time, and n is the number of construction options. is the average structural stability coefficient, σ 1max is the maximum variance of all solutions; α1, α2, w1, w2 are weight coefficients, and α1+α2=1, w1+w2=1.

[0071] Based on the above steps, this embodiment takes structural stability as an important evaluation indicator, which can ensure that the selected construction plan fully considers the mechanical properties and stability of the arch ring structure during the construction process. During the construction phase, it effectively reduces the risk of structural instability, reduces the possibility of safety accidents, and ensures the safety of construction workers and the smooth progress of the project.

[0072] Furthermore, in order to enhance the stability of the solution, this embodiment determines the evaluation index from the perspective of objective function stability, specifically:

[0073] Divide different scenarios based on key variables in historical data (such as weather, material prices, equipment failures, etc.) and associate the characteristics of each scenario with the objective function of the non-dominated solution;

[0074] For each non-dominated solution, multiple sets of parameter perturbations are generated based on the historical data distribution, the target values under different scenarios are simulated, and multiple objective function values of the non-dominated solution under each scenario are recorded;

[0075] Construct the objective function stability index I2:

[0076]

[0077] Where: σ2 is the standard deviation of the target f in a certain scenario, N is the number of simulations, f (i) The function value of the target f simulated i times, μ f is the mean of the target f, M is the total number of scenarios, w j is the probability of occurrence of scenario j.

[0078] Based on the above steps, this embodiment introduces an objective function stability index, which quantifies the volatility of the solution through standard deviation to replace manual experience judgment; it gives priority to solutions with small fluctuations in the objective function to ensure the stable execution of the construction plan in a changing environment, and reduces engineering risks by eliminating solutions with high fluctuations.

[0079] Furthermore, to enhance the stability of the solution, this embodiment also considers determining evaluation indicators from the perspective of solution robustness, specifically:

[0080] Identify the key decision variables that affect the objective function and obtain the benchmark objective value f0 of the non-dominated solution;

[0081] Apply ±10% random perturbation to each parameter (or set the perturbation amplitude according to the historical data distribution), generate the perturbed parameter combination, and obtain the objective function value f of the pth perturbation parameter combination (p) ;

[0082] Construct the robustness index I3 of the solution:

[0083]

[0084] Where: Δ (p) is the change rate of a single disturbance, and P is the number of disturbances.

[0085] Based on the above steps, this embodiment introduces a robustness indicator for the solution, directly comparing the stability of different solutions through the mean value to quantify the anti-interference ability; preferentially selects solutions with smaller I3 to reduce the risk of project implementation; adjusts the disturbance model according to actual construction data to improve the adaptability of the method, and ultimately achieves a balance between theoretical optimality and engineering reliability.

[0086] In summary, this embodiment introduces the objective function stability index (the degree of fluctuation of each objective function under different scenarios) and the solution robustness index (the adaptability of the solution under parameter perturbations), so that the construction plan can still maintain relatively stable performance when facing various uncertainties and interferences. The construction plan can better cope with unexpected situations during the construction process and ensure that the quality of the project is not greatly affected.

[0087] Furthermore, in order to adapt to dynamic changes, this embodiment considers determining evaluation indicators from the perspective of dynamic adaptability, specifically:

[0088] Based on historical data and risk databases (such as geological disaster probability and supply chain disruptions), we define multiple emergency scenarios (such as heavy rain, earthquakes, extreme temperatures, delayed material delivery, and equipment failures) and provide parameterized descriptions for each scenario.

[0089] The construction plan is input into the discrete event simulation model, and sudden scenarios are randomly injected to trigger the preset adaptive strategies (such as resource reallocation, process substitution, schedule compression, etc.). The construction process is iteratively simulated and the changes in the objective function value are recorded.

[0090] Collect the response time (the time from the occurrence of an event to the restoration of stability), cost increment (additional resource investment), and target deviation (difference from the original plan) of each simulation to calculate the dynamic adaptability index I4:

[0091]

[0092] Where: R ο is the response success rate, r is the number of simulations in which the target deviation does not exceed the preset threshold, and N is the total number of simulations; T ο is the average recovery time, t i is the time from the occurrence of the event to the restoration of stability in the i-th simulation; E ο is the adaptive cost efficiency (the larger the value, the lower the cost of achieving the target recovery), f0 is the benchmark target value, f is the actual target value, ΔE is the cost increment; T max is the maximum allowed recovery time, γ1, γ2, and γ3 are weight parameters, and γ1+γ2+γ3=1.

