Large-span arch bridge reasonable arch axis design method based on hybrid algorithm and dynamic load

Abstract

According to the method for designing the reasonable arch axis of the large-span arch bridge based on the hybrid calculation algorithm and the self-adaptive load distribution, an analytic equation method, a curve fitting method and an intelligent optimization algorithm are combined, and by selecting the initial arch axis, introducing a dynamic load distribution model and applying a genetic algorithm and a particle swarm optimization algorithm, the reasonable arch axis of the large-span arch bridge is designed. Global and local optimization is carried out, and the optimal shape and load distribution of the arch axis are ensured. And finally outputting design parameters, such as a control point, a bending moment, thrust and the like. According to the method, the design precision, flexibility and safety can be effectively improved, the material utilization rate is optimized, the cost is reduced, and the method is particularly suitable for design of large-span bridges and has high practical value.

Description

Technical Field

[0001] The present invention relates to the field of bridge engineering design, and in particular to a method for designing a reasonable arch axis of a long-span arch bridge based on a hybrid algorithm and dynamic loads. Background Art

[0002] Arch bridges are widely used in the design and construction of long-span bridges due to their unique stress-bearing characteristics and excellent load-bearing performance. The proper design of the arch axis is crucial to the stress state, structural stability, and material utilization of arch bridges, and has long been a hot topic and a difficult topic in arch bridge design research.

[0003] Currently, methods for calculating the ideal arch axis of arch bridges are primarily divided into analytical equations and curve fitting. The analytical equation method solves for the ideal arch axis by establishing the arch bridge's load equations and analyzing its mechanical behavior under dead and live loads. Its core approach is to determine the shape of the main arch axis by studying the changes in the dead load pressure line. Commonly used methods include the minimum bending moment method and the limit analysis method. However, this method presents numerous challenges in the design of long-span arch bridges, including computational complexity, excessive local bending moments, and incompatibility with dynamic loads.

[0004] The curve fitting method selects an appropriate curve type (such as a catenary, parabola, or spline) and fits control points to obtain a reasonable arch axis. The calculation process is relatively simple and efficient. However, this method also has problems such as insufficient fitting accuracy, unscientific control point selection, and failure to consider dynamic load changes.

[0005] While existing technologies have achieved some success, significant shortcomings remain in the design of long-span arch bridges, particularly in handling complex loads and optimizing design accuracy. Existing methods suffer from insufficient accuracy, low computational efficiency, and a lack of dynamic adaptability when addressing arch axis problems under complex loads. Consequently, a new design approach is urgently needed that combines modern computer technology with dynamic load response to optimize arch axis design and improve the structural performance, safety, and cost-effectiveness of long-span arch bridges. Summary of the Invention

[0006] To address the aforementioned challenges of the existing technology, the present invention provides a method for designing the optimal arch axis for long-span arch bridges based on a hybrid algorithm and dynamic loads. By combining the advantages of analytical equations and curve fitting, the method incorporates dynamic load distribution and an intelligent optimization algorithm to achieve more accurate, rapid, and flexible optimal arch axis design for long-span arch bridges. This method effectively improves design accuracy and ensures structural safety, stability, and cost-effectiveness in the design of complex-load, long-span bridges.

[0007] In order to achieve the above object, the specific scheme of the present invention is as follows:

[0008] The reasonable arch axis design method for long-span arch bridges based on a hybrid algorithm and dynamic loads includes the following steps:

[0009] Step 1: Select the initial arch axis type: Based on the span and load type of the bridge, select a catenary, parabola, or spline curve as the initial arch axis type, determine the initial positions of the control points, and generate a preliminary arch axis design plan;

[0010] Step 2, optimization using analytical equation method: Based on the preliminary arch axis design scheme generated in step (1), the dead load action mode of the arch bridge is calculated using analytical equation method, including the stress analysis, bending moment calculation and horizontal thrust calculation of the main arch. The control point position and arch axis shape are adjusted according to the calculation results to generate the optimized arch axis design scheme;

[0011] Step 3: Introduce the dynamic load distribution model for adaptive adjustment: Based on the optimized arch axis design scheme in step (2), adaptive adjustment is performed in combination with dynamic load factors, which include traffic load, temperature change load and earthquake load;

[0012] Step 4: Apply intelligent optimization algorithm to optimize the design: Based on the arch axis adjusted in step (3), use intelligent optimization algorithm to perform multiple rounds of iterative optimization on the arch axis. The optimization objectives include minimizing bending moment, minimizing eccentricity and optimizing load distribution.

[0013] Step 5, output the final arch axis shape and determine the design parameters: Based on the optimization results in step (4), output the final arch axis shape, determine the precise positions of all control points, and output the design parameters. The design parameters include the final arch axis geometry, load distribution information, and key structural parameters including horizontal thrust, bending moment, and eccentricity.

[0014] Furthermore, the force analysis formula of the main arch in step 2 is as follows:

[0015] ,

[0016] Where, is the bending moment of the main arch; The horizontal thrust of the main arch;

[0017] The bending moment calculation formula is as follows:

[0018] ,

[0019] Where, is the horizontal distance from the vault; is a uniformly distributed load;

[0020] The horizontal thrust calculation formula is as follows:

[0021] ,

[0022] Where, is a uniformly distributed load; is the span of the arch bridge; For arch height.

[0023] Furthermore, the adaptive adjustment of the arch axis design scheme in combination with the dynamic load factor described in step 3 includes the following steps:

[0024] Step 31, establish a dynamic load distribution model: Based on changes in traffic flow and vehicle load, a traffic load model is established to simulate the impact of dynamic traffic loads on the arch axis; considering the thermal expansion effect of temperature changes on bridge materials, a temperature change load model is established to evaluate the impact of temperature changes on the arch axis; based on changes in earthquake wave acceleration, a seismic load model is established to analyze the impact of seismic forces on the arch axis;

[0025] Step 32, load response analysis: Based on the dynamic load distribution model constructed in step 31, use finite element analysis to analyze the effects of traffic load, temperature load, and earthquake load on the arch bridge, and calculate the deformation and stress distribution of the bridge under dynamic load;

[0026] Step 33, real-time adjustment of the arch axis: Based on the load response analysis results of step 32, the shape of the arch axis is adjusted through an intelligent optimization algorithm;

[0027] Step 34, dynamic feedback mechanism: Through real-time sensor data and monitoring systems, the stress and deformation status of the bridge are monitored in real time, and the design parameters are automatically adjusted according to the dynamic data.

[0028] Furthermore, the formula of the traffic load model in step 31 is as follows:

[0029] ,

[0030] Where, For location Dynamic load at, over time change; For the Vehicle load; is a unit pulse function, indicating that the vehicle is at position The load effect;

[0031] The calculation formula of the temperature change load model is as follows:

[0032] ,

[0033] Where: represents temperature stress; Represents the elastic modulus of the material; Indicates the linear expansion coefficient of the material; Indicates the uniform temperature change to which the structure is subjected;

[0034] The calculation formula of the earthquake load model is as follows:

[0035] ,

[0036] Where, is the mass of the arch bridge structure; is the function of earthquake acceleration changing with time;

[0037] The formula for calculating the deformation and stress distribution of the bridge under dynamic load described in step 32 is as follows:

[0038] ,

[0039] in, is the stiffness matrix of the arch bridge structure; is the displacement vector of the arch bridge; External loads include traffic loads, temperature loads, and earthquake loads;

[0040] The formula for adjusting the arch axis shape using the intelligent optimization algorithm described in step 33 is as follows:

[0041] ,

[0042] in, For the Bending moment at the location; is the minimum bending moment target value after optimization;

[0043] The formula for automatically adjusting the design parameters according to dynamic data in step 34 is as follows:

[0044] ,

[0045] in, The increment for adjusting the arch axis; is the design maximum bending moment; is the currently measured bending moment; is the adjustment factor.

[0046] Furthermore, the calculation formula for minimizing the bending moment in step 4 is as follows:

[0047] ,

[0048] Where, For the Bending moment at the location;

[0049] The calculation formula for minimizing the eccentricity is as follows:

[0050] ,

[0051] Where, For the The eccentricity of the position, is the optimal eccentricity.

[0052] Furthermore, the step of performing multiple rounds of iterative optimization on the arch axis using the intelligent optimization algorithm in step 4 includes:

[0053] Step 41, using a genetic algorithm optimization step to perform a global search on the arch axis to obtain multiple solutions;

[0054] Step 42, using the multiple solutions obtained in step 41 as initial input, and using the particle swarm optimization step to perform local optimization and refine the design solution;

[0055] Step 43, alternating iteration: in each iterative cycle, multiple rounds of alternating execution of the genetic algorithm optimization step for global search and the particle swarm algorithm optimization step for local optimization operations are performed to output the final optimal arch axis design solution.

[0056] Furthermore, the genetic algorithm optimization step in step 41 includes:

[0057] Step 411, population initialization: generating a set of initial populations, each individual representing an arch axis design scheme, including the design variables of the arch axis control point, bending moment, and thrust;

[0058] Step 412, fitness evaluation: calculate the fitness value of each individual, and the fitness function comprehensively considers the maximum bending moment of the arch bridge and the eccentricity of the arch axis;

[0059] Step 413, selection operation: selecting parent individuals based on fitness values, using a roulette wheel selection or tournament selection method, and individuals with higher fitness are selected as parent individuals;

[0060] Step 414, crossover operation: performing a crossover operation between parent individuals to generate new offspring individuals, wherein the crossover operation adopts a single-point crossover, a double-point crossover or a uniform crossover method;

[0061] Step 415, mutation operation: perform mutation operation on offspring individuals, randomly change some genes, introduce diversity, and prevent falling into local optimal solutions;

[0062] Step 416, population update: merge the newly generated offspring individuals with the parent individuals, and select individuals with higher fitness to form the next generation population;

[0063] Step 417, termination condition judgment: judge whether the stopping criteria are met, such as reaching the maximum number of iterations, the fitness change is less than the set threshold, or the fitness value reaches the preset target. If so, the genetic algorithm optimization process ends, otherwise return to step 412 to continue iteration.

