A method for optimizing the design parameters of steel-concrete composite inclined columns

Abstract

This invention relates to a method for optimizing the design parameters of steel-concrete composite inclined column sections. First, based on the optimization objective of the steel-concrete composite inclined column section with shear studs, the optimization variable X is determined, and the upper and lower limits of each parameter in the variable are determined. Then, an optimization objective function is established for X, and conditional constraints are applied to each optimization variable. Finally, an improved genetic algorithm is used to optimize X to obtain the optimal values ​​of the design parameters X for the steel-concrete composite inclined column section. The improved genetic algorithm proposed in this invention overcomes the defect of local convergence in algorithms. Embedding an elite strategy selection operator reduces the number of iterations while ensuring that all individuals in the population have a chance of being selected. Furthermore, embedding dynamic mutation probability and state probability acceptance criteria into the mutation operator can reduce the number of evolutions while improving the degree of evolution, obtaining an approximate optimal solution closer to the optimal solution.

Description

Technical Field

[0001] This invention relates to the technical field of design optimization of steel-concrete composite inclined columns with shear studs, and particularly to a method for optimizing the cross-sectional design parameters of steel-concrete composite inclined columns. Background Technology

[0002] The load-bearing capacity and interface slip of existing steel-concrete composite structures have long been a focus of research in academia and industry. Optimizing the design of such composite structural components often requires ensuring optimal weight, cost, and stiffness while meeting relevant codes and specific requirements. In other words, the interface design of inclined steel-concrete composite columns requires selecting the best solution from all feasible options according to predetermined objectives. Furthermore, for steel-concrete composite structures with shear studs, simultaneously increasing the amount of steel and shear studs can significantly improve the column's load-bearing capacity, reduce the maximum slip, and control the extension of interface slip. However, excessive steel usage and overly dense shear stud placement can lead to significant waste and excessively high costs. Therefore, the design problem of inclined steel-concrete composite columns with shear studs is essentially a parameter optimization problem with the objective functions of maximizing the inclined column's load-bearing capacity, minimizing the steel-concrete interface slip, and minimizing the project cost.

[0003] Conventional parametric design processes often employ a trial-and-error method, which involves assuming key parameters for each section based on experience and then verifying them against the calculation formulas in the specifications. If the specifications are not met, the parameters are adjusted accordingly to satisfy the requirements. However, this conventional trial-and-error method inevitably requires repeated calculations, which is time-consuming. Moreover, repeated calculations only involve a limited number of attempts, and may only yield a feasible solution, failing to guarantee global optimality and failing to comprehensively consider both the structural performance and project cost requirements.

[0004] With the advancement of computer technology, intelligent optimization algorithms have been widely applied to multi-objective engineering optimization problems. Among them, genetic algorithms, which simulate the biological evolution process in nature, are suitable for multi-objective optimization of design parameters. However, basic genetic algorithms have two significant drawbacks: early convergence and poor local search ability. Summary of the Invention

[0005] To address the aforementioned problems in existing technologies, this invention proposes an improved genetic algorithm that is applicable to multiple combined structural design parameters and complex constraints, while also possessing global search capabilities.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: a method for optimizing the design parameters of steel-concrete composite inclined columns, comprising the following steps:

[0007] S01: Based on the optimization objective of the steel-concrete inclined column section with shear studs, the optimization variable X is determined, and the expression is as follows:

[0008] X = [b,t] w ,b af ,h w ,t af ,d s ,n s ,d sv ,s sv ,d ss ,d];(1)

[0009] Where b is the side length of the square cross section, t w b is the thickness of the web of the steel section. af h is the flange length of the steel section. w t is the web height. af d is the flange width. s n is the diameter of the longitudinal reinforcing bar. s d represents the number of longitudinal reinforcing bars. sv s is the diameter of the stirrup. sv d represents the stirrup spacing. ss d represents the vertical spacing of the shear studs, and d represents the diameter of the shear studs.