[0093] Based on the above steps, this embodiment sets a dynamic adaptability index. By quantifying the resilience of the construction plan under sudden disturbances, it effectively makes up for the shortcomings of the traditional static optimization model, enabling the construction plan to better cope with various changes in the construction process. The selected construction plan has greater flexibility and adaptability, and can adjust the construction strategy in time to ensure that the project can proceed smoothly under different circumstances.

[0094] Furthermore, in order to reduce life cycle costs, this embodiment considers determining evaluation indicators from the perspective of life cycle costs, specifically:

[0095]

[0096] Where r is the discount rate and T is the design life cycle.

[0097] Based on the above steps, this embodiment incorporates life cycle costs into the evaluation system, which helps to comprehensively consider the entire process costs of engineering construction, operation and maintenance when selecting a construction plan, avoiding focusing only on short-term construction costs while ignoring later operation and maintenance costs, thereby achieving cost optimization throughout the entire life cycle and improving the economic benefits of the project.

[0098] Furthermore, the comprehensive weight of each evaluation indicator is determined as follows:

[0099] Using the analytic hierarchy process (AHP), experts compared the importance of indicators in pairs, constructed a judgment matrix, and calculated the subjective weight W1. Specifically, the values were assigned according to the 1-9 scale (1-equally important, 3-slightly important, 5-obviously important, 7-strongly important, 9-extremely important). For n indicators, an n*n judgment matrix was constructed.

[0100] Through the entropy weight method, the degree of data dispersion is obtained and the objective weight W2 is calculated;

[0101] Based on the subjective weight W1 and the objective weight W2, the comprehensive weight W of each indicator is obtained:

[0102] W=δW1+(1-δ)W2

[0103] Where: δ is the balance coefficient.

[0104] Based on the above steps, experts can make subjective judgments and assign values to the importance of each evaluation indicator based on their in-depth understanding of the construction of the main arch ring of a rigid skeleton arch bridge, taking into account some factors that are difficult to directly reflect through data, so that the weight distribution is more in line with the actual project situation and professional cognition; the objective weighting method determines the weights based on the characteristics and laws of the data itself, which can objectively reflect the degree of variation of each indicator at the data level and the degree of influence on the results, avoid interference from human factors, and make the weight distribution more objective and scientific. Therefore, this embodiment can better meet the complex needs of actual decision-making, provide a more reasonable basis for the selection of construction plans, and help construction units, design units, supervision units, etc. reach a consensus on the selection of construction plans, and promote the smooth progress of the project.

[0105] Furthermore, the calculation formula of the comprehensive stability coefficient is:

[0106]

[0107] Where: W k is the comprehensive weight of the kth evaluation index, Sk is the standardized score of the kth evaluation indicator.

[0108] In addition, after the construction plan is selected, this embodiment can also dynamically adjust the construction plan based on the construction feedback results, so that the construction plan always matches the actual construction situation, which helps to promptly discover and solve problems that arise during the construction process, ensure the quality and progress of the project, and improve the overall controllability of the project.

[0109] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0110] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for evaluating the construction scheme of the main arch ring of a rigid skeleton arch bridge based on a comprehensive stability coefficient, characterized in that: The following steps are involved: Based on the multi-objective optimization algorithm, the non-dominated solution set of the construction plan is obtained; Determine the evaluation indicators from the perspectives of structural stability, objective function stability, solution robustness, dynamic adaptability, and life cycle cost, and construct a comprehensive stability coefficient evaluation system; Standardize each evaluation indicator and determine the comprehensive weight of each evaluation indicator by combining subjective and objective weighting methods; The comprehensive weight and standardized score of each evaluation indicator are weighted and summed to obtain the comprehensive stability coefficient; The comprehensive stability coefficients of different construction schemes are sorted from large to small according to their values, and the non-dominated solution with the highest comprehensive stability coefficient is selected as the final construction scheme, and dynamically adjusted according to the construction feedback results.

2. The method for evaluating construction plans of main arch rings of rigid skeleton arch bridges based on comprehensive stability coefficient according to claim 1, characterized in that: Multi-objective optimization algorithms include: non-dominated sorting genetic algorithm II, decomposition-based multi-objective evolutionary algorithm, and multi-objective particle swarm optimization algorithm.

