CN-121997770-A - Anchor buckling cable force optimization method based on improved second-generation genetic algorithm

CN121997770ACN 121997770 ACN121997770 ACN 121997770ACN-121997770-A

Abstract

The invention relates to the technical field of evolutionary algorithms, in particular to a cable force optimization method of a buckle and anchor cable based on an improved second-generation genetic algorithm, which comprises the following steps of obtaining cable force scheme data, calculating the square sum of eccentricity and the overstretched cubic sum of stress, and comparing the dominant relations and grading, assigning grades to the combined population to fill the new population, calling the kernel density estimation screening if the number exceeds the limit, and finally generating offspring by Gray code coding, crossing and self-adaptive variation of the new population. According to the invention, a multi-objective function of cable force optimization is constructed by calculating the square sum of eccentricity in an operation period and the overstretched cubic sum of stress in a construction period, construction safety and operation performance are balanced, then a non-dominant sorting mechanism is adopted to screen individuals, a kernel density estimation function is utilized to evaluate population crowding degree, a solution set of diversity is reserved, the algorithm is prevented from sinking into local optimum, finally Gray code coding and self-adaptive mutation rate changing along with iteration algebra are combined, robustness and convergence efficiency of searching are enhanced, and a more balanced anchor cable prestress configuration scheme is obtained.

Inventors

ZHANG ZUJUN
PENG WENPING
ZENG GUOLIANG
TIAN ZHONGCHU
LIN YIXIN
FENG ZHIXIAN
LONG JINHUA

Assignees

湖南文理学院

Dates

Publication Date: 20260508
Application Date: 20260225

Claims (10)