[0064] The particle swarm algorithm optimization steps include:

[0065] Step 421, particle swarm initialization: Initialize the particle swarm, where each particle represents a design solution, including parameters such as the control point position, thrust, and bending moment of the arch axis;

[0066] Step 422, fitness evaluation: calculating the fitness value of each particle;

[0067] Step 423, speed and position update: update the particle speed and particle position according to the current speed, individual optimal position and global optimal position;

[0068] Step 424, individual optimal and global optimal update: update the individual optimal position of each particle, and select the particle position with the best fitness value among all particles as the global optimal position;

[0069] Step 425, termination condition judgment: judge whether the stopping criteria are met, such as reaching the maximum number of iterations, fitness convergence or change less than a predetermined threshold, and finding the global optimal solution. If so, the particle swarm optimization process ends, otherwise returns to step 422 to continue iteration.

[0070] The output of the final optimal arch axis design solution includes:

[0071] Arch axis geometry: Output the final arch axis shape including the exact positions of all control points;

[0072] Key structural parameters: Output includes key structural parameters such as horizontal thrust, bending moment, and eccentricity;

[0073] Load distribution information: Output load distribution models including traffic loads, temperature loads, and seismic loads.

[0074] Furthermore, the calculation formula of the fitness value of each individual in step 412 is as follows:

[0075] ,

[0076] Where, For the Maximum bending moment of each individual; For the The eccentric moment of each individual; and is the weight factor used to balance the contribution of bending moment and eccentricity to fitness;

[0077] The calculation formula of the fitness value of each particle in step 422 is as follows:

[0078] ,

[0079] in, and For particles corresponding bending moments and eccentricities;

[0080] The formula for updating the particle velocity in step 423 is as follows:

[0081] ,

[0082] Where, For particles In the The speed of generation; is the inertia weight; For particles In the The speed of generation; and is the learning factor; and is a random number; For particles The best historical position; is the global optimal position; For particles In the The position of the generation;

[0083] The formula for updating the particle position in step 423 is as follows:

[0084]

[0085] Where, For particles In the Generation position.

[0086] Advantages of the present invention

[0087] The method for designing a reasonable arch axis of a long-span arch bridge based on a hybrid algorithm and dynamic loads has the following advantages:

[0088] 1. To address the inaccuracies of existing analytical equation and curve fitting methods under complex loads, this present invention utilizes a hybrid calculation algorithm (combining analytical equation and curve fitting) with an adaptive load distribution model to simultaneously optimize the arch axis shape and load distribution during the design process. This allows for more precise and comprehensive optimization when considering both static and dynamic loads (such as traffic loads, temperature fluctuations, and seismic loads). This is particularly effective in the design of long-span arch bridges, effectively reducing local bending moments and eccentricity, ensuring design accuracy.

[0089] 2. To address the lack of dynamic load adaptability in existing technologies, this invention utilizes an adaptive load distribution model that can dynamically simulate and adjust the distribution and variations of a variety of complex loads, such as traffic loads, temperature fluctuations, wind loads, and seismic loads, ensuring that the arch bridge design can effectively adapt to diverse loading conditions. Furthermore, based on real-time monitoring data (such as sensor monitoring and field data feedback), this invention enables continuous design adjustments during actual construction and operation to optimize load response. This innovation, lacking in traditional design methods, makes arch bridge design more adaptable and flexible.

[0090] 3. To address the low computational efficiency and tendency to fall into local optimal solutions in existing optimization methods, this paper introduces intelligent optimization algorithms (such as genetic algorithms and particle swarm optimization algorithms). By combining global search with local optimization, this method enables faster and more accurate search for optimal solutions. These intelligent optimization algorithms not only handle multiple objective functions (such as minimizing bending moment, minimizing eccentricity, and optimizing materials), but also avoid falling into local optimal solutions, significantly improving design efficiency and accuracy. In practical engineering applications, the introduction of these optimization algorithms reduces manual adjustments and computational errors, thereby increasing the degree of design automation and reliability.

[0091] 4. Addressing the difficulties faced by existing technologies in addressing the complex load and structural optimization challenges of long-span arch bridges, the present invention's hybrid calculation method (combining analytical and curve-fitting methods) and intelligent optimization algorithm effectively address the design requirements of long-span bridges. By taking into account the unique load distribution of long-span bridges (such as the time-varying nature of traffic loads and temperature loads), the invention dynamically adjusts the arch axis shape to optimize structural stability, minimize material waste, and maximize the structure's load-bearing capacity and durability. This feature makes the invention particularly suitable for long-span arch bridges and complex engineering environments.

[0092] 5. Addressing the low material utilization and poor cost-effectiveness of existing technologies, this present invention, by introducing an intelligent optimization algorithm and a dynamic load distribution model, maximizes material utilization while ensuring the safety and stability of the arch bridge structure. During the design process, material selection and structural layout can be optimized based on load response and actual operating conditions, thereby reducing construction costs and eliminating unnecessary resource waste. This innovation gives this method significant advantages in terms of cost savings and improved efficiency.

[0093] 6. To address the lack of dynamic adaptability during the construction phase in existing technologies, this invention integrates a real-time monitoring and feedback mechanism that dynamically adjusts the design based on sensor data during construction. This adaptive optimization during the construction phase ensures the stability and safety of the arch bridge during construction, while also improving the efficiency of the collaborative design and construction process.

[0094] 7. Addressing the problem of existing technologies failing to fully integrate the strengths of multiple disciplines, this invention integrates innovative technologies from multiple disciplines, including structural mechanics, computer science, intelligent optimization, and materials science, providing a novel solution for the design of long-span arch bridges. This interdisciplinary integration has driven technological advancements in bridge design, particularly in large-scale infrastructure construction, effectively improving design efficiency, reducing costs, and ensuring the long-term safety of bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 This is a flow chart of the method for designing a reasonable arch axis of a large-span arch bridge based on a hybrid algorithm and dynamic loads according to the present invention. DETAILED DESCRIPTION

[0096] The present invention will be further explained and illustrated below in conjunction with the accompanying drawings and specific embodiments. It should be noted that this specific embodiment is not intended to limit the scope of rights of the present invention.

[0097] like Figure 1 As shown, this specific embodiment provides a method for designing a reasonable arch axis of a long-span arch bridge based on a hybrid algorithm and dynamic loads, comprising the following steps:

[0098] Step 1. In the first round of iterative optimization, select the initial arch axis type and use the curve fitting method for preliminary design: according to the span and load type of the bridge, select any one of the catenary, parabola or spline curves as the initial arch axis type. The catenary is suitable for situations where the structural load is mainly a constant load and has a small bending moment; therefore, for constant loads, select the catenary; the parabola is suitable for situations where the constant load and live load are relatively evenly distributed, and the calculation is simple; therefore, for uniform loads, select the parabola; the spline curve is suitable for complex load distributions and can accurately match the pressure line through fitting. Therefore, for irregular loads or complex situations, select the spline curve. And determine the preliminary position of the control point, the preliminary position of the control point includes the arch crown, arch foot and several intermediate segment points to generate a preliminary arch axis design scheme. The details are as follows:

[0099] 1. Selection of initial arch axis type

[0100] According to the load characteristics of the arch bridge, the initial axis adopts one of the following three typical curves:

[0101] Catenary: Applicable to structures with mainly dead loads;

[0102] Parabola: Suitable for structures with uniform distribution of dead and live loads;

[0103] Spline curve: suitable for irregular or complex load conditions, and can flexibly fit any pressure line.

[0104] 2. Determination of the preliminary position of the control point

[0105] Assume the bridge span is , the arch height is , select the control point in:

[0106] : horizontal coordinates of the control point, control points;

[0107] : vertical coordinates of the control point, elevation;

[0108] : The total number of control points, including the arch foot, arch top and several intermediate points.

[0109] (1) Uniform step method

[0110] On the horizontal axis, span Divide into part:

[0111] ,

[0112] (2) Determine the vertical coordinate by fitting function

[0113] 1) Catenary form:

[0114] ,

[0115] Where: is the shape coefficient, according to and Numerical fitting; is the hyperbolic cosine function.

[0116] 2) Parabolic form:

[0117] ,

[0118] Where: is the height of the vault (sagitta); It is the full span of the arch bridge; is the horizontal distance from the left arch foot.

[0119] 3) Cubic Spline:

[0120] Use cubic spline interpolation fitting between control points:

[0121] ,

[0122] Each interval satisfies the first-order and second-order continuity of function values ​​and derivatives at adjacent control points.

[0123] 3. Contents of Generating Preliminary Arch Axis Design

[0124] Control point coordinates , ;

[0125] Preliminary arch axis curve function , or the set of spline function coefficients;

[0126] Initial estimation of structural parameters, such as horizontal thrust , arch bending moment

[0127] Graphic display: schematic diagram of arch axis shape and control point layout.

[0128] Step 2, optimization using analytical equation method: Based on the preliminary arch axis design scheme generated in step (1), the dead load action mode of the arch bridge is calculated using analytical equation method, including the stress analysis, bending moment calculation and horizontal thrust calculation of the main arch. The control point position and arch axis shape are adjusted according to the calculation results to generate an optimized arch axis design scheme. This can reduce the bending moment under the preliminary axis and improve rationality.

[0129] By calculating the bending moment and horizontal thrust under the action of constant load, the rationality of the arch axis is judged, and the position of the control point is adjusted accordingly to make the structure bear better stress.

[0130] (1) Force analysis of the main arch: For the main arch of an arch bridge, assuming that it is primarily subjected to compression and ignoring other influencing factors (such as shear), the shape of the arch axis can be expressed using the following force analysis formula. This force analysis formula is based on the force theory of simply supported beams of equal span and describes the relationship between bending moment and horizontal thrust. By solving this equation, a preliminary estimate of the arch axis shape can be obtained.

[0131] The stress analysis formula of the main arch is as follows:

[0132] ,

[0133] Where, Indicates location Bending moment at represents the horizontal thrust of the main arch; Indicates the span of the arch bridge; Indicates the horizontal distance from the arch to a certain point. For the vault, For the arch foot.