3. The method for evaluating construction plans of main arch rings of rigid skeleton arch bridges based on comprehensive stability coefficient according to claim 2, characterized in that: Obtain the non-dominated solution set of the construction plan, specifically: Select the non-dominated sorting genetic algorithm II as the multi-objective optimization algorithm and initialize the parameters; The non-dominated sorting genetic algorithm II is used to iteratively solve the construction optimization problem of the main arch ring of the rigid skeleton arch bridge. The solution sets obtained in each iterative solution are merged into one set as the optimal solution set for the construction optimization problem of the main arch ring of the rigid skeleton arch bridge. The optimal solution set is sorted by non-dominated sorting, the dominated solutions are filtered out, and the non-dominated solution set is obtained.

4. The method for evaluating construction plans of main arch rings of rigid skeleton arch bridges based on comprehensive stability coefficient according to claim 1, characterized in that: The evaluation index is determined from the perspective of structural stability. Specifically, considering the risk of instability of the rigid skeleton arch bridge during the construction process of the outer concrete, the structural stability coefficient λ is introduced. c and the stability coefficient variance σ1 2 To assess the overall stability of the structure during construction; Structural stability coefficient λ c Defined as: Stability coefficient variance σ1 2 Defined as: Based on the structural stability coefficient λ c and the stability coefficient variance σ1 2 , construct the structural stability index I1: Where: min is the minimum value of the structural stability coefficient during the entire construction process, λ(t) is the structural stability coefficient at time t, Δt is the construction time, T is the total construction time, and n is the number of construction options. is the average structural stability coefficient, σ 1max is the maximum variance of all solutions; α1, α2, w1, w2 are weight coefficients, and α1+α2=1, w1+w2=1.

5. The method for evaluating construction plans of main arch rings of rigid skeleton arch bridges based on comprehensive stability coefficient according to claim 1, characterized in that: Determine the evaluation indicators from the perspective of objective function stability, specifically: Divide different scenarios based on key variables in historical data and associate the characteristics of each scenario with the objective function of the non-dominated solution; For each non-dominated solution, multiple sets of parameter perturbations are generated based on the historical data distribution, the target values under different scenarios are simulated, and multiple objective function values of the non-dominated solution under each scenario are recorded to construct the objective function stability index I2.

6. The method for evaluating construction plans of main arch rings of rigid skeleton arch bridges based on comprehensive stability coefficient according to claim 1, characterized in that: The evaluation indicators are determined from the perspective of the robustness of the solution, specifically: Identify the key decision variables that affect the objective function and obtain the benchmark objective value f0 of the non-dominated solution; Apply ±10% random perturbation to each parameter, generate the perturbed parameter combination, and obtain the objective function value f of the pth perturbation parameter combination (p) , construct the robustness index I3 of the solution.

7. The method for evaluating construction plans of main arch rings of rigid skeleton arch bridges based on comprehensive stability coefficient according to claim 1, characterized in that: Determine the evaluation indicators from the perspective of dynamic adaptability, specifically: Based on historical data and risk database, define multiple emergency scenarios and provide parameterized descriptions for each scenario; The construction plan is input into the discrete event simulation model, and emergency scenarios are randomly injected to trigger the preset adaptive strategy. The construction process is iteratively simulated and the changes in the objective function value are recorded. The response time, cost increment and target deviation of each simulation are collected to calculate the dynamic adaptability index I4.

8. The method for evaluating construction plans of main arch rings of rigid skeleton arch bridges based on comprehensive stability coefficient according to claim 1, characterized in that: Confirm the comprehensive weight of each evaluation indicator, specifically: Using the analytic hierarchy process, experts conduct pairwise comparisons of the importance of indicators, construct a judgment matrix, and calculate the subjective weight W1; Through the entropy weight method, the degree of data dispersion is obtained and the objective weight W2 is calculated; Based on the subjective weight W1 and the objective weight W2, the comprehensive weight W of each indicator is obtained: W=δW1+(1-δ)W2 Where: δ is the balance coefficient.

9. The method for evaluating construction plans of main arch rings of rigid skeleton arch bridges based on comprehensive stability coefficient according to claim 1, characterized in that: The calculation formula of the comprehensive stability coefficient is: Where: W k is the comprehensive weight of the kth evaluation index, S k is the standardized score of the kth evaluation indicator.

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