[0010] S02: Determine the upper limit of the value X for variable X max And the lower limit of the value X min To clarify the feasible region of the variables, and within the feasible region, to obtain the initial value X0 of each variable in X;

[0011] The upper limit of the value of X is as follows:

[0012] X max =[b max ,t w max ,b af max ,h w max ,t af max ,d s max ,n s max ,d sv max ,s sv max ,d ss max ,d max (2) The lower limit of X is as follows:

[0013] X min =[b min ,tw min ,b af min ,h w min ,t af min ,d s min ,n s m in,d sv min ,s sv min ,d ss min ,d min (3) X0 is represented as follows:

[0014] X0 = [b 0 ,t w 0 ,b af 0 ,h w 0 ,t af 0 ,d s 0 ,n s 0 ,d sv 0 ,s sv 0 ,d ss 0 ,d 0 (4)

[0015] S03: After introducing linear weighting coefficients into X, construct the optimization objective function, the specific expression of which is as follows:

[0016]

[0017] Where α is the cost weighting coefficient; β is the bearing capacity weighting coefficient; γ is the interface slip weighting coefficient; C(x) is the engineering cost calculation formula; V(x) is the bearing capacity calculation formula; S(x) is the steel-concrete interface slip calculation formula; C0 is the initial value of engineering cost; V0 is the initial value of bearing capacity; S0 is the initial value of steel-concrete interface slip.

[0018] S04: Apply conditional constraints to each optimization variable according to the specification requirements. The specific constraints are as follows:

[0019] The dimensional constraints for concrete and steel sections are as follows:

[0020]

[0021]

[0022] The constraints for the construction requirements of longitudinal reinforcing bars are as follows:

[0023]

[0024] The constraints for stirrup construction requirements are as follows:

[0025]

[0026] The constraints on the spacing and diameter requirements of shear studs are as follows:

[0027] 6d≤d ss ≤d ss max ;d min ≤d≤d max (9)

[0028] Where r represents The feasible range of values;

[0029] S05: Establish an initial population and calculate the fitness value of each individual in the initial population using the optimization objective function. The individual is a parameter contained in the optimization variable X and its value conforms to the upper and lower limits of the parameter.

[0030] The elite strategy is embedded into the selection of the existing genetic algorithm model, that is, the new selection operator replaces the roulette wheel selection method to obtain the improved genetic algorithm model and initialize the model.

[0031] S06: For the fitness value of each individual obtained, the offspring population is calculated using the improved genetic algorithm;

[0032] S07: Perform chromosome crossover and mutation operations:

[0033] S071: Randomly select the number of points for crossover between parent individuals, then select two points for crossover between parent individuals, and use the multi-point crossover operator to complete the crossover calculation.

[0034] S072: Use the perturbation formula instead of the mutation operator to perform the mutation operation. The specific calculation formula is as follows:

[0035] m i '=m i +y i (m imax -m imin (10)

[0036]

[0037] Where, mi The value is the unperturbed value; m′ i The value after perturbation; sign is the sign function; u is a random number uniformly distributed on [0,1]; T k This refers to the system temperature value. It is the attenuation factor;

[0038] S08: Calculate the probability of being accepted by the population, the specific expression is as follows:

[0039]

[0040] Among them, f i p represents the difference in the individual's objective function before and after the perturbation; p is the probability that the individual is accepted.

[0041] If the fitness value of an individual after perturbation is high, then the individual after perturbation is accepted into the population; if the fitness value of an individual after perturbation is low, then the probability p of being accepted by the population is calculated according to formula (13). If p is less than a random number between [0,1], then the individual after perturbation is accepted; otherwise, the individual before perturbation is retained.

[0042] S09: Determine whether the improved genetic algorithm has ended. When the fitness value of the best individual in the offspring population no longer increases for N consecutive generations, terminate the algorithm and output the individual with the highest fitness value in the final offspring population as the approximate optimal solution. This approximate optimal solution is the optimal value of the design parameter X of the steel-concrete inclined column section.

[0043] Preferably, in step S05, the fitness of each individual in the initial population is calculated using an optimization objective function after establishing the population.

[0044] The specific steps for obtaining the value are as follows:

[0045] S051: Set the values ​​for each system parameter of the improved genetic algorithm, including the number of individuals N in the population and the initial temperature value.

[0046] T0, temperature decay factor Individual multi-point crossover probability p c The initial mutation probability p of an individual m ;

[0047] S052: Randomly select N groups of individuals from the upper and lower limits of each parameter in S02 to form the initial population;

[0048] S053: Use real number encoding to encode the initial population, and then use the optimization objective function to calculate the fitness value of each individual in the initial population;

[0049] As a preferred embodiment, the specific steps in S06 for calculating the offspring population using the improved genetic algorithm are as follows:

[0050] S061: Sort the obtained fitness values ​​in descending order, and select the individual in the initial population corresponding to the highest fitness value to be added to the offspring population;

[0051] S062: For individuals with fitness values ​​other than the highest fitness value:

[0052] Randomly select the remaining fitness values. If the fitness value ranks in the top 30%, then use P... top The individual corresponding to the fitness value is selected with a probability and added to the offspring population; if it is not selected, it is returned to the initial population.