[0134] (2) Bending moment calculation formula: Under constant load, the bending moment calculation formula is often used to describe the bending moment distribution of arch bridges under uniformly distributed load:

[0135] ,

[0136] Where, Indicates location Bending moment at is the uniformly distributed load (load per unit length); Indicates the span of the arch bridge; Indicates the horizontal distance from the arch to a certain point. For the vault, For the arch foot.

[0137] This formula is used to calculate the bending moment values ​​at different locations in order to adjust the arch axis shape.

[0138] (3) Calculation formula for horizontal thrust (simply supported state):

[0139] The calculation formula of horizontal thrust is approximately estimated under constant load as follows:

[0140] ,

[0141] in: The horizontal thrust of the main arch; is the uniformly distributed load (load per unit length); Indicates the span of the arch bridge.

[0142] This formula calculates the horizontal thrust of an arch bridge under a uniformly distributed load and is often used in analysis of simply supported conditions.

[0143] The control point adjustment strategy and calculation method are as follows:

[0144] (1) Minimize the objective function (sum of squared moments):

[0145] ,

[0146] Where: is the objective function value, which represents the sum of the squares of the bending moments at all points on the bridge under the current control point arrangement (i.e., the total bending moment energy); is a set of control points, expressed as , is the design parameter set of the arch axis; Indicates the number of control points (excluding fixed boundary points), that is, the number of points involved in optimization; Indicates the The horizontal coordinates of the control points; Indicates the The longitudinal coordinate of each control point (axis height) is the optimization variable; Indicates the arch is in position The bending moment value at is obtained from static analysis; It represents the horizontal thrust of the main arch and is an internal force parameter approximately estimated by dead load analysis or analytical formula.

[0147] (2) Gradient descent adjustment method:

[0148] The control point adjustment amount is:

[0149] ,

[0150] Where: Indicates the The adjustment amount of the longitudinal coordinate of each control point (i.e. the step size of each iterative update); is the learning rate or adjustment coefficient, which is a positive number that controls the adjustment step size (the empirical value is recommended to be 0.01 to 0.1); is the objective function, i.e. the sum of square moments: : is the objective function For the control point ordinate The partial derivative of represents the "optimization direction" of the point in the current state; represents the horizontal thrust of the arch bridge under static load (determined by the structural geometry and load, and can be approximated as a constant); Represents control points The current vertical coordinate is the optimization variable.

[0151] Update the control point ordinates as follows:

[0152] ,

[0153] Where: Indicates the The control point is The vertical coordinate after iteration indicates the updated value; Indicates the The control point is The vertical coordinate at the iteration is the value in the current state; Indicates the The adjustment amount of the longitudinal coordinate of each control point, that is, the step size, represents the amount by which the control point changes along the gradient direction.

[0154] Note: The arch foot control points (two ends) are usually fixed, and only the middle point is adjusted.

[0155] Output content of the adjusted arch axis design plan:

[0156] New control point set ;

[0157] Refitted arch axis function ;

[0158] Adjusted horizontal thrust and bending moment distribution ;

[0159] Graphical output comparing original / optimized arch axis, original / optimized bending moment diagram

[0160] Quantitative comparison of indicators: maximum bending moment drop, control point offset, etc.

[0161] Step 3: Introduce a dynamic load distribution model for adaptive adjustment: In practical applications, the load of an arch bridge is not a static load. Especially in the design of a large-span arch bridge, dynamic factors such as traffic load, temperature change, wind load, and earthquake load have a very important impact on the arch bridge structure. Therefore, a dynamic load distribution model is introduced to make adaptive adjustments based on the arch axis design scheme optimized in step (2) combined with dynamic load factors to ensure that the preliminary arch axis design scheme can adapt to different load changes and optimize the design results. Dynamic load factors include traffic load, temperature change load, and earthquake load.

[0162] Adaptively adjusting the arch axis design scheme in combination with dynamic load factors includes the following steps:

[0163] Step 31: Establish a dynamic load distribution model. The construction of the dynamic load distribution model is based on the load changes of the arch bridge in the actual environment, taking into account traffic loads, temperature change loads, and earthquake loads and their effects on the arch axis:

[0164] First, traffic loads are the primary time-varying load type faced by arch bridge structures during operation. They are characterized by diverse vehicle types, uneven traffic flow, and spatial and temporal randomness. Therefore, traffic loads not only account for changes in vehicle weight distribution and position, but also for changes in traffic flow. To construct a more realistic traffic load model, this embodiment combines changes in traffic flow and vehicle load obtained through traffic data acquisition to establish a dynamic traffic load spatiotemporal distribution model to simulate the impact of dynamic traffic loads on the arch axis.

[0165] The method for obtaining the traffic load data is as follows:

[0166] (1) Historical traffic data statistics

[0167] Source: Historical traffic records provided by traffic management departments and road administration agencies.

[0168] Content: Average traffic volume, typical vehicle ratio, and axle load distribution by hour / day / season.

[0169] Application: Used to construct long-term load spectra and identify statistical laws of traffic loads.

[0170] (2) Real-time traffic monitoring system

[0171] Technical means include:

[0172] Ground sensor coil (installed on the bridge deck to detect vehicle passing and speed);

[0173] Video recognition (camera combined with AI to identify vehicle models and lanes);

[0174] Dynamic axle load detection system (Weigh-in-Motion, WIM);

[0175] Data item: Vehicle passing time , vehicle type classification ,speed , axle weight ,Location .

[0176] (3) Traffic simulation data (supplementary)

[0177] Use simulation tools such as VISSIM to generate traffic load samples under future scenarios;

[0178] It is especially used for simulating extreme working conditions (such as holiday traffic and areas with frequent overloading).

[0179] 2. Mathematical Representation and Modeling Method of Traffic Load Model

[0180] (1) Expression of basic traffic load model

[0181] Set up arch bridge at time The traffic load on is:

[0182] ,

[0183] Where: Indicates time Location Total traffic load at (unit: kN / m); Indicates time Total number of vehicles on the bridge; Indicates the Car at time Equivalent concentrated load (unit: kN); Indicates the The current position of the vehicle on the bridge (unit: m); Represents the unit impulse function, which indicates the vehicle load acting at the current position.

[0184] Note: This basic traffic load model considers vehicles as concentrated forces and is suitable for static analysis or simplified dynamic analysis.

[0185] Assume that there is The position of each vehicle changes with time. The formula of the traffic load model is as follows:

[0186] ,

[0187] in, For location Dynamic load at, over time change; For the Vehicle load; is a unit pulse function, indicating that the vehicle is at position of load action.

[0188] This formula takes into account the time-varying nature of vehicles and realizes the synthesis of multiple vehicle loads through summation.

[0189] 3. Stochastic Modeling of Vehicle Loads

[0190] (1) Vehicle type and axle load modeling

[0191] The transportation components include Class Vehicle, the type set is:

[0192]

[0193] The following parameter distribution is defined for each type of vehicle:

[0194] Item: Type Probability, Symbol: , Description: The probability of the vehicle appearing is satisfied ;

[0195] Item: Total weight distribution, symbol: ,Description: The total mass of the vehicle is normally distributed (unit: kN);

[0196] Item: Axis number, Symbol: , Description: Fixed value or random variable (such as 4 to 6 axes for large vehicles).

[0197] Item: Axle load, Symbol: , Description: Load per axle (total weight can be equally divided or set to distributed).

[0198] (2) Modeling spatial and temporal randomness

[0199] 1) Distribution of vehicle spacing:

[0200]

[0201] It means that the distance between adjacent vehicles follows an exponential distribution, reflecting the fluid traffic flow (Poisson flow assumption).

[0202] 2) Inter-arrival time:

[0203]

[0204] represents the time interval for vehicles to enter the bridge, which is also a Poisson process.

[0205] 5. Traffic Load Expectation Model (Continuous Simplified Form)

[0206] For use in finite element or analytical calculations, the discretized model can be converted to the desired continuous load intensity:

[0207] ,

[0208] Where: Indicates the average traffic load intensity in time and space (unit: kN / m); Indicates the The probability of the occurrence of the vehicle type; Indicates the Vehicles at time Linear density (vehicles / m), from statistics / monitoring; Indicates the The average concentrated load on a vehicle of this type (unit: kN).

[0209] The traffic load model constructed in this embodiment can adopt the following three combinations according to actual needs:

[0210] Model type: Concentrated force-pulse model. Features: Accurately simulates parking spaces and is suitable for small bridges / special vehicles crossing bridges. Application scenarios: Local impact analysis and extreme load event simulation.

[0211] Model category: Random sample simulation model, Features: Monte Carlo sample generation, reflecting traffic volatility, Application scenarios: Statistical strength assessment, fatigue life simulation.

[0212] Model type: Continuous equivalent load model, Features: Simplified calculation, suitable for macroscopic force analysis, Application scenario: Iterative analysis in arch axis optimization.

[0213] This model can also be input into the finite element analysis system together with the temperature change model and earthquake load model to construct a complete dynamic load response system.

[0214] Fourth, temperature changes can cause thermal expansion or contraction of bridge materials. Therefore, it is necessary to consider the thermal expansion effect of temperature changes on bridge materials and establish a temperature change load model to evaluate the impact of temperature changes on the arch axis.

[0215] The steps for establishing the temperature change load model are as follows:

[0216] 1. Internal forces caused by uniform temperature changes

[0217] Uniform temperature change Under this condition, if the structural deformation is constrained (such as fixed at both ends), axial stress will be generated: The calculation formula of the temperature change load model is as follows:

[0218] ,

[0219] Where: represents temperature stress (unit: MPa); Indicates the elastic modulus of the material (unit: MPa); Indicates the linear expansion coefficient of the material (unit: 1 / °C); Indicates the uniform temperature change to which the structure is subjected (unit: °C).

[0220] The thermal stress of the arch bridge structure under different temperature conditions can be simulated through the formula of the temperature change load model.

