Lightweight design method for girder of bridge girder erection machine
By optimizing the main beam design of the bridge erecting machine using the dynamic gray wolf optimization algorithm, the problems of material redundancy and insufficient safety assessment were solved, achieving lightweighting of the main beam and improving safety assessment, thus enhancing mobility and transportation efficiency.
Patent Information
- Application Number
- CN202510916232.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-03
- Publication Date
- 2025-11-21
AI Technical Summary
Traditional bridge erecting machine main beam design suffers from problems such as high material redundancy, poor mobility, high transportation costs, lack of quantitative indicators for safety assessment, and poor algorithm adaptability, making it difficult to meet the multi-objective optimization requirements under complex working conditions.
A dynamic gray wolf optimization algorithm combined with Lévy flight disturbance and differential evolution cross-operation is adopted to establish a main beam safety evaluation system. The main beam design parameters are optimized through a dynamic weighting mechanism to achieve lightweighting and safety assessment.
The main beam's self-weight is reduced by 20%-30%, material consumption is reduced, safety quantification is accurate, optimization efficiency is improved, and it is suitable for complex nonlinear problems.
Smart Images
Figure CN120995602A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of bridge girder design. More particularly, the present application relates to a method for lightweight design of a bridge girder of a bridge girder erection machine. BACKGROUND
[0002] The bridge girder erection machine is a core equipment in bridge construction, and the structure weight of the bridge girder directly affects the mobility and construction efficiency of the machine. The traditional design of the bridge girder of the bridge girder erection machine has the following problems: 1. The design relies on empirical formula, and the material redundancy is as high as 35%-40%, which leads to poor mobility of the machine and high transportation cost. The conventional optimization algorithms (such as genetic algorithm and particle swarm algorithm) have the problems of premature convergence and local optimum, and cannot meet the multi-objective optimization requirements under complex working conditions. 2. The safety evaluation is missing, and there is a lack of quantitative indicators, which need to be verified by later experiments, increasing the design cycle and cost. 3. Poor adaptability of the algorithm: the traditional algorithm is difficult to handle nonlinear constraints such as manufacturing process limitations and safety threshold requirements. SUMMARY
[0003] An object of the present application is to solve at least the above problems and to provide at least the advantages to be described later.
[0004] In order to achieve these objects and other advantages according to the present application, a method for lightweight design of a bridge girder of a bridge girder erection machine is provided, comprising the following steps: S1, establishing a safety evaluation system of the bridge girder comprising a plurality of evaluation indexes and a safety scoring model based on the safety evaluation system of the bridge girder; S2, improving the grey wolf optimization algorithm to form a dynamic grey wolf optimization algorithm, the dynamic grey wolf optimization algorithm dynamically updates the positions of the grey wolf individuals in the iteration process through three strategies of dynamic weight mechanism, Lévy flight disturbance and DE crossover operation, until the termination condition is met, and the optimal solution is output; S3, establishing a mathematical model for optimization of the design parameters of the bridge girder, including an objective function and constraint conditions; S4, substituting the objective function and the constraint conditions into the dynamic grey wolf optimization algorithm for solving until the termination condition is met, and outputting the optimal solution.
[0005] Preferably, the evaluation indexes in step S1 include static strength, fatigue strength, static stiffness and overall stability.
[0006] Preferably, the safety scoring model in step S1 is established specifically as follows: S11, determining the weight of each evaluation index by using a three-scale fuzzy analytic hierarchy process; S12, establishing a membership function for each evaluation index; S13, establishing the safety scoring model as follows: In the above formula, n represents the number of evaluation indicators, i = 1, 2, ..., n; w i For the weight of the i-th evaluation index, µ i The membership value is obtained based on the membership function of the i-th evaluation index.
[0007] Preferably, the dynamic weighting mechanism includes setting the position update strategy for individual gray wolves in the early and middle stages of iteration by using exploration weights and development weights, respectively; the exploration weight is: The development weight is: In the above formula, t is the current iteration number, and T is the maximum iteration number.