[0053] If the fitness value ranks between 31% and 60%, then use P. med The individual corresponding to the fitness value is selected with a probability and added to the offspring population; if it is not selected, it is returned to the initial population.

[0054] If the fitness value ranks between 61% and 100%, then use P... low The individual corresponding to the fitness value is selected with a certain probability and added to the offspring population; if the individual is not selected, it is returned to the initial population.

[0055] S063: Iterate through all fitness values, repeat S062, and obtain the final offspring population.

[0056] Compared with the prior art, the present invention has at least the following advantages:

[0057] 1. This invention embeds an elite strategy, dynamic mutation probability, perturbation formula, and state acceptance probability criterion into a genetic algorithm, forming an improved genetic algorithm with higher computational accuracy. The improved genetic algorithm proposed in this invention overcomes the defect of local convergence. Embedding the elite strategy selection operator reduces the number of iterations while ensuring that all individuals in the population have a chance of being selected. Furthermore, embedding the dynamic mutation probability and state acceptance probability criterion into the mutation operator can reduce the number of evolutions while improving the evolutionary degree, obtaining an approximate optimal solution closer to the optimal solution.

[0058] 2. This invention focuses on the optimization of cross-sectional design parameters for steel-concrete composite inclined columns with shear studs. With the objective functions of higher bearing capacity, smaller interface slip, and lower engineering cost, the proposed improved genetic algorithm has higher computational accuracy and faster convergence speed, and is suitable for multi-objective engineering optimization problems. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating the technical process of the present invention.

[0060] Figure 2 This is a comparison of the load-bearing capacity convergence process using the improved genetic algorithm and the basic genetic algorithm of the present invention in Example 1.

[0061] Figure 3 This is a comparison of the interface sliding convergence process optimized using the improved genetic algorithm and the basic genetic algorithm of the present invention in Example 1.

[0062] Figure 4 This is a comparison of the convergence process of engineering cost optimization design using the improved genetic algorithm and the basic genetic algorithm of the present invention in Example 1. Detailed Implementation

[0063] The present invention will now be described in further detail.

[0064] This invention addresses the shortcomings of basic genetic algorithms in the design optimization of composite structural components by introducing an elite strategy, dynamic compilation probability, and state acceptance probability criteria to modify the selection and mutation operators of the basic genetic algorithm. The aim is to propose an improved genetic algorithm specifically applicable to the optimization of design parameters of steel-concrete composite inclined columns with shear studs.

[0065] A method for optimizing the design parameters of steel-concrete composite inclined columns includes the following steps:

[0066] S01: Based on the optimization objective of the steel-concrete inclined column section with shear studs, the optimization variable X is determined, and the expression is as follows:

[0067] X = [b,t] w ,b af ,h w ,t af ,d s ,n s ,d sv ,s sv ,d ss ,d];(1)

[0068] Where b is the side length of the square cross section, t w b is the thickness of the web of the steel section. af h is the flange length of the steel section. w t is the web height. af d is the flange width. s n is the diameter of the longitudinal reinforcing bar. s d represents the number of longitudinal reinforcing bars. sv s is the diameter of the stirrup. sv d represents the stirrup spacing. ss Let d be the vertical spacing of the shear studs and d be the diameter of the shear studs. For the design problem of the cross-sectional parameters of steel-concrete inclined columns with shear studs, the design optimization objectives are clarified based on the actual working conditions, and the variables that need to be optimized are determined.

[0069] S02: Based on the design process of the steel-concrete composite inclined column section parameters, determine the range of each design parameter to clarify the feasible region, and determine the upper limit of variable X. max And the lower limit of the value X min To define the feasible region of the variables, and within the feasible region, to obtain the initial value X0 of each variable in X.