[0221] 2. Thermal expansion effect of different materials

[0222] In composite structures, such as steel arches and concrete decks, the expansion characteristics of steel and concrete differ:

[0223] Steel:

[0224] Concrete:

[0225] The difference in elongation caused by the temperature rise between the two will form additional interface stress, which should be coordinated through shear connectors. In actual modeling, equivalent thermal load can be set:

[0226] ,

[0227] Where: It represents the additional stress at the interface between steel and concrete due to the inconsistent thermal expansion of the materials. It represents the elastic modulus of concrete (unit: MPa), reflecting the concrete's ability to restrain deformation; The linear expansion coefficient of steel (unit: 1 / °C), which indicates the linear expansion capacity of steel under temperature changes; The linear expansion coefficient of concrete (unit: 1 / °C) indicates the linear expansion capacity of concrete under temperature changes; It represents the temperature change (unit: °C), which is the range of temperature increase or decrease to which the structure is subjected.

[0228] 3. Additional bending moment and deformation caused by temperature gradient

[0229] When there is a temperature gradient along the height direction of the structural section, the thermal expansion of different parts of the section is different, which will cause the temperature gradient bending effect, which manifests as additional bending moment or bending deformation.

[0230] (1) Simplified linear gradient model

[0231] Assume that the temperature gradient is distributed linearly along the height direction:

[0232] ,

[0233] Where: It represents the vertical coordinate relative to the neutral point of the cross section; Indicates the neutral axis temperature; It represents the temperature gradient per unit length (°C / m).

[0234] (2) Additional bending moment caused by temperature gradient

[0235] ,

[0236] Where: represents the additional bending moment due to temperature gradient (unit: kN·m); Indicates the thermal expansion coefficient of the material; represents the elastic modulus; represents the temperature gradient (unit: °C / m); Represents the section inertia moment (unit: m 4 ); Indicates the cross-sectional area of ​​the structure; represents the height coordinate of the cross section relative to the neutral axis; Indicates relative height The temperature at Indicates the reference temperature at the central axis; Represents a microelement of area.

[0237] 4. Finite element temperature field input

[0238] In numerical calculations, temperature loads can be input into the structural finite element model as "volume temperature field" or "thermal stress load":

[0239] Input method 1: Node temperature function (directly specify node temperature)

[0240] Input method 2: Equivalent thermal load (prestress introduced by thermal expansion)

[0241] It is recommended to combine the body sensor data to perform time-varying temperature field fitting, such as:

[0242] ,

[0243] Where, Indicates the Nodes at time temperature; Represents the structure at time average temperature; represents the temperature gradient at that moment; Indicates the The vertical coordinate of a node relative to the neutral axis.

[0244] 5. Engineering application selection

[0245] If the annual temperature changes (slowly), the recommended model or data source is: Use weather station data to build Model;

[0246] If the daily temperature difference / short-term shock temperature change is involved, the recommended model or data source is to use the data from the on-site temperature monitoring system (5-10 minute sampling) for fitting.

[0247] If the temperature gradient / uneven heating is present, the recommended model or data source is: field distribution data combined with cross-sectional heat flow simulation. .

[0248] If the structural materials have different thermal expansion matching, the recommended model or data source is: set the material properties in layers in the model and handle the joint interface (consider the shear stress and tensile stress transfer mechanism).

[0249] If the design condition is one of extreme high temperature response, the recommended model or data source is: simulate a typical extreme day (such as high sun exposure at noon in summer and cooling at night) and superimpose static loads to analyze the arch axis stability.

[0250] Fifth, to comprehensively assess the structural stability and arch axis rationality of long-span arch bridges under earthquakes, this embodiment also introduces a seismic load model to simulate the dynamic response of the structure to earthquakes and closely integrates this response index with the arch axis optimization process. In arch bridge design, seismic loads are calculated by simulating the acceleration of earthquakes. Therefore, based on the acceleration changes of seismic waves, a seismic load model is established to analyze the impact of seismic forces on the arch axis.

[0251] Assuming that the earthquake acceleration changes with time, the calculation formula of the earthquake load model is as follows:

[0252] ,

[0253] Where, is the mass of the arch bridge structure; is the function of earthquake acceleration changing with time;

[0254] The calculation formula of the earthquake load model simulates the influence of earthquake waves and calculates the load response of the structure under the action of earthquake.

[0255] 1. The basis for establishing the earthquake load model:

[0256] (1) National standard basis: The earthquake load model complies with technical standards such as the "Code for Seismic Design of Buildings" and the "Detailed Rules for Seismic Design of Highway Bridges", and adopts the earthquake response spectrum and earthquake fortification parameters recommended by the standards.

[0257] (2) Selection of design earthquake parameters: Determine the design baseline seismic parameters based on the seismic fortification intensity of the area where the bridge is located, including: peak seismic acceleration (Unit: m / s²); earthquake duration; response spectrum characteristic period, etc.

[0258] (3) Seismic wave types

[0259] Actual recorded waves: We select the measured records of typical historical earthquakes, such as the El Centro and Kobe earthquakes, which are representative;

[0260] Artificial synthetic wave: Generates the wave through spectrum matching method according to the standard design spectrum to ensure that the input wave meets the regional defense requirements;

[0261] Earthquake Response Spectrum: Used in response spectrum method to simplify the assessment of the maximum response of the structure.

[0262] 2. The steps for establishing the earthquake load model are as follows:

[0263] (1) Input form

[0264] Ground motion as a function of ground acceleration time history Input structure system in the form of

[0265] The input directions include the bridge axis direction (longitudinal) and the direction perpendicular to the bridge axis (transverse), which can be considered separately according to different analysis objectives.

[0266] (2) Impact of site conditions on seismic motion

[0267] According to the Code for Seismic Design of Buildings, sites are classified into categories I, II, III, and IV;

[0268] Site type has a significant amplification effect on seismic motion. Arch bridges are often located in valleys or on soft soil foundations and are often classified as Class II or III.

[0269] The seismic amplification effect is determined by the modified response spectrum method or the seismic wave amplification factor. To implement the correction, the formula is as follows:

[0270] ,

[0271] Where: represents the response spectrum after considering the site effect; represents the response spectrum under bedrock conditions; represents the amplification factor, which depends on the period and soil type.

[0272] 3. Coupling analysis method of earthquake load and dynamic response of arch bridge structure

[0273] In order to effectively incorporate seismic loads into the optimization design process of the arch axis, the present invention precisely couples seismic excitation with the structural dynamic response process. The specific steps are as follows:

[0274] (1) Establishment of finite element dynamic model of arch bridge

[0275] The structural model includes key components such as arch ribs, bridge deck, hangers, and supports;

[0276] Material properties define the mass matrix , damping matrix , stiffness matrix ;

[0277] The degree of freedom selection includes horizontal constraints of the arch foot, vertical response of the arch crown, lateral vibration of key nodes of the main span, etc.

[0278] (2) Seismic response control equations (MDOF system)

[0279] ,

[0280] Where: represents the mass matrix; C represents the damping matrix; K represents the stiffness matrix; represents the acceleration response vector; represents the speed response vector; Represents the structural node displacement response vector; represents the unit vector of the earthquake excitation direction; Represents the earthquake acceleration time history.

[0281] The Newmark-β method or the Hilber-Hughes-Taylor method (HHT method) is used for numerical integration to obtain the full time history response of the structure.

[0282] 3. Dynamic response result extraction and index definition

[0283] The following key parameters are extracted from the solution results as feedback indicators for arch axis shape optimization:

[0284] index: , meaning and function: The maximum bending moment at any point in the arch bridge under earthquake action, reflecting the most unfavorable internal force position of the structure.

[0285] index: , meaning and function: The maximum displacement of the arch node reflects the stability of the arch axis after an earthquake.

[0286] index: , meaning and function: The equivalent stress of the structure under earthquake conditions should be controlled within the material strength limit.

[0287] index: , meaning and function: The fluctuation range of the axial force of the main arch under the action of earthquake. Excessive fluctuation may cause structural thrust instability.

[0288] 4. Combination mechanism of dynamic response results and arch axis optimization

[0289] The core technological innovation of this embodiment lies in using the feedback of earthquake response results for the optimized design of the control points of the arch axis shape, and using intelligent optimization algorithms (such as genetic algorithms and particle swarm algorithms) to dynamically and iteratively adjust the positions of the arch axis control points to achieve an earthquake-resistant and reasonable structural form.

[0290] (1) Optimization objective function design (with response minimization as the goal)

[0291] ,

[0292] Where: represents the optimization objective function value, which represents the comprehensive performance index of the arch axis scheme under static and seismic conditions. The overall goal is to minimize this value; , , , Represents the weight factor, which indicates the relative importance of each objective component in the overall optimization, satisfying ≥0, can be set manually or adjusted adaptively; It represents the maximum bending moment generated in the structure under static load conditions, reflecting the peak internal force of the structure under constant load; It represents the maximum bending moment generated in the structure under earthquake conditions, reflecting the most unfavorable response of the structure to earthquake loads; It represents the maximum displacement of the arch node during the entire earthquake process, and measures the stability and deflection control of the arch axis under vibration; It represents the eccentricity, which refers to the maximum distance between the actual arch axis and the constant load pressure line, indicating the rationality of the axis shape.

[0293] The smaller the objective function is, the more reasonable the arch axis is and the better the seismic response is.

[0294] (2) Optimize constraints (to ensure structural safety as the bottom line):

[0295] ,

[0296] (3) Optimization process iterative logic:

[0297] 1) Input the initial arch axis and control points;

[0298] 2) Calculation of earthquake dynamic response ( , wait);

[0299] 3) Evaluate fitness and adjust control point positions;

[0300] 4) Iterate until the objective function converges or the constraints are satisfied.

[0301] 5. Engineering application selection

[0302] It is recommended to use at least three seismic waves (including measured and synthetic) for each arch bridge;

[0303] The site amplification effect should be selected and corrected in combination with the geological survey report;

[0304] If it is an important bridge, a multi-load combination analysis (such as dead load + temperature difference + earthquake) should be conducted;

[0305] The method of this embodiment is applicable to the active seismic design stage and the seismic reinforcement scheme comparison and selection stage.