[0008] Preferably, in the early stages of iteration, the position update formula for individual gray wolves is as follows: In the middle of the iteration, the position update formula for individual gray wolves is as follows: In the middle of the iteration, the position update formula for individual gray wolves is as follows: In the above formula, p α κ is the current optimal solution, r is a random number in the interval [0,1], and κ is a random number in the interval [-1,1].
[0009] Preferably, in the later stages of iteration, the m% of individuals with the worst fitness are replaced every k generations, where k∈[5, 20] and m∈[5,15].
[0010] Preferably, the Lévy flight perturbation strategy involves applying Lévy flight perturbation to a subset of gray wolf individuals during each iteration, with the Lévy flight step size s calculated using the following formula: In the above formula, η and v are random variables that follow a standard normal distribution, and Γ is the Gamma function.
[0011] Preferably, the DE crossover strategy is to perform the crossover operation for each gray wolf individual x in each iteration. i Randomly select three other individuals x r1 x r2 x r3 Generate a new test vector u i Then, based on the crossover probability CR, it is decided whether to replace the components of the experimental vector with those of the current individual, as shown in the following formula: In the above formula, t is the current iteration number, rand() is a random number in the interval [0, 1], and jrand is a randomly selected component index.
[0012] Preferably, in step S3, the objective function is as follows: The constraint condition is as follows: In the above formula, B is the cross-sectional area of the main beam, h w is the web height, t f is the flange thickness, t w is the web thickness, b w is the web width; and RE is the safety score of the main beam obtained by the safety score model.
[0013] Preferably, the process of obtaining the optimal solution in step S4 by the dynamic grey wolf optimization algorithm specifically includes: S41, a fitness function is established, and the formula is as follows: S42, generate N groups of initial solutions randomly in the value range of h w , t f , t w , b w , as the initial population of the grey wolf optimization algorithm, set the iteration number and population size; S43, in each iteration process, calculate the fitness value of each solution according to the fitness function, sort the population according to the fitness value, then update the position of the grey wolf individual according to the three strategies of dynamic weight mechanism, Lévy flight disturbance and DE crossover operation, until the termination condition is met; output the optimal solution, the main beam safety score corresponding to the optimal solution and the self weight of the bridge erecting machine.
[0014] The present application at least includes the following beneficial effects: 1. The improved dynamic grey wolf algorithm is used for optimizing and lightweight design improvement of the main beam of the bridge erecting machine, the self weight of the main beam can be reduced by 20%-30%, and the material consumption is reduced; 2. The safety of the design result is quantified intuitively based on the fuzzy hierarchical evaluation method, and specific safety requirements can be met; 3. The improved dynamic gray wolf algorithm enhances optimization efficiency and global optimization capability, making it suitable for complex nonlinear problems. Other advantages, objectives, and features of this invention will be partly apparent from the following description, and partly understood by those skilled in the art through study and practice of the invention. Attached Figure Description
[0015] Figure 1 This is a flowchart of the lightweight design method for the main beam of the bridge erecting machine described in this invention; Figure 2 This is a flowchart illustrating the implementation of the dynamic gray wolf optimization algorithm described in this invention. Detailed Implementation
[0016] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.
[0017] It should be noted that, unless otherwise specified, the experimental methods described in the following embodiments are all conventional methods, and the reagents and materials described are all commercially available unless otherwise specified. In the description of this invention, the terms "lateral", "longitudinal", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.
[0018] like Figure 1 As shown, the present invention provides a lightweight design method for the main girder of a bridge erecting machine, comprising the following steps: S1. Establish a main beam safety evaluation system that includes multiple evaluation indicators and a safety scoring model based on the main beam safety evaluation system; S2. Improve the gray wolf optimization algorithm to form a dynamic gray wolf optimization algorithm. The dynamic gray wolf optimization algorithm updates the position of individual gray wolves using three strategies during the iteration process: dynamic weight mechanism, Lévy flight perturbation and DE crossover operation, until the termination condition is met and the optimal solution is output. S3. Establish a mathematical model for optimizing the design parameters of the main beam, including the objective function and constraints; S4. Substitute the objective function and constraints into the dynamic gray wolf optimization algorithm to solve the problem until the termination condition is met, and output the optimal solution.