[0070] The upper limit of the value of X is as follows:

[0071] X max =[b max ,t w max ,b af max ,h w max ,t af max ,d s max ,n s max ,d sv max ,s sv max ,d ss max ,d max (2) The lower limit of X is as follows:

[0072] X min =[b min ,t w min ,b af min ,h w min ,t af min ,d s min ,n s m in,d sv min ,s sv min ,d ss min ,d min (3) X0 is represented as follows:

[0073] X0 = [b 0 ,t w 0 ,b af 0 ,h w 0 ,t af 0 ,ds 0 ,n s 0 ,d sv 0 ,s sv 0 ,d ss 0 ,d 0 (4)

[0074] S03: After introducing linear weighting coefficients into X, an optimization objective function is constructed. The optimization objectives for the design of steel-concrete composite section parameters are higher bearing capacity of inclined columns, smaller interface slip, and lower engineering cost. By introducing initial linear weighting coefficients, the differences in dimensions between different calculation formulas are eliminated, thereby achieving the goal of simultaneous optimization of multiple objectives. Based on this, the optimization objective function is constructed, and the specific expression is as follows:

[0075]

[0076] Where α is the cost weighting coefficient; β is the bearing capacity weighting coefficient; γ is the interface slip weighting coefficient; C(x) is the engineering cost calculation formula; V(x) is the bearing capacity calculation formula; S(x) is the steel-concrete interface slip calculation formula; C0 is the initial value of engineering cost; V0 is the initial value of bearing capacity; S0 is the initial value of steel-concrete interface slip.

[0077] S04: Apply conditional constraints to each optimization variable according to the specifications. Here, "specificational requirements" refers to ensuring that existing indicators comply with national regulations. All implementations within this field must adhere to the conditional constraints within these specifications. This document uses the "Code for Design of Concrete Structures" (GB50010-2010), and the specific constraints are as follows:

[0078] The dimensional constraints for concrete and steel sections are as follows:

[0079]

[0080] The constraints for the construction requirements of longitudinal reinforcing bars are as follows:

[0081]

[0082] The constraints for stirrup construction requirements are as follows:

[0083]

[0084] The constraints on the spacing and diameter requirements of shear studs are as follows:

[0085] 6d≤d ss ≤d ss max ;dmin ≤d≤d max (9)

[0086] The upper and lower limits of each parameter can be customized according to the specific engineering optimization problem, where r represents... The feasible domain values.

[0087] S05: Establish an initial population and calculate the fitness value of each individual in the initial population using the optimization objective function. The individual is a parameter contained in the optimization variable X, and the parameter individual takes values ​​that conform to the upper and lower limits of the parameter.

[0088] This involves embedding an elite strategy into the selection process of an existing genetic algorithm model. Essentially, a new selection operator replaces the roulette wheel selection method, resulting in an improved genetic algorithm model. This model is then initialized. The genetic algorithm is an existing technology, and the initialization parameters are the values ​​set for various system parameters of the improved genetic algorithm, including the number of individuals N in the population, the initial temperature T0, and the temperature decay factor. Individual multi-point crossover probability p c The initial mutation probability p of an individual m The elite strategy is based on existing technology.

[0089] The specific steps for establishing a population and calculating the fitness value of each individual in the initial population using an optimization objective function are as follows:

[0090] S051: Set the values ​​for each system parameter of the improved genetic algorithm, including the number of individuals N in the population, the initial temperature T0, and the temperature decay factor. Individual multi-point crossover probability p c The initial mutation probability p of an individual m .

[0091] S052: Randomly select N groups of individuals from the upper and lower limits of each parameter in S02 to form the initial population.

[0092] S053: The initial population is encoded using a real number encoding method, and then the fitness value of each individual in the initial population is calculated using an optimization objective function. The real number encoding method is an existing technology.

[0093] S06: For the fitness value of each individual obtained, the offspring population is calculated using the improved genetic algorithm.

[0094] The specific steps in S06 to calculate the offspring population using the improved genetic algorithm are as follows:

[0095] S061: Sort the obtained fitness values ​​in descending order, and select the individual in the initial population corresponding to the highest fitness value to be added to the offspring population.

[0096] S062: For individuals with fitness values ​​other than the highest fitness value:

[0097] Randomly select the remaining fitness values. If the fitness value ranks in the top 30%, then use P... top The individual corresponding to the fitness value is selected with a certain probability and added to the offspring population. If it is not selected, it is returned to the initial population.