[0306] Step 32, load response analysis: The introduction of dynamic loads will directly affect the stress state of the arch axis, especially in areas where large bending moments may occur under load. To ensure the reliability of the design results, based on the dynamic load distribution model constructed in step 31, finite element analysis is used to analyze the effects of traffic loads, temperature loads, and seismic loads on the arch bridge, and the deformation and stress distribution of the bridge under dynamic loads are calculated; in order to obtain the stress and deformation state under load, the formula for calculating the deformation and stress distribution of the bridge under dynamic loads is as follows:

[0307] ,

[0308] in, is the stiffness matrix of the arch bridge structure; is the displacement vector of the arch bridge; External loads include traffic loads, temperature loads, and earthquake loads;

[0309] By solving this set of linear equations, the deformation and stress state of the arch bridge under load can be obtained.

[0310] Step 33, real-time adjustment of the arch axis: Based on the load response analysis results of step 32, especially in the load concentration area, the arch axis shape is adjusted through an intelligent optimization algorithm; in order to minimize the local bending moment, the arch axis is adjusted using an intelligent optimization algorithm to ensure that the bending moment at each position is as close to the minimum as possible, thereby reducing the local bending moment.

[0311] The formula for adjusting the arch axis shape by the intelligent optimization algorithm is as follows:

[0312] ,

[0313] in, For the Bending moment at the location; is the minimum bending moment target value after optimization;

[0314] Step 34, Dynamic Feedback Mechanism: Using real-time sensor data and monitoring systems, the bridge's stress and deformation status is monitored in real time, automatically adjusting design parameters based on this dynamic data. If the local bending moment of an arch bridge exceeds a predetermined allowable value, the system automatically adjusts the arch axis shape or material parameters through this feedback mechanism to ensure the safety and durability of the bridge throughout its lifecycle.

[0315] The formula for automatically adjusting the design parameters according to dynamic data is as follows:

[0316] ,

[0317] in, The increment for adjusting the arch axis; is the design maximum bending moment; is the currently measured bending moment; is the adjustment factor.

[0318] Step 4: Apply the intelligent optimization algorithm to optimize the design: Based on the arch axis adjusted in step (3), the intelligent optimization algorithm is used to perform multiple rounds of iterative optimization to obtain the optimal design scheme for the arch axis to ensure that the design results meet the requirements of the actual working conditions. The optimization objectives include minimizing the bending moment, minimizing the eccentricity, and optimizing the load distribution.

[0319] (1) Selection of intelligent optimization algorithm

[0320] This intelligent optimization algorithm is a hybrid optimization strategy that combines a genetic algorithm (GA) and a particle swarm optimization algorithm (PSO). The GA simulates natural selection and genetic mechanisms to find the optimal design solution. Its core operations include selection, crossover, mutation, and fitness evaluation. The GA effectively avoids local optima and seeks the global optimal solution. The particle swarm optimization algorithm (PSO) searches for the optimal design solution by simulating the foraging behavior of a flock of birds. PSO has strong global search capabilities when exploring space, effectively reducing design errors.

[0321] (2) Optimization objectives and constraints

[0322] During the optimization process, the optimization objectives and constraints are as follows:

[0323] Minimize bending moments in arch bridges: Ensure that the arch axis is designed to effectively reduce bending moments, especially at the load application points.

[0324] ,

[0325] in, For the Bending moment at the location.

[0326] Minimize eccentricity: The optimized design minimizes the deviation between the arch axis and the load pressure line.

[0327] ,

[0328] in, For the The eccentricity of the position, is the optimal eccentricity.

[0329] Ensure structural safety and stability: Through optimization, the arch bridge structure is guaranteed not to be damaged and the structural safety requirements are met.

[0330] (3) Iterative optimization process

[0331] The optimization steps of genetic algorithm and particle swarm algorithm are used to perform multiple rounds of iterations, update the design parameters, and evaluate the results of each iteration; at the end of each round of iteration, the fitness function of the design results is evaluated to ensure that each round moves towards the optimal design direction.

[0332] The specific steps of performing multiple rounds of iterative optimization on the arch axis using the intelligent optimization algorithm include:

[0333] Step 41: A genetic algorithm is used for global optimization, searching for a global optimal solution by simulating natural selection, crossover, and mutation operations. Therefore, this embodiment first uses the genetic algorithm optimization step to perform a global search of the arch axis to obtain multiple solutions.

[0334] The genetic algorithm optimization step comprises:

[0335] Step 411, population initialization: Generate a set of initial populations, each individual represents an arch axis design scheme, and the gene of each individual contains design variables such as the control point, bending moment, thrust, etc. of the arch axis; these design variables are usually represented by real number coding.

[0336] The calculation formula of the fitness value of each individual in step 412 is as follows:

[0337] ,

[0338] Where, For the Maximum bending moment of each individual; For the The eccentric moment of each individual; and is the weight factor used to balance the contribution of bending moment and eccentricity to fitness;

[0339] Step 412, fitness evaluation: Calculate the fitness value of each individual. The fitness function comprehensively considers the maximum bending moment of the arch bridge and the eccentricity of the arch axis. The definition of the fitness function can be combined with the following objectives:

[0340] ,

[0341] in, For the Maximum bending moment of each individual; For the The eccentric moment of each individual; and is a weighting factor used to balance the contribution of bending moment and eccentricity to fitness.

[0342] In this embodiment, a fitness function is used to evaluate the structural performance of each set of arch axis control points. Its goal is to optimize the structure by integrating multiple design indicators (such as maximum bending moment, eccentricity, and deformation). The fitness function is defined as follows:

[0343] ,

[0344] Where: Indicates the maximum bending moment of the optimized solution under dead load or combined load (unit: kN·m); Indicates the eccentricity (the maximum deviation between the arch axis and the pressure line, unit: m); represents the maximum displacement of the arch (indicating the stability of the arch, unit: m); 、 、 It represents the weight factor of each performance indicator, reflecting its relative importance in fitness evaluation.

[0345] 1. Value range of weight factor

[0346] ,and

[0347] The default setting range in the present invention is as follows (adjustable):

[0348] index: Bending moment, recommended weight range: 0.3 ~ 0.6, Note: Controls the structural strength index and should be one of the main evaluation factors.

[0349] index: Eccentricity, recommended weight range: 0.2 ~ 0.5, Description: Control the rationality of the axis to prevent the arch from deviating from the pressure line and affecting the bending moment.

[0350] index: Displacement, recommended weight range: 0.1 ~ 0.3, Description: Controls the overall stability of the bridge, especially under earthquake conditions.

[0351] 2. Method for determining weight factors

[0352] This embodiment uses a multi-source basis method to comprehensively determine the weight of each indicator to ensure its engineering rationality and algorithm effectiveness. The details are as follows:

[0353] (1) Empirical Weighting

[0354] The initial weights are set based on the degree of attention paid to bending moment, axis stability, and eccentric response in bridge engineering practice;

[0355] For arch bridges with larger spans and heavier loads, the moment weight Should be slightly higher (e.g. set to 0.5);

[0356] For special-shaped or high-arch ratio structures, the eccentricity weight It should be raised appropriately to ensure a reasonable shape.

[0357] (2) Normalized response sensitivity analysis method

[0358] Through finite element analysis, each performance index is normalized and its sensitivity coefficient is obtained;

[0359] If the eccentricity has a significant effect on the bending moment change, then increase ;

[0360] If the displacement of the arch varies greatly under earthquake conditions, the .

[0361] Normalization example:

[0362] , ,

[0363] Where, Indicates the maximum bending moment generated in the structure under the current design scheme; represents the normalized maximum bending moment value, which is used to compare the relative sizes of different designs; Indicates the maximum bending moment under the benchmark solution (such as the initial design or engineering allowable value) for comparison; Indicates the normalized eccentricity, which represents the ratio of the current eccentricity to the maximum allowable value; Indicates the eccentricity in the current design (unit: m), that is, the offset between the arch axis and the dead load pressure line; Indicates the upper limit of eccentricity allowed or recommended by engineering experience.

[0364] Quantitative adjustment of relative weights is performed based on sensitivity comparison.

[0365] (3) Experimental or simulation verification method (Simulation-guided Weighting)

[0366] According to the target bridge type, multiple initial control point combination simulations are performed;

[0367] Observe the impact of different indicators on the arch axis optimization results (such as bending moment reduction rate vs. eccentricity increase);

[0368] Set the weight combination that meets engineering performance and optimizes convergence efficiency;

[0369] After optimization, the weights are adjusted in reverse order according to performance ranking.

[0370] (4) Dynamic Weighting Mechanism (Optional Extension of the Present Invention)

[0371] In the early stages of algorithm iteration, emphasis is placed on eccentricity and morphological rationality ( high);

[0372] In the late convergence stage, it emphasizes minimization of internal forces and stability (improving , );

[0373] You can use:

[0374] ,

[0375] ,

[0376] Where, Indicates the current iteration The weight of the first optimization objective in the round; Indicates the weight value of the first target at the initial iteration; Indicates the change (increase value) of the first target weight during the entire optimization process; Indicates the current iteration number (from 0 to the maximum number of generations); Indicates the current iteration The weight of the second optimization objective in the round; Indicates the weight value of the second target at the initial iteration; Indicates the change (increase value) of the second objective weight during the entire optimization process; Indicates the maximum number of iterations.

[0377] 3. Weight balance between bending moment and eccentricity

[0378] Bending moment and eccentricity are the two core objectives in arch axis optimization. Their balance determines the rationality of the design's force and the aesthetics of its form:

[0379] Comparison items: Result characteristics, overemphasis on bending moment (high ): The arch approaches the theoretical pressure line, but the eccentricity is poorly controlled and the eccentricity is overemphasized (high ): The arch shape is beautiful but may cause large local bending moments.

[0380] Comparison project: Engineering risk, over-emphasis on bending moment (high ): The arch axis is out of balance, the construction accuracy is high, and the eccentricity is overemphasized (high ): The cross-section of the component needs to be increased, as stress concentration is prone to exceeding the limit.

[0381] Comparison project: Balanced strategy, overemphasis on bending moment (high ): Overemphasis on eccentricity (high ): Re-evaluate the fitness composition in combination with the structural shape function and constructibility.