[0019] In the technical scheme, a safety evaluation system of the main beam is first established to quantitatively evaluate the safety of the main beam of the bridge erecting machine, and the safety score model is established to solve the problem that traditional safety evaluation is mainly qualitative analysis and is subjective and lacks accurate quantification. The dynamic grey wolf optimization algorithm is formed by introducing a dynamic weight mechanism, Lévy flight disturbance and DE crossover operation to improve the basic grey wolf optimization algorithm, thereby enhancing the global search ability and local development ability of the algorithm, improving the convergence speed and optimization precision. The dynamic weight mechanism can dynamically adjust the weights of exploration and development according to the number of iterations, so that the algorithm can widely explore the search space in the early stage and accurately develop locally in the later stage. The Lévy flight disturbance introduces a random long-step search for the algorithm, which helps to jump out of the local optimum. The DE crossover operation increases the diversity of the population and improves the search efficiency of the algorithm. A mathematical model of the main beam design parameter optimization is established, the objective function and the constraint condition are substituted into the dynamic grey wolf optimization algorithm for solving, and the optimal main beam section parameters and the corresponding main beam safety score are obtained.
[0020] Specifically, the evaluation indexes in step S1 include static strength, fatigue strength, static stiffness and overall stability.
[0021] The static strength index: the static strength reflects the ability of the main beam to resist damage under static load. According to the principle of material mechanics, the maximum bending normal stress σ of the beam is calculated by the formula: (1) In formula (1), M is the bending moment on the section of the main beam, which can be calculated by the method of structural mechanics combined with the working condition parameters of the bridge erecting machine (such as the weight of the box girder, the span, etc.); y is the distance from the stress point to the neutral axis of the main beam; I is the moment of inertia of the section of the main beam, which can be calculated according to the geometric parameters of the common I-shaped section, such as the web height h w , the flange thickness t f , the web thickness t w , the flange width b f , and the formula is: (2).
[0022] The allowable stress [σ] is calculated by the formula: (3) In formula (3), σ s is the yield strength of steel, σ ≤ [σ].
[0023] The fatigue strength index: mainly considers the ability of the main beam to resist fatigue failure under repeated loading. According to the theory of fatigue mechanics, the maximum cyclic stress σ maxThe calculation needs to be combined with Miner linear cumulative damage theory. It is assumed that the main girder bears multiple different stress levels σ k under cyclic loading, the number of cycles at each stress level is n k , and the fatigue life of the material at this stress level is N k , then σ max can be obtained by fitting the fatigue test data or finite element simulation. The fatigue allowable stress is , where σ -1 =215MPa is the fatigue limit of the steel material, and ɛ=1.3 is the safety factor; σ max ≤ .
[0024] Static stiffness index: measures the ability of the main girder to resist deformation under load. For the case of simply supported beam under uniform load q, the calculation formula of mid-span deflection f is (4) In formula (4), L is the span of the beam, E is the elastic modulus of the steel material, and I is the moment of inertia of the main girder section. The allowable deflection is , and f ≤ L / 400.
[0025] Overall stability index: considers whether the main girder will have overall instability phenomenon under load. The slenderness ratio calculation formula is: (5) In formula (5), φ is the length coefficient, and for the beam with both ends hinged, µ=1; l is the calculation length of the main girder; R is the gyration radius of the main girder section, and for the I-shaped section, (B is the cross-sectional area of the main girder). The Euler critical slenderness ratio is , and λ ≤ λcr.