[0098] If the fitness value ranks between 31% and 60%, then use P. med The individual corresponding to the fitness value is selected with a certain probability and added to the offspring population. If it is not selected, it is returned to the initial population.

[0099] If the fitness value ranks between 61% and 100%, then use P... low The individual with the fitness value is selected with a certain probability and placed into the offspring population. If the individual is not selected, it is returned to the initial population.

[0100] S063: Iterate through all fitness values, repeat S062, and obtain the final offspring population.

[0101] S07: Perform chromosome crossover and mutation operations:

[0102] S071: Randomly select the number of points for crossover between parent individuals, then select two points for crossover between parent individuals, and use a multi-point crossover operator to complete the crossover calculation; Since there are many parameters that need to be designed and optimized, and there are certain constraints between them, the improved genetic algorithm uses a multi-point crossover operator for crossover.

[0103] S072: A perturbation formula is used instead of the mutation operator for mutation operations. Considering that mutation operations are highly likely to lose superior individuals, the mutation probability and mutation method in the basic genetic algorithm are modified. During evolution, the mutation probability decreases as the average fitness of the population increases. Based on the average fitness value of the first-generation population and the initial mutation probability, the mutation probability decreases by 10% for every 50% increase in fitness value. Simultaneously, a perturbation formula is used instead of the mutation operator for mutation operations, and the state acceptance probability criterion is used to determine whether an individual accepting the perturbation should enter the offspring population. The improved mutation method can both retain superior individuals and improve population diversity. The specific calculation formula is as follows:

[0104] m i '=m i +y i (m imax -m imin (10)

[0105]

[0106] Where, mi The value is the unperturbed value; m′ i The value after perturbation; sign is the sign function; u is a random number uniformly distributed on [0,1]; T k This refers to the system temperature value. This is the attenuation factor.

[0107] S08: Calculate the probability of being accepted by the population, the specific expression is as follows:

[0108]

[0109] Among them, f i p represents the difference in the individual's objective function before and after the perturbation; p is the probability that the individual is accepted.

[0110] If the fitness value of the perturbed individual is high, then the perturbed individual is accepted into the population; if the fitness value of the perturbed individual is low, then the probability p of being accepted by the population is calculated according to formula (13). If p is less than a random number between [0,1], then the perturbed individual is accepted; otherwise, the individual before the perturbed individual is retained. The state acceptance probability criterion determines whether to accept the perturbed individual into the offspring population by comparing the fitness values ​​of the individual before the perturbed individual and the individual after the perturbed individual.

[0111] S09: Determine whether the improved genetic algorithm has ended. When the fitness value of the best individual in the offspring population no longer increases for N consecutive generations, terminate the algorithm and output the individual with the highest fitness value in the final offspring population as the approximate optimal solution. This approximate optimal solution is the optimal value of the design parameter X of the steel-concrete inclined column section.

[0112] Example 1: To further illustrate the feasibility of this technical method, taking the problem of optimizing the cross-section of a steel-concrete inclined column with shear studs to obtain the cross-section dimensions, reinforcement details, and shear stud arrangement as an example, this invention further illustrates an improved genetic algorithm for optimizing the design parameters of a steel-concrete inclined column cross-section.

[0113] See Figure 1 A method for optimizing the design parameters of steel-concrete composite inclined columns includes the following steps:

[0114] S01: For the design problem of cross-sectional parameters of steel-concrete composite inclined columns with shear studs, determine the variables X = [b,t] that need to be optimized. w ,b af ,h w ,t af ,d s ,n s ,d sv ,s sv ,d ss ,d].

[0115] Where b is the side length of the square cross section, t w b is the thickness of the web of the steel section. af h is the flange length of the steel section. w t is the web height. af d is the flange width. s n is the diameter of the longitudinal reinforcing bar. s d represents the number of longitudinal reinforcing bars. sv s is the diameter of the stirrup. sv d represents the stirrup spacing. ss d represents the vertical spacing of the shear studs, and d represents the diameter of the shear studs.

[0116] S02: Based on the design process of the steel-concrete composite inclined column section parameters, determine the range of each design parameter and clarify the feasible region, that is, determine the lower limit of each variable's value as X. min = [300, 10, 100, 200, 10, 20, 2, 16, 50, 90, 16], where the upper limit of each variable's value is X. max =[2000,70,500,1000,70,32,11,32,400,600,22]; Based on the feasible region of the design parameters, the initial values ​​of each variable are randomly assigned as X0 = [1300,40,350,820,40,25,9,18,100,200,19].