[0382] Therefore, this embodiment adopts the weighted harmonization method to ensure that the arch axis is as close to the constant load pressure line (small eccentricity) as possible while meeting the structural strength (small bending moment), thereby achieving dual rationality of structural mechanics and geometric form.

[0383] 4. Recommended combinations of typical parameters

[0384] Working condition combination: normal constant load + temperature difference control, : 0.5, : 0.4, : 0.1, Application scenario description: Eccentricity control is important and is suitable for arch bridges with high arch ratio or medium span.

[0385] Working condition combination: strong earthquake control-dominated design, : 0.3, : 0.3, : 0.4, Application scenario description: Arch displacement and dynamic response need to be controlled first, suitable for areas with high fortification intensity.

[0386] Working condition combination: general engineering with medium emphasis on structural rationality, : 0.4, : 0.4, : 0.2, Application scenario description: Suitable for most general design requirements.

[0387] This embodiment scientifically sets the fitness function weights through a combination of multi-source data drive + engineering experience guidance + response analysis feedback, provides dynamic adjustment and problem-adaptive strategies, improves the performance of the optimization algorithm, and supports the multi-objective coordination and design robustness of the arch axis design process under multiple load conditions such as static load, temperature difference, and earthquake.

[0388] Step 413, selection operation: select parent individuals according to fitness values, using roulette wheel selection or tournament selection methods, and individuals with higher fitness are selected as parent individuals to prepare for crossover operation.

[0389] Step 414, crossover operation: a crossover operation is performed between parent individuals to generate new offspring individuals. Common crossover operations use single-point crossover, double-point crossover, or uniform crossover methods. The purpose of the crossover operation is to pass on the excellent genes of the parent generation to the offspring and generate a new design scheme.

[0390] Step 415, mutation operation: Mutation operation is performed on the offspring individuals, randomly changing some genes. The purpose of mutation operation is to introduce diversity and prevent falling into local optimal solutions. The mutation rate is usually set to a small value (such as 1%).

[0391] Step 416, population update: merge the newly generated offspring individuals with the parent individuals, and select individuals with higher fitness to form the next generation population, preparing for the next round of iteration.

[0392] Step 417, termination condition judgment: judge whether the stopping criteria are met, such as reaching the maximum number of iterations, the fitness change is less than the set threshold, or the fitness value reaches the preset target. If so, the genetic algorithm optimization process ends, otherwise return to step 412 to continue iteration.

[0393] To ensure the efficiency and stability of the genetic algorithm in the arch axis design optimization of this embodiment, this embodiment systematically designs and verifies the setting basis and value range of the core parameters of the genetic algorithm, mainly including key parameters such as population size, crossover rate, and mutation rate. The specific descriptions are as follows:

[0394] 1. Population Size

[0395] Parameter meaning: Population size refers to the number of solution individuals that exist simultaneously in each generation of genetic algorithm, denoted as .

[0396] Recommended value range:

[0397] Selection basis:

[0398] Small population (<30): suitable for limited computing resources and few design variables (such as adjusting only 5 control points);

[0399] Medium scale (30-60): Recommended default range, suitable for most bridge optimization problems, taking into account both search capability and computational efficiency;

[0400] Large population (>60): Suitable for complex multi-objective optimization or situations with a large number of control points (>10), improving global search capabilities.

[0401] This embodiment recommends the following settings:

[0402] This value can significantly control the calculation time while ensuring the optimization accuracy, and is suitable for bridge engineering structure problems.

[0403] 2. Crossover Probability

[0404] Parameter meaning: crossover rate It represents the probability of generating offspring by crossover operation between parent individuals, which is used to expand the solution space exploration.

[0405] Recommended value range:

[0406] Selection basis:

[0407] A higher crossover rate (>0.8) helps speed up global search and improve population diversity;

[0408] Too high a value may destroy excellent genes and affect local convergence in the later stage;

[0409] Medium to high crossover rates are often used in engineering design problems to maintain exploratory nature.

[0410] This example recommends the following settings:

[0411] The double-point crossover method is adopted, which is applicable to the arch axis solution structure encoded as a sequence of real control points.

[0412] 3. Mutation Probability

[0413] Parameter meaning: mutation rate It represents the probability of random disturbances in offspring individuals and is an important mechanism to prevent the algorithm from falling into local optimality.

[0414] Recommended value range:

[0415] Selection basis:

[0416] Low mutation rate (<0.02): suitable for the late convergence stage to keep the solution stable;

[0417] Moderate mutation rate (0.03-0.07): recommended range, taking into account both global jump-out capability and local accuracy;

[0418] High mutation rate (>0.08): Can be used in the initial stage to prevent the initial population from being too concentrated.

[0419] This example recommends the following settings:

[0420] The variation method adopts Gaussian perturbation method, that is, adding small perturbation values ​​that obey normal distribution to the control point positions to retain the feasibility of the design.

[0421] 4. Other related parameter settings

[0422] Parameters: Encoding method, meaning and setting suggestions: real number encoding (direct representation of control point positions), suitable for continuous space optimization problems.

[0423] Parameters: Selection mechanism, meaning and setting suggestions: Tournament Selection, retaining outstanding individuals.

[0424] Parameter: elite retention strategy, meaning and setting suggestions: retain the first 1 to 2 individuals with the best fitness in each generation to ensure convergence stability.

[0425] Parameter: Termination criteria, meaning and setting suggestions: terminate when the maximum number of generations (such as 100 generations) or the fitness change is less than the set threshold (such as 1e-3).

[0426] 5. Impact of parameter settings on convergence speed and solution quality

[0427] Parameters: population size, impact on convergence speed: the larger the size, the slower the initial search, but the more stable the global convergence, impact on solution quality: too small may fall into local optimality.

[0428] Parameters: Crossover rate, impact on convergence speed: a higher value helps speed up global search, impact on solution quality: too high a value will destroy excellent genes and cause oscillation and non-convergence.

[0429] Parameters: mutation rate, impact on convergence speed: high mutation can jump out of local optimality and slow convergence, impact on solution quality: too low mutation cannot jump out of local trap and poor solution quality.

[0430] This embodiment adopts a combination strategy of medium population + high crossover + moderate mutation + elite retention, which can take into account the convergence speed and the physical rationality and engineering applicability of the design solution.

[0431] Step 42, using the multiple solutions obtained in step 41 as initial input, and using the particle swarm optimization step to perform local optimization and refine the design solution;

[0432] Step 43, Alternating Iterations: In each iteration cycle, the genetic algorithm and particle swarm optimization are performed alternately. In each iteration cycle, the genetic algorithm is used for global search, followed by particle swarm optimization for local optimization. Through multiple rounds of alternating optimization, the search efficiency and accuracy are improved, and the optimal arch axis design is output.

[0433] The particle swarm optimization step is mainly used for local optimization. It adjusts the design solution by simulating the behavior of particles in searching for the optimal solution in the search space. The particle swarm optimization step includes:

[0434] Step 421, particle swarm initialization: Initialize the particle swarm, where each particle represents a design solution, including parameters such as the control point position of the arch axis, thrust, and bending moment; the initial position and velocity of each particle are randomly generated.

[0435] Step 422, fitness evaluation: Calculate the fitness value of each particle. The fitness function is usually the same as the fitness function in GA, which is used to evaluate the quality of the design. The fitness value calculation formula is as follows:

[0436] ,

[0437] in: Represents particles The fitness value of (the larger the value, the better the design); Represents particles The maximum bending moment of the corresponding design scheme (which can be understood as a structural strength index); Represents particles The maximum eccentricity of the corresponding design scheme (which can be understood as an indicator of structural rationality); Represents the weight factor of the bending moment index, which is used to adjust its influence on fitness; Indicates the weight factor of the eccentricity index.

[0438] Step 423, speed and position update: update the particle speed and particle position according to the current speed, individual optimal position and global optimal position;

[0439] The formula for updating particle velocity is as follows:

[0440] ,

[0441] Where, For particles In the The speed of generation; is the inertia weight; For particles In the The speed of generation; and is the learning factor; and is a random number; For particles The best historical position; is the global optimal position; For particles In the The position of the generation;

[0442] The formula for updating the particle position in step 423 is as follows:

[0443] ,

[0444] Where, For particles In the The position of the generation; Represents particles In the The position of the generation; Represents particles In the The speed of generation.

[0445] Step 424, individual optimal and global optimal update: update the individual optimal position of each particle, and select the particle position with the best fitness value among all particles as the global optimal position;

[0446] Individual optimal position update: Each particle updates its individual optimal position according to its current fitness .

[0447] Global optimal position update: Among all particles, the particle position with the best fitness value is selected as the global optimal position .

[0448] Step 425, termination condition judgment: judge whether the stopping criteria are met, such as reaching the maximum number of iterations, fitness convergence or change less than a predetermined threshold, and finding the global optimal solution. If so, the particle swarm optimization process ends, otherwise return to step 3 to continue iteration.

[0449] In this embodiment, the particle swarm optimization algorithm is used for local optimization of the control points of the arch axis of the arch bridge. Its performance depends largely on the rationality of the parameter settings. To this end, combined with the engineering characteristics of the structural optimization problem, the inertia weight is used to and learning factors 、 On the two aspects, the parameter selection strategy and the dynamic adjustment method based on problem characteristics are systematically explained to achieve the optimal balance between algorithm convergence speed and solution quality.

[0450] 1. Inertia Weight The value strategy

[0451] (1) Parameter function

[0452] The inertia weight determines the degree to which the particle maintains its historical velocity, and balances exploration ability with convergence ability:

[0453] Larger : Enhance global search capabilities;

[0454] Smaller : Promote local convergence and improve accuracy.

[0455] (2) Benchmark value range

[0456]

[0457] (3) Dynamic adjustment strategy (the present invention adopts: linear decrease strategy)

[0458] Considering that the arch axis optimization problem of an arch bridge requires a large-scale search in the early stage and precise convergence in the later stage, the following linear descent strategy is adopted:

[0459] ,

[0460] : Strengthen global search at the beginning;

[0461] : Enhance local fine adjustment at the end stage;

[0462] : current iteration number;

[0463] : Maximum number of iterations.