[0026] The establishment of the safety score model in step S1 specifically includes: S11, using a three-scale fuzzy analytic hierarchy process to determine the weight of each evaluation index; specifically including: S111, constructing a judgment matrix of the evaluation index , a ij index i relative to index j importance comparison; S112, calculating the product M i of each row element of the judgment matrix; S113, calculating the fourth root of M i S114, normalizing to obtain the weight w i After calculation, the weight vector w = [0.35, 0.25, 0.20, 0.20] is obtained.
[0027] S12, a membership function of each evaluation index is established; The membership function of the static strength index adopts a trapezoidal membership function, and the formula is as follows: (6) The actual stress value of the static strength is mapped to the interval [0, 1] through formula (6). The smaller the stress value is, the smaller the membership value is, and the lower the safety degree is.
[0028] The membership function of the static stiffness index adopts a triangular membership function, and the formula is as follows: (7) In formula (7), the larger the deflection f is, the smaller the membership value is, indicating that the stiffness of the main beam is worse, and the safety degree is lower.
[0029] The membership function of the fatigue strength index (8) The membership function of the overall stability index (9) S13, the safety score model is established, as follows: (10) In formula (10), n is the number of the evaluation indexes, i = 1, 2, …, n; w i is the weight of the i-th evaluation index, µ i is the membership function of the i-th evaluation index. The membership values of the evaluation indexes calculated through the membership functions are multiplied by the corresponding weights and summed to obtain the safety score of the main beam.
[0030] In step S2, the dynamic grey wolf optimization algorithm is improved on the basis of the traditional grey wolf optimization algorithm. The traditional grey wolf optimization algorithm is prone to fall into local optimum in the search process, and the convergence speed is slow in the later period. The algorithm enhances the global search ability and local development ability of the algorithm, and improves the convergence speed and optimization precision by introducing a dynamic weight mechanism, Lévy flight disturbance and DE crossover operation.
[0031] The dynamic weight mechanism includes setting the position update strategy of the grey wolf individual through an exploration weight and a development weight in the early and middle iterations, respectively; the exploration weight is: (11) The development weight is: (12) In formula (11)~(12), t is the current iteration number, and T is the maximum iteration number.
[0032] In the early stage of iteration, is larger, the algorithm has strong global exploration ability and can search the solution space widely; with the increase of iteration number, is gradually reduced, and the algorithm gradually turns to local development.
[0033] In the middle stage of iteration, is gradually increased, and the algorithm pays more attention to local development near the current optimal solution to improve the accuracy of the solution.
[0034] Specifically: In the early stage of iteration, the position update formula of the gray wolf individual is as follows: (13) (14) In the middle stage of iteration, the position update formula of the gray wolf individual is as follows: (15) (16) In formula (13)~(16), p α is the current optimal solution, r is a random number in the interval [0,1], and κ is a random number in the interval [-1,1].
[0035] In the late stage of iteration, the m% individuals with the worst fitness are replaced every k generations, k∈[5, 20], m∈[5, 15], to maintain the diversity of the gray wolf population. That is, the individual replacement operation is performed once every 5 to 20 generations, and 5%~15% individuals with the worst fitness in the population are replaced each time to balance the population diversity and convergence efficiency.
[0036] The Lévy flight disturbance strategy is to perform Lévy flight disturbance on part of the gray wolf individuals in each iteration process, so that they can jump out of the local optimum. The Lévy flight step length S is calculated as follows: (17) In formula (17), η and v are random variables obeying standard normal distribution, and Γ is the Gamma function The DE crossover operation strategy is to randomly select another three individuals x i , x r1 , x r2 , x r3 for each gray wolf individual x iThen, according to the cross probability CR, it is determined whether the component of the test vector is replaced into the current individual, and the formula is as follows: (18) (19) In formula (18) and (19), t is the current iteration number, rand() is a random number in the interval [0, 1], and jrand is a randomly selected component index.
[0037] At the beginning of iteration, CR is large, which increases the diversity of the grey wolf population; with the increase of the iteration number, CR gradually decreases, so that the algorithm is more stable.