[0117] S03: The optimization objectives for steel-concrete composite section parameter design are higher load-bearing capacity, smaller interface slip, and lower engineering cost for inclined columns. An optimization objective function is constructed. Initial coefficients are introduced to eliminate dimensional differences between different calculation formulas. To achieve simultaneous optimization of multiple objectives, linear weighting coefficients are introduced when constructing the objective function. The specific formula for the objective function is as follows:

[0118]

[0119] Where α is the cost weighting coefficient, which is 0.5; β is the bearing capacity weighting coefficient, which is 0.4; γ is the interface slip weighting coefficient, which is 0.1; C(x) is the engineering cost calculation formula; V(x) is the bearing capacity calculation formula; C0 is the initial value of engineering cost; V0 is the initial value of bearing capacity; S0 is the initial value of steel-concrete interface slip.

[0120] S04: The design optimization results of the steel-concrete composite column section must meet the code's requirements for section bearing capacity and structural integrity. Therefore, constraints for subsequent steps in calling the optimization algorithm are established based on the calculation formulas in the code. In composite structures, concrete can provide a certain degree of protection for the internal steel sections, meeting fire protection requirements and preventing large-scale concrete spalling before the column reaches its service life. Therefore, certain requirements are placed on the dimensions of both concrete and steel sections. Simultaneously, the steel content in the steel-concrete composite column must be appropriate. If the steel content is too low, the effect of the added steel sections cannot be fully realized, and the confinement effect of the concrete is weak; if the steel content is too high, it will increase construction difficulties and raise costs.

[0121] h w ≥100mm; b af ≥100mm

[0122] t af ≥8mm; t w ≥8mm

[0123]

[0124] The constraints for the construction requirements of longitudinal reinforcing bars are as follows:

[0125]

[0126] d s ≥16mm

[0127] n s ≥2

[0128] The constraints for stirrup construction requirements are as follows:

[0129]

[0130] s sv ≤min{400,b,15d s}

[0131] If the vertical spacing of shear studs is too small, concrete cracking will first occur at the location where the shear studs are placed, which will have an adverse effect on the load-bearing performance of the column; if the vertical spacing of shear studs is too large, it will not be able to effectively suppress the extension of slip at the steel-concrete interface

[55] . Therefore, the requirements for the spacing and diameter of shear studs are as follows.

[0132] 6d≤d ss ≤300mm

[0133] 19mm≤d≤22mm

[0134] S05: Using S04 as the optimization constraint, an improved genetic algorithm is selected to solve the optimization objective function of S03. The system parameters of the improved genetic algorithm are set, including the number of individuals in the population N = 100, the initial temperature T0 = 500℃, and the temperature decay factor. The crossover probability at multiple points is pc = 0.75, and the initial mutation probability is pm = 0.3. 100 individuals are randomly selected from each value range of S02 to form the initial population. Since the design parameters related to the inclined column section are all within a certain range and meet the requirements, a real-number encoding method is used to encode the generated initial population, and the fitness value of each individual in the population is calculated according to the objective function.

[0135] S06: An elite strategy is embedded into the selection process of a genetic algorithm, and a new selection operator is designed to replace the commonly used roulette wheel selection method. The individual with the highest fitness value in the initial population is directly copied into the offspring population; from the remaining individuals, a random individual is selected, and if that individual's fitness value ranks in the top 30%, it is selected using P... top The individual is selected with a probability of 0.8; if the individual's fitness value ranks between 31% and 60%, the individual is selected with a probability of P. med Select the individual with a probability of 0.5; otherwise, select the individual with a probability of P. low The individual is selected with a probability of 0.2. Unselected individuals are returned to the initial population.

[0136] S07: Due to the large number of parameters requiring design optimization and their interrelationships, a multi-point crossover operator is used in the algorithm. First, the number of points to be crossed is randomly selected, then the points where two parent individuals are crossed are selected, and finally the crossover is completed.