[0464] This strategy can effectively balance search speed and accuracy, and improve the diversity and rationality of arch axis design schemes.

[0465] 2. Learning Factor 、 The value strategy

[0466] (1) Parameter function

[0467] : Individual learning factor, which controls the speed at which the particle moves toward its historical optimal position (influenced by individual experience);

[0468] : Social learning factor, which controls the speed at which particles move toward the current optimal position of the group (group synergy influence).

[0469] (2) Benchmark value range

[0470] , [1.5,2.5]

[0471] (3) Dynamic symmetry strategy (traditional method)

[0472]

[0473] It is suitable for general equilibrium problems and has neutral stability, but lacks problem specificity.

[0474] 3. This embodiment adjusts parameters based on the characteristics of the optimization problem

[0475] In view of the structural characteristics of arch bridge axis optimization, the present invention adopts the following asymmetric dynamic adjustment strategy:

[0476] (1) Three-stage structure of stage identification-optimization problem

[0477] Optimization phase: initial exploration phase. Problem characteristics: need to quickly search for diverse arch axis shapes to avoid local traps. Strategic goal: improve global search capabilities.

[0478] Optimization stage: mid-term transition stage. Problem characteristics: convergence trend begins to appear. It is necessary to maintain a balance between particle diversity and convergence direction. Strategic goal: balance exploration and convergence.

[0479] Optimization stage: late convergence stage, problem characteristics: need to quickly concentrate on the local optimal area, fine-tune the control point position, strategic goal: accelerate convergence and improve accuracy.

[0480] (2) Dynamic adjustment formula - asymmetric learning factor variation mechanism:

[0481] ,

[0482] ,

[0483] , : Individual exploratory nature changes from strong to weak;

[0484] , : Group synergy changes from weak to strong.

[0485] This strategy significantly improves the convergence speed and the structural rationality of the arch axis solution by strengthening early diverse search and late concentrated convergence.

[0486] 4. Summary of the effect of parameter adjustment on algorithm performance

[0487] Problem characteristics: significant multimodality, easy to fall into local optimum, parameter response adjustment strategy: initially take high ,big and small ,Improvement points: Improve the ability to jump out of local problems and maintain solution diversity.

[0488] Problem characteristics: high convergence accuracy requirements, parameter response adjustment strategy: low in the later stage ,Low and high , lifting point: quickly converge to the optimal arch axis to reduce oscillation convergence.

[0489] Problem Characteristics: The arch axis design variable dimension is medium (5-10 points). Parameter response adjustment strategy: Use linear weighting + asymmetric learning factor. Improvement: Avoid search stagnation and improve local search capabilities.

[0490] Problem characteristics: The response function is highly nonlinear and the gradient is discontinuous. Parameter response adjustment strategy: Set limits on particle speed and position + elite retention mechanism. Improvement points: Stable search, maintain engineering feasible solutions, and do not cross the boundary.

[0491] 5. Recommended parameter combinations for this embodiment

[0492] Parameter item: Number of particles, initial value / description: 30~50 (adaptive according to the number of control points).

[0493] Parameter item: Maximum number of iterations, initial value / description: 100.

[0494] Parameter: Inertia weight , Initial value / Description: Linearly decreasing: 0.9 → 0.4.

[0495] Parameter: Learning Factor and , initial value / description: asymmetric dynamic adjustment strategy (above formula).

[0496] Parameter item: Speed ​​limit, initial value / description: Set a limit on the range of change of coordinates of each control point (such as ±10%).

[0497] Parameters: elite retention, initial value / explanation: retain the individuals with the best fitness in each generation to ensure convergence.

[0498] The particle swarm optimization algorithm parameter setting strategy employed in this embodiment implements a dynamic adjustment mechanism based on the specific stage and response characteristics of the structural optimization problem. This significantly improves: the speed of solving arch axis shape optimization; the convergence accuracy of the bending moment and eccentricity objective functions; and the stability adaptability of the arch line under seismic conditions and thermal loads. This parameter setting strategy has clear engineering adaptability and universality, making it suitable for the optimization design of long-span arch bridges under a variety of span and load scenarios.

[0499] Step 5: Output the final arch axis shape and determine the design parameters: Based on the optimization results in step (4), output the final arch axis shape, determine the precise positions of all control points, and output the design parameters. The output design parameters include:

[0500] Arch axis geometry: Output the final arch axis shape including the exact positions of all control points;

[0501] Key structural parameters: Output includes key structural parameters such as horizontal thrust, bending moment, and eccentricity;

[0502] Load distribution information: Output load distribution models including traffic loads, temperature loads, and seismic loads.

[0503] The output design parameters can be directly applied to the construction, quality monitoring, construction control and other aspects of actual bridges to ensure the safety, reliability and economy of the bridge during long-term use.

[0504] Through a refined iterative optimization process, combining the global search and local optimization advantages of genetic algorithms and particle swarm optimization, this example provides an efficient and accurate design solution for long-span arch bridges. This method effectively addresses arch axis design issues under complex loading environments, ensuring optimized bridge design and providing solid technical support for subsequent construction and operation.

[0505] To ensure that the arch axis of an arch bridge maintains a reasonable stress distribution and structural stability over the long term during operation, this embodiment proposes an embedded real-time monitoring and feedback mechanism. By installing sensors at key bridge locations, this mechanism enables online sensing of the structural state, real-time data collection, and intelligent feedback optimization. This mechanism specifically includes four core steps: sensor system installation and deployment, data collection and transmission, model comparison and analysis, and automatic correction of design parameters.

[0506] 1. Types and Functions of Real-Time Sensors

[0507] To comprehensively monitor structural stress, deformation, and external environmental changes, this embodiment uses the following sensor types:

[0508] Sensor Type Main Function Description Fiber Bragg Grating Strain Gauge (FBG) Highly sensitive monitoring of strain at key locations such as arch ribs and hangers to reflect internal force status Resistance strain gauge Used for local strain monitoring of reinforced concrete parts such as arch feet and bridge decks Laser displacement meter / LVDT Monitor the relative displacement of arch tops, arch feet and other parts under traffic or temperature loads Three-axis accelerometer Real-time capture of structural vibration response, suitable for traffic load and earthquake dynamic analysis Distributed Temperature Fiber / Thermocouple Obtain the internal and ambient temperature fields of the structure and establish a temperature load model Support force sensor Real-time recording of structural support reaction changes for overall internal force distribution verification

[0509] The above sensors have the characteristics of high precision, low drift, and suitability for long-term deployment, meeting the monitoring needs of the entire bridge life cycle.

[0510] 2. Installation method and layout of sensors

[0511] (1) Installation method:

[0512] Embedded installation: For example, the optical fiber strain gauge is embedded along the inner groove of the main arch;

[0513] External mounting: For example, the resistance strain gauge is glued to the surface of the steel structure and encapsulated with a protective layer;

[0514] Fixed bracket installation: The laser displacement meter is installed in a protective box and the displacement is monitored by a reflective target;

[0515] Protection design: All sensors are covered with protective sleeves or anti-corrosion coatings to meet IP67 protection level.

[0516] (2) Recommended layout points:

[0517] Structural location Mounting sensor type Purpose and function dome Fiber optic strain gauge + displacement gauge + temperature sensor Monitor the maximum bending moment point and vault deformation caused by thermal expansion arch foot Support force sensor + strain gauge Monitor thrust changes and earthquake response propagation paths Symmetrical position of arch ribs at mid-span Fiber optic strain gauges Capture the strain changes under dead load + traffic load to assist in verifying the pressure line shape Bridge deck edge and center Thermocouple or distributed temperature fiber Obtain temperature distribution gradient and modify temperature load model Boom connection node Accelerometer + strain gauge Capture high-frequency vibration responses and force transmission paths, suitable for traffic and seismic load analysis

[0518] 3. Data Collection Frequency and Transmission Method

[0519] (1) Sampling frequency setting basis:

[0520] Monitoring targets Recommended sampling frequency Reason Strain caused by traffic loads 20~50 Hz Accurately capture strain fluctuations during vehicle passage Acceleration under earthquake excitation ≥100 Hz Capture high-frequency components of earthquake acceleration and support dynamic response time history analysis Vault / Arch Foot Displacement 1~10 Hz Monitor slow or sudden deformation trends Temperature changes 0.11 Hz (1 time / 10 seconds, 1 time / 10 minutes) Meet the requirements for data collection of day and night temperature difference and seasonal fluctuations

[0521] (2) Data transmission method:

[0522] Wiring within the bridge: Use RS485 bus or fiber optic network to connect to the edge data acquisition controller (DAQ);

[0523] Wireless transmission: Remote nodes transmit data to the Bridge Cloud Platform via LoRa, NB-IoT, or 5G networks;

[0524] Gateway integration: The bridge monitoring terminal is equipped with an edge computing module to implement pre-processing and initial screening of abnormalities.

[0525] 4. Real-time feedback and automatic adjustment mechanism of design parameters

[0526] (1) Data feedback path:

[0527] Sensor → Data collector → Monitoring host / cloud platform → Arch axis optimization model

[0528] 2. Data processing flow:

[0529] Data preprocessing: outlier removal, noise filtering, wavelet analysis;

[0530] Feature extraction: Extracting maximum strain , vault displacement , temperature gradient ;

[0531] Response-Model Comparison: with Initial Design Values 、 、 etc. for comparison.

[0532] 3. Parameter adjustment logic (feedback optimization):

[0533] If the monitoring indicators exceed the design expectations, the control point optimization algorithm is triggered to readjust the arch axis shape:

[0534] Example 1: If the measured bending moment

[0535]

[0536] Where, Indicates the The vertical adjustment of each arch axis control point (can be positive or negative); Indicates the adjustment of the proportional coefficient (controls the response strength, usually an empirical value or set through sensitivity analysis); Indicates the bending moment of a key section (such as the middle of the arch rib or the arch foot) measured by the monitoring system; Indicates the theoretical bending moment value of the corresponding position in the initial design scheme.