[0038] In step S3, a mathematical model of the girder design parameter optimization is established, and the core of the mathematical model is to find a design scheme that minimizes the girder cross-sectional area under the premise of meeting the size constraint condition, so as to realize the lightweight of the girder. At the same time, the safety constraint is used to ensure that the optimized girder has sufficient safety. The objective function is: (20) In formula (20), B is the cross-sectional area of the girder, h w is the web height, t f is the flange thickness, t w is the web thickness, b w is the web width. By optimizing the web height hw, the flange thickness tf and the web thickness tw and other parameters, the cross-sectional area A is minimized, so as to reduce the self weight of the girder.
[0039] The constraint conditions include size constraints and safety constraints, specifically: Size constraints: , to ensure that the flange thickness is large enough to meet the force requirement of the structure; , considering the restrictions of transportation and installation.
[0040] Safety constraints: , to ensure that the optimized girder has sufficient safety.
[0041] The process of obtaining the optimal solution by the dynamic grey wolf optimization algorithm in step S4 specifically includes: S41, establish a fitness function, and the formula is as follows: (21) In formula (21), B is the cross-sectional area of the main girder, and RE is the safety score of the main girder obtained through the safety score model; the fitness function is used to evaluate the pros and cons of each solution, and according to formula (21), the higher the safety score, the safer the solution, and the smaller the penalty given in the fitness function; the smaller the cross-sectional area of the main girder, the smaller the fitness value, and the better the solution.
[0042] S42, in h w , t f , t w , b w , b The random N groups of initial solutions are generated in the value range, as the initial population of the grey wolf optimization algorithm, and the number of iterations and the population size are set; the value range of the solution is determined according to the actual engineering requirements and manufacturing process restrictions, for example , , .
[0043] S43, in each iteration process, the fitness value of each solution is calculated according to the fitness function, and the population is sorted according to the fitness value, and then the position of the grey wolf individual is updated according to the dynamic weight mechanism, Lévy flight disturbance and DE crossover operation three strategies, until the termination condition is met; the optimal solution and the main girder safety score corresponding to the optimal solution and the self weight of the bridge erecting machine are output.
[0044] Firstly, the membership functions of each evaluation index are brought into each evaluation index fuzzy value corresponding to each group of initial solutions and the working condition parameters of the bridge erecting machine, formula (7)~formula (10), and then the safety score of each group of initial solutions is obtained by bringing the safety score model, if μ1=0.85, μ2=0.8, μ3=0.92, μ4=0.88 are calculated, and the weight vector w is combined, and RE=0.35*85+0.25*80+0.20*92+0.20*88=85.3 points are obtained. Finally, the fitness value of each solution is calculated through the fitness function. Then in each iteration process, the position of the grey wolf individual is updated according to the dynamic weight mechanism, Lévy flight disturbance and DE crossover operation three strategies, until the termination condition is met.
[0045] The termination condition of iteration is that when the change of fitness value is less than 0.1% for 20 generations in succession, it is considered that the algorithm converges, the iteration is terminated, and the optimal solution is output.
[0046] Although the embodiments of the present application have been disclosed as above, they are not limited to the application listed in the specification and the embodiments, and can be fully applied to various fields suitable for the present application, and additional modifications can be easily realized by those skilled in the art, therefore the present application is not limited to specific details and the figures shown and described herein without departing from the general concept defined by the claims and the equivalent scope.
Claims
1. A lightweight design method for the main beam of a bridge erecting machine, characterized in that, Includes the following steps: S1. Establish a main beam safety evaluation system that includes multiple evaluation indicators and a safety scoring model based on the main beam safety evaluation system; S2. Improve the gray wolf optimization algorithm to form a dynamic gray wolf optimization algorithm. The dynamic gray wolf optimization algorithm updates the position of individual gray wolves using three strategies during the iteration process: dynamic weight mechanism, Lévy flight perturbation and DE crossover operation, until the termination condition is met and the optimal solution is output. S3. Establish a mathematical model for optimizing the design parameters of the main beam, including the objective function and constraints; S4. Substitute the objective function and constraints into the dynamic gray wolf optimization algorithm to solve the problem until the termination condition is met, and output the optimal solution.