[0137] S08: Considering that mutation operations are highly likely to lose superior individuals, the mutation probability and mutation method in the basic genetic algorithm have been modified. During evolution, the mutation probability decreases as the average fitness of the population increases. Based on the average fitness value of the first-generation population and the initial mutation probability, the mutation probability decreases by 10% for every 50% increase in fitness value. Simultaneously, a perturbation formula is used instead of the mutation operator for mutation operations, and the state acceptance probability criterion is used to determine whether an individual accepts the perturbation and enters the offspring population. The improved mutation method can both retain superior individuals and improve population diversity. The perturbation formula is as follows:

[0138] m i '=m i +y i (m imax -m imin )

[0139]

[0140] Where, mi The value is the unperturbed value; m′ i The value after perturbation; sign is the sign function; u is a random number uniformly distributed on [0,1]; Tk is the system temperature value; y is the attenuation factor. i m has no practical meaning imax and m imin These are the upper and lower limits of the disturbance, respectively.

[0141] S09: The state acceptance probability criterion determines whether to accept the perturbed individual into the offspring population by comparing the fitness values ​​of the individual before and after the perturbation. If the fitness value of the perturbed individual is higher, it is accepted into the population; if the fitness value of the perturbed individual is lower, its probability of being accepted by the population, p, is calculated according to the following formula. If p is less than a random number between [0,1], the perturbed individual is accepted; otherwise, the individual before the perturbation is retained.

[0142]

[0143] Among them, f i denoted as denoted as the difference in the individual's objective function before and after the perturbation; p is the probability that the individual is accepted.

[0144] S10: When the fitness value of the best individual in the offspring population no longer increases for consecutive Niter generations, the algorithm terminates, and the individual with the highest fitness value in the final offspring population is output as the approximate optimal solution. This optimal solution is the optimal value of the design parameter X for the steel-concrete composite inclined column section. The optimal value of X is X opt =[1250,34,250,774,38,28,8,20,60,150,19].

[0145] To verify the accuracy and reliability of the improved genetic algorithm for global optimization proposed in this invention, implementation case 1 of this invention was optimized using a basic genetic algorithm, and the optimization performance of the basic genetic algorithm and the improved genetic algorithm proposed in this invention was compared. The optimal value X obtained after optimization by the basic genetic algorithm was... opt = [1250,36,300,770,40,25,9,20,80,160,19]. The evolutionary comparison diagrams of the load-bearing capacity, maximum interface slip, and engineering cost of the two genetic evolutionary algorithms during the optimization process are shown below. Figure 2 , Figure 3 and Figure 4 As shown.

[0146] As can be seen from the comparison results, the improved genetic algorithm has higher computational accuracy and faster convergence speed. Using the improved genetic algorithm for design optimization can yield cross-sectional design parameters with higher load-bearing capacity, smaller interface slippage, and lower engineering cost.