[0537] Example 2: If the temperature gradient increases, then the temperature load model should be modified. parameter:

[0538]

[0539] Where, Represents the corrected temperature gradient parameter, which is used for subsequent thermal load analysis; Indicates the initial temperature gradient parameters used in the design stage or early optimization stage; Indicates the feedback adjustment coefficient, which controls the degree of correction and is usually an empirical value or fitting parameter; Represents the actual temperature gradient measured by the structural monitoring system, which is calculated by the temperature sensor; Indicates the theoretical temperature gradient value used in the original temperature load model.

[0540] The parameter adjustment results will trigger an intelligent optimization algorithm (such as particle swarm optimization) to update the arch axis control points, re-output the structural internal force parameters and use them for construction guidance or operation scheduling.

[0541] 5. Application Models in Construction and Operation

[0542] stage Implementation Method Feedback Construction phase Real-time monitoring of arch axis deviation during formwork support Automatically adjust the construction arch form shape or construction load sequence Operational stage Continuous monitoring of arch bridge structural response and long-term morphological evolution Provide real-time data support for health assessment, maintenance decision-making and secondary reinforcement Earthquakes / unusual events Rapidly record the vibration response of the entire bridge structure + automatic comparison and early warning Prompt structural deformation trends and trigger safety analysis and alarms at local control points

[0543] The innovative value of the real-time monitoring and feedback mechanism of this embodiment is:

[0544] 1. Multi-source monitoring coupling: integrating multiple types of sensors such as strain, displacement, and temperature to obtain a complete response spectrum of the structure;

[0545] 2. Model adaptive iteration: Feedback on-site monitoring data to the arch axis optimization model in real time to achieve self-correction of design parameters;

[0546] 3. Support full life cycle optimization: It can be adapted to the entire process of design, construction, and operation to achieve intelligent evolutionary design of bridges;

[0547] 4. Improve safety and economy: Through precise dynamic adjustment, the stress peak and eccentricity of the arch bridge are reduced, safety redundancy is improved, and material costs are saved.

Claims

1. A reasonable arch axis design method for long-span arch bridges based on a hybrid algorithm and dynamic loads is characterized by: The steps include: Step 1: Select the initial arch axis type: Based on the span and load type of the bridge, select a catenary, parabola, or spline curve as the initial arch axis type, determine the initial positions of the control points, and generate a preliminary arch axis design plan; Step 2, optimization using analytical equation method: Based on the preliminary arch axis design scheme generated in step (1), the dead load action mode of the arch bridge is calculated using analytical equation method, including the stress analysis, bending moment calculation and horizontal thrust calculation of the main arch. The control point position and arch axis shape are adjusted according to the calculation results to generate the optimized arch axis design scheme; Step 3: Introduce the dynamic load distribution model for adaptive adjustment: Based on the optimized arch axis design scheme in step (2), adaptive adjustment is performed in combination with dynamic load factors, which include traffic load, temperature change load and earthquake load; Step 4: Apply intelligent optimization algorithm to optimize the design: Based on the arch axis adjusted in step (3), use intelligent optimization algorithm to perform multiple rounds of iterative optimization on the arch axis. The optimization objectives include minimizing bending moment, minimizing eccentricity and optimizing load distribution. Step 5, output the final arch axis shape and determine the design parameters: Based on the optimization results in step (4), output the final arch axis shape, determine the precise positions of all control points, and output the design parameters. The design parameters include the final arch axis geometry, load distribution information, and key structural parameters including horizontal thrust, bending moment, and eccentricity.

2. The method according to claim 1, characterized in that The force analysis formula of the main arch in step 2 is as follows: ， Where, is the bending moment of the main arch; The horizontal thrust of the main arch; The bending moment calculation formula is as follows: ， Where, is the horizontal distance from the vault; is a uniformly distributed load; The horizontal thrust calculation formula is as follows: ， Where, is a uniformly distributed load; is the span of the arch bridge; For arch height.

3. The method according to claim 1, characterized in that Adaptive adjustment of the arch axis design scheme in combination with dynamic load factors as described in step 3 includes the following steps: Step 31, establish a dynamic load distribution model: Based on changes in traffic flow and vehicle load, a traffic load model is established to simulate the impact of dynamic traffic loads on the arch axis; considering the thermal expansion effect of temperature changes on bridge materials, a temperature change load model is established to evaluate the impact of temperature changes on the arch axis; based on changes in earthquake wave acceleration, a seismic load model is established to analyze the impact of seismic forces on the arch axis; Step 32, load response analysis: Based on the dynamic load distribution model constructed in step 31, use finite element analysis to analyze the effects of traffic load, temperature load, and earthquake load on the arch bridge, and calculate the deformation and stress distribution of the bridge under dynamic load; Step 33, real-time adjustment of the arch axis: Based on the load response analysis results of step 32, the shape of the arch axis is adjusted through an intelligent optimization algorithm; Step 34, dynamic feedback mechanism: Through real-time sensor data and monitoring systems, the stress and deformation status of the bridge are monitored in real time, and the design parameters are automatically adjusted according to the dynamic data.

4. The method according to claim 3, characterized in that The formula of the traffic load model in step 31 is as follows: ， Where, For location Dynamic load at, over time change; For the Vehicle load; is a unit pulse function, indicating that the vehicle is at position The load effect; The calculation formula of the temperature change load model is as follows: ， Where: represents temperature stress; Represents the elastic modulus of the material; Indicates the linear expansion coefficient of the material; Indicates the uniform temperature change to which the structure is subjected; The calculation formula of the earthquake load model is as follows: ， Where, is the mass of the arch bridge structure; is the function of earthquake acceleration changing with time; The formula for calculating the deformation and stress distribution of the bridge under dynamic load described in step 32 is as follows: ， in, is the stiffness matrix of the arch bridge structure; is the displacement vector of the arch bridge; External loads include traffic loads, temperature loads, and earthquake loads; The formula for adjusting the arch axis shape using the intelligent optimization algorithm described in step 33 is as follows: ， in, For the Bending moment at the location; is the minimum bending moment target value after optimization; The formula for automatically adjusting the design parameters according to dynamic data in step 34 is as follows: ， in, The increment for adjusting the arch axis; is the design maximum bending moment; is the currently measured bending moment; is the adjustment factor.

5. The method according to claim 1, wherein The calculation formula for minimizing the bending moment in step 4 is as follows: ， Where, For the Bending moment at the location; The calculation formula for minimizing the eccentricity is as follows: ， Where, For the The eccentricity of the position, is the optimal eccentricity.

6. The method according to claim 1, characterized in that The step of performing multiple rounds of iterative optimization on the arch axis using the intelligent optimization algorithm in step 4 includes: Step 41, using a genetic algorithm optimization step to perform a global search on the arch axis to obtain multiple solutions; Step 42, using the multiple solutions obtained in step 41 as initial input, and using the particle swarm optimization step to perform local optimization and refine the design solution; Step 43, alternating iteration: in each iterative cycle, multiple rounds of alternating execution of the genetic algorithm optimization step for global search and the particle swarm algorithm optimization step for local optimization operations are performed to output the final optimal arch axis design solution.

7. The method according to claim 6, characterized in that The genetic algorithm optimization step in step 41 includes: Step 411, population initialization: generating a set of initial populations, each individual representing an arch axis design scheme, including the design variables of the arch axis control point, bending moment, and thrust; Step 412, fitness evaluation: calculate the fitness value of each individual, and the fitness function comprehensively considers the maximum bending moment of the arch bridge and the eccentricity of the arch axis; Step 413, selection operation: selecting parent individuals based on fitness values, using a roulette wheel selection or tournament selection method, and individuals with higher fitness are selected as parent individuals; Step 414, crossover operation: performing a crossover operation between parent individuals to generate new offspring individuals, wherein the crossover operation adopts a single-point crossover, a double-point crossover or a uniform crossover method; Step 415, mutation operation: perform mutation operation on offspring individuals, randomly change some genes, introduce diversity, and prevent falling into local optimal solutions; Step 416, population update: merge the newly generated offspring individuals with the parent individuals, and select individuals with higher fitness to form the next generation population; Step 417, termination condition judgment: judge whether the stopping criteria are met, such as reaching the maximum number of iterations, the fitness change is less than the set threshold, or the fitness value reaches the preset target. If so, the genetic algorithm optimization process ends, otherwise return to step 412 to continue iteration; The particle swarm algorithm optimization steps include: Step 421, particle swarm initialization: Initialize the particle swarm, where each particle represents a design solution, including parameters such as the control point position, thrust, and bending moment of the arch axis; Step 422, fitness evaluation: calculating the fitness value of each particle; Step 423, speed and position update: update the particle speed and particle position according to the current speed, individual optimal position and global optimal position; Step 424, individual optimal and global optimal update: update the individual optimal position of each particle, and select the particle position with the best fitness value among all particles as the global optimal position; Step 425, termination condition judgment: judge whether the stopping criteria are met, such as reaching the maximum number of iterations, fitness convergence or change less than a predetermined threshold, and finding the global optimal solution. If so, the particle swarm optimization process ends, otherwise returns to step 422 to continue iteration; The output of the final optimal arch axis design solution includes: Arch axis geometry: Output the final arch axis shape including the exact positions of all control points; Key structural parameters: Output includes key structural parameters such as horizontal thrust, bending moment, and eccentricity; Load distribution information: Output load distribution models including traffic loads, temperature loads, and seismic loads.

8. The method according to claim 7, characterized in that The calculation formula of the fitness value of each individual in step 412 is as follows: ， Where, For the Maximum bending moment of each individual; For the The eccentric moment of each individual; and is the weight factor used to balance the contribution of bending moment and eccentricity to fitness; The calculation formula of the fitness value of each particle in step 422 is as follows: ， in, and For particles corresponding bending moments and eccentricities; The formula for updating the particle velocity in step 423 is as follows: ， Where, For particles In the The speed of generation; is the inertia weight; For particles In the The speed of generation; and is the learning factor; and is a random number; For particles The best historical position; is the global optimal position; For particles In the The position of the generation; The formula for updating the particle position in step 423 is as follows: ， Where, For particles In the Generation position.

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