2. The lightweight design method for the main beam of a bridge erecting machine as described in claim 1, characterized in that, The evaluation indicators mentioned in step S1 include static strength, fatigue strength, static stiffness, and overall stability.
3. The lightweight design method for the main beam of the bridge erecting machine as described in claim 1, characterized in that, Step S1, establishing the security scoring model, specifically includes: S11. The weights of each evaluation index are determined using the three-scale fuzzy hierarchical analysis method. S12. Establish the membership function for each of the evaluation indicators; S13. Establish the security scoring model as follows: In the above formula, n represents the number of evaluation indicators, i = 1, 2, ..., n; w i For the weight of the i-th evaluation index, µ i The membership value is obtained based on the membership function of the i-th evaluation index.
4. The lightweight design method for the main beam of a bridge erecting machine as described in claim 1, characterized in that, The dynamic weighting mechanism includes setting the position update strategy for individual gray wolves in the early and middle stages of iteration using exploration weights and development weights, respectively; the exploration weight is: The development weight is: In the above formula, t is the current iteration number, and T is the maximum iteration number.
5. The lightweight design method for the main beam of a bridge erecting machine as described in claim 4, characterized in that, In the early stages of iteration, the position update formula for individual gray wolves is as follows: In the middle of the iteration, the position update formula for individual gray wolves is as follows: In the above formula, p α κ is the current optimal solution, r is a random number in the interval [0,1], and κ is a random number in the interval [-1,1].
6. The lightweight design method for the main beam of a bridge erecting machine as described in claim 4, characterized in that, In the later stages of iteration, the m% of individuals with the worst fitness are replaced every k generations, where k∈[5, 20] and m∈[5, 15].
7. The lightweight design method for the main beam of a bridge erecting machine as described in claim 1, characterized in that, The Lévy flight perturbation strategy involves applying Lévy flight perturbations to a subset of gray wolf individuals during each iteration. The Lévy flight step size s is calculated using the following formula: In the above formula, η and v are random variables that follow a standard normal distribution, and Γ is the Gamma function.
8. The lightweight design method for the main beam of a bridge erecting machine as described in claim 1, characterized in that, The DE crossover strategy is to perform a crossover operation on each gray wolf individual x during each iteration. i Randomly select three other individuals x r1 x r2 x r3 Generate a new test vector u i Then, based on the crossover probability CR, it is decided whether to replace the components of the experimental vector with those of the current individual, as shown in the following formula: In the above formula, t is the current iteration number, rand() is a random number in the interval [0,1], and jrand is a randomly selected component index.
9. The lightweight design method for the main beam of a bridge erecting machine as described in claim 1, characterized in that, In step S3, the objective function is as follows: The constraints are as follows: In the above formula, B is the cross-sectional area of the main beam, and h w t is the web height. f For the flange thickness, t w b is the web thickness. w denoted as the web width; RE is the main beam safety score obtained through the aforementioned safety scoring model.
10. The lightweight design method for the main beam of a bridge erecting machine as described in claim 9, characterized in that, Step S4, the process of finding the optimal solution using the dynamic gray wolf optimization algorithm, specifically includes: S41. Establish the fitness function, as shown in the following formula: S42, in h w t f t w b w N sets of initial solutions are randomly generated within the range of values to serve as the initial population for the Grey Wolf optimization algorithm. The number of iterations and the population size are set. S43. In each iteration, the fitness value of each solution is calculated according to the fitness function, and the population is sorted according to the fitness value. Then, the position of the gray wolf individuals is updated according to three strategies: dynamic weighting mechanism, Lévy flight disturbance, and DE crossover operation, until the termination condition is met. The optimal solution and the main beam safety score and bridge erecting machine self-weight corresponding to the optimal solution are output.