[0147] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for optimizing the design parameters of steel-concrete composite inclined columns, characterized in that: Includes the following steps: S01: Based on the optimization objective of the steel-concrete inclined column section with shear studs, the optimization variable X is determined, and the expression is as follows: X=[b,t w ,b af ,h w ,t af ,d s ,n s ,d sv ,s sv ,d ss ,d]; (1) Where b is the side length of the square cross section, t w b is the thickness of the web of the steel section. af h is the flange length of the steel section. w t is the web height. af d is the flange width. s n is the diameter of the longitudinal reinforcing bar. s d represents the number of longitudinal reinforcing bars. sv s is the diameter of the stirrup. sv d represents the stirrup spacing. ss d represents the vertical spacing of the shear studs, and d represents the diameter of the shear studs. S02: Determine the upper limit of the value X for variable X max And the lower limit of the value X min To clarify the feasible region of the variables, and within the feasible region, to obtain the initial value X0 of each variable in X; The upper limit of the value of X is as follows: X max =[b max ,t w max ,b af max ,h w max ,t af max ,d s max ,n s max ,d sv max ,s sv max ,d ss max ,d max ];(2) The lower bounds for the value of X are as follows: X min =[b min ,t w min ,b af min ,h w min ,t af min ,d s min ,n s min ,d sv min ,s sv min ,d ss min ,d min ];(3) X0 is represented as follows: X0=[b 0 , p w 0 ,b af 0 , h w 0 , p af 0 ,d s 0 ,n s 0 ,d sv 0 , s sv 0 ,d ss 0 ,d 0 ];(4) S03: After introducing linear weighting coefficients into X, construct the optimization objective function, the specific expression of which is as follows: Where α is the cost weighting coefficient; β is the bearing capacity weighting coefficient; γ is the interface slip weighting coefficient; C(x) is the engineering cost calculation formula; V(x) is the bearing capacity calculation formula; S(x) is the steel-concrete interface slip calculation formula; C0 is the initial value of engineering cost; V0 is the initial value of bearing capacity; S0 is the initial value of steel-concrete interface slip. S04: Apply conditional constraints to each optimization variable according to the specification requirements. The specific constraints are as follows: The dimensional constraints for concrete and steel sections are as follows: The constraints for the construction requirements of longitudinal reinforcing bars are as follows: The constraints for stirrup construction requirements are as follows: The constraints on the spacing and diameter requirements of shear studs are as follows: 6d≤d ss ≤d ss max ;d min ≤d≤d max ;(9) Where r represents The feasible range of values; S05: Establish an initial population and calculate the fitness value of each individual in the initial population using the optimization objective function. The individual is a parameter contained in the optimization variable X and its value conforms to the upper and lower limits of the parameter. The elite strategy is embedded into the selection of the existing genetic algorithm model, that is, the new selection operator replaces the roulette wheel selection method to obtain the improved genetic algorithm model and initialize the model. The elite strategy is the existing technology. S06: For the fitness value of each individual obtained, the offspring population is calculated using the improved genetic algorithm; S07: Perform chromosome crossover and mutation operations: S071: Randomly select the number of points for crossover between parent individuals, then select two points for crossover between parent individuals, and use the multi-point crossover operator to complete the crossover calculation. S072: Use the perturbation formula instead of the mutation operator to perform the mutation operation. The specific calculation formula is as follows: m i '=m i +y i (m imax -m imin );(10) Where, m i The value is the unperturbed value; m' i The value after perturbation; sign is the sign function; u is a random number uniformly distributed on [0,1]; T k This refers to the system temperature value. T0 represents the initial temperature value, where T is the attenuation factor. S08: Calculate the probability of being accepted by the population, the specific expression is as follows: Among them, f i p represents the difference in the individual's objective function before and after the perturbation; p is the probability that the individual is accepted. If the fitness value of an individual after perturbation is high, then the individual after perturbation is accepted into the population; if the fitness value of an individual after perturbation is low, then the probability p of being accepted by the population is calculated according to formula (13). If p is less than a random number between [0,1], then the individual after perturbation is accepted; otherwise, the individual before perturbation is retained. S09: Determine whether the improved genetic algorithm has ended. When the fitness value of the best individual in the offspring population no longer increases for N consecutive generations, terminate the algorithm and output the individual with the highest fitness value in the final offspring population as the approximate optimal solution. This approximate optimal solution is the optimal value of the design parameter X of the steel-concrete inclined column section.

2. The method for optimizing the design parameters of a steel-concrete composite inclined column as described in claim 1, characterized in that: The specific steps in S05 for establishing a population and calculating the fitness value of each individual in the initial population using the optimization objective function are as follows: S051: Set the values ​​for each system parameter of the improved genetic algorithm, including the number of individuals N in the population, the initial temperature T0, and the temperature decay factor. Individual multi-point crossover probability p c The initial mutation probability p of an individual m ; S052: Randomly select N groups of individuals from the upper and lower limits of each parameter in S02 to form the initial population; S053: Use real number encoding to encode the initial population, and then use the optimization objective function to calculate the fitness value of each individual in the initial population.

3. The method for optimizing the design parameters of a steel-concrete composite inclined column as described in claim 2, characterized in that: The specific steps in S06 to calculate the offspring population using the improved genetic algorithm are as follows: S061: Sort the obtained fitness values ​​in descending order, and select the individual in the initial population corresponding to the highest fitness value to be added to the offspring population; S062: For individuals with fitness values ​​other than the highest fitness value: Randomly select the remaining fitness values. If the fitness value ranks in the top 30%, then use P... top The individual corresponding to the fitness value is selected with a probability and added to the offspring population; if it is not selected, it is returned to the initial population. If the fitness value ranks between 31% and 60%, then use P. med The individual corresponding to the fitness value is selected with a probability and added to the offspring population; if it is not selected, it is returned to the initial population. If the fitness value ranks between 61% and 100%, then use P... low The individual with the fitness value is selected with a certain probability and added to the offspring population; if the individual is not selected, it is returned to the initial population. S063: Iterate through all fitness values, repeat S062, and obtain the final offspring population.

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