1. The anchor cable buckling force optimization method based on the improved second-generation genetic algorithm is characterized by comprising the following steps of: S1, obtaining a maximum tensile stress value in a construction period, a bending moment value in an operation period, an axial force value in the operation period and a reference value of an allowable upper limit of the maximum tensile stress in the construction period of an individual cable force scheme, calculating section eccentricity, obtaining an eccentric distance square sum in the operation period, and calculating an exceeding part of the reference value exceeding the allowable upper limit of the maximum tensile stress in the construction period to obtain an overrun cubic sum of the stress in the construction period; S2, based on the square sum of the eccentricity in the operation period and the overlimit cubic sum of the stress in the construction period, comparing the two-by-two dominance relation of the individual cable force scheme, screening an unordinated individual set as a first grade, and repeating screening until a grade value is given; S3, assigning the grade value to a combined population formed by father cable force scheme individuals and child cable force scheme individuals, filling a new population, when the number of cable force scheme individuals of a certain grade exceeds the number of the remaining space, calling a nuclear density estimation function to obtain a nuclear density estimated value, and screening the lowest nuclear density estimated value to fill the number of the remaining space; S4, executing Gray code coding on the individual with the cable force scheme in the new population, executing cross operation to generate a child numerical sequence, obtaining iteration algebra, calculating self-adaptive mutation rate, and perturbing the child numerical sequence to generate the individual with the cable force scheme.
2. The improved second generation genetic algorithm-based anchor line buckling and pulling force optimization method according to claim 1, wherein the square sum of eccentricity in the operation period specifically refers to an objective function value representing long-term structural eccentricity in the operation period, the stress overrun cube in the construction period specifically refers to a penalty function value representing instantaneous stress safety in the construction period, the grade value specifically refers to pareto front-edge level identification of an individual cable force scheme, the nuclear density estimated value specifically refers to a scalar value representing sparsity of the individual cable force scheme distributed in a normalized objective space, the child value sequence specifically refers to a cable force parameter sequence obtained through Gray code coding and cross operation combination, the adaptive mutation rate specifically refers to a mutation probability value decreasing along with the increase of iteration algebra, and the child cable force scheme individual comprises a group of anchor line buckling and pulling force initial tensile values generated through decoding after mutation perturbation.
3. The method for optimizing the cable force of the anchor cable based on the improved second-generation genetic algorithm according to claim 2, wherein the step of obtaining S1 is specifically: S101, acquiring a maximum tensile stress value, an operation period bending moment value, an operation period axial force value and a reference value of a maximum tensile stress allowable upper limit of an operation period of a cable force scheme individual, and aggregating four types of numerical data to establish an initial cable force state matrix; S102, based on the initial cable force state matrix, calling the bending moment value in the operation period and the axial force value in the operation period, and aiming at each corresponding section in the cable force scheme, executing numerical calculation by dividing the bending moment value in the operation period by the axial force value in the operation period to obtain section eccentricity and generating a section eccentricity vector; S103, square operation is carried out one by one on a plurality of element values in the section eccentricity vector to obtain multi-section eccentricity square values, all the section eccentricity square values are aggregated, and summation calculation is carried out on an aggregation result to obtain an operation period eccentricity square sum; S104, calling the maximum tensile stress value of the construction period and the standard value of the maximum tensile stress allowable upper limit of the construction period in the initial cable force state matrix, traversing all the maximum tensile stress values of the construction period, executing subtraction operation, judging and extracting the stress overrun part exceeding the standard value of the maximum tensile stress allowable upper limit of the construction period, executing cubic operation on all the stress overrun part values, aggregating all the cubic operation results and summing to generate the stress overrun cubic sum of the construction period.
4. The improved second generation genetic algorithm-based anchor line buckling cable force optimization method according to claim 3, wherein the step of obtaining the grade value is specifically as follows: S201, acquiring an individual set of all cable force schemes, and calling the square sum of the eccentricity of each cable force scheme and the overlimit cube sum of the stress of the construction period, constructing an individual target value matrix of the cable force schemes, traversing the matrix to execute pairwise comparison between any two cable force scheme individuals, judging the dominant and dominant states between the individuals, and generating an individual dominant relation identification set; S202, according to the individual dominance relation identification set, initializing a grade counter to be one, searching all cable force scheme individuals, screening individuals which are not dominated by any other cable force scheme individuals in the individual dominance relation identification set, establishing a first grade non-dominated individual set, and endowing the grade counter value to all cable force scheme individuals in the set to obtain a first grade cable force scheme set; S203, aiming at the rest cable force scheme individuals except the first grade cable force scheme set, forming a pending grade set, increasing the grade counter value, repeatedly calling the individual dominance relation identification set in the pending grade set to execute screening, endowing the increased grade counter value until the pending grade set is empty, establishing indexes of all cable force scheme individuals and corresponding grade identifications thereof, and obtaining the grade value.
5. The improved second generation genetic algorithm based anchor line buckling cable force optimization method according to claim 4, wherein the step of filling the new population is specifically as follows: S301, acquiring a father cable force scheme individual set and a child cable force scheme individual set, aggregating the two sets to construct a combined population, initializing an empty new population and acquiring a preset capacity value, and setting the empty new population as an initial residual empty number; S302, calling the square sum of the eccentricity of the corresponding operation period and the overlimit cubic sum of the stress of the construction period aiming at all cable force scheme individuals in the combined population, executing the determination of the dominant relationship, screening the set of the non-dominant individuals, repeatedly screening the rest cable force scheme individuals, increasing the grade value, and establishing the combined population grade index; S303, according to the combined population grade index, searching individuals in the combined population from an increment according to the grade value, judging whether the number of individuals at the current grade exceeds the initial residual space number, if not, filling all the individuals at the cable force scheme of the grade into the empty new population, and subtracting the number from the initial residual space number to obtain an updated residual space number; S304, if the number of individuals in the current level is judged to exceed the updated number of the remaining space bits, a kernel density estimation function is called, kernel density estimation values of all the cable force scheme individuals in the level are calculated, the cable force scheme individuals with the number corresponding to the updated number of the remaining space bits are selected according to the sequence from low to high of the kernel density estimation values, the empty population is filled, and a new population is obtained.
6. The improved second generation genetic algorithm-based anchor line buckling cable force optimization method according to claim 5, wherein the step of obtaining the individual child cable force scheme is specifically as follows: S401, traversing all cable force scheme individuals in the new population based on the new population, extracting a plurality of decision variable values of the cable force scheme individuals, executing Gray code conversion operation on each decision variable value, generating a corresponding binary Gray code coding sequence, aggregating all binary Gray code coding sequences, and establishing a Gray code coding population; S402, selecting a parent binary Gray code sequence pair according to a preset pairing rule from the Gray code population, randomly setting a crossing point position, executing gene segment exchange of the parent binary Gray code sequence pair after the crossing point position, and recombining the parent binary Gray code sequence pair to generate a child numerical sequence; S403, acquiring a current iteration algebra and a preset maximum iteration algebra, executing the operation of dividing the current iteration algebra by the preset maximum iteration algebra ratio to acquire an iteration process proportion, substituting the iteration process proportion into a preset nonlinear decreasing function, and generating a self-adaptive mutation rate by combining initial mutation rate parameter calculation; S404, aiming at the child numerical value sequence, calling the self-adaptive variation rate as a disturbance probability reference, traversing all gene loci in the child numerical value sequence, judging and executing locus turning disturbance to generate a mutated numerical value sequence, then executing Gray code reverse decoding conversion on the mutated numerical value sequence, recovering the decision variable value, and obtaining a child cable force scheme individual.
7. The improved second generation genetic algorithm-based anchor line buckling cable force optimization method according to claim 5, wherein the calculation mode of the nuclear density estimated value is specifically as follows: Acquiring the square sum of the eccentricities of all the cable force scheme individuals in the same grade and the stress overrun cubic sum of the construction period to form an objective function value set; normalizing the objective function value set to obtain a normalized objective vector set; for any individual cable force scheme to be calculated, the estimated value of the nuclear density of the individual cable force scheme is calculated by the following formula: Calculating to obtain; Wherein, the Is the first Nuclear density estimates for individual ones of the cable force protocols, For the total number of individual cable force protocol units in the current class, And Respectively the first And (b) Normalized target vectors corresponding to the individual cable force schemes, For a preset bandwidth matrix to be used, As a multi-element gaussian kernel function, And Index identification for individual cable force schemes within the current level.
8. The improved second generation genetic algorithm-based anchor line buckling cable force optimization method according to claim 6, wherein the adaptive mutation rate is calculated in the following specific manner: Acquiring the current iteration algebra, the preset maximum iteration algebra, a preset initial mutation rate and a preset minimum mutation rate; Substituting the obtained four values into a nonlinear decreasing function: Calculating to generate the self-adaptive variation rate; Wherein, the For the said rate of variation to be adapted, For the predetermined initial rate of variation to be set, For the predetermined minimum rate of variation, For the current iteration number of the set, For the preset maximum number of iteration algebra, To control the nonlinear adjustment coefficient of the variation rate attenuation rate.
9. The improved second generation genetic algorithm-based anchor line buckling cable force optimization method according to claim 4, wherein the determination criteria of the dominant and dominated states among individuals are specifically as follows: randomly selecting a first rope force scheme individual and a second rope force scheme individual from the rope force scheme individual target value matrix; Acquiring a first operation period eccentricity square sum and a first construction period stress overrun cube sum corresponding to the first cable force scheme individual, and a second operation period eccentricity square sum and a second construction period stress overrun cube sum corresponding to the second cable force scheme individual; When the first operation period eccentricity square sum is smaller than or equal to the second operation period eccentricity square sum and the first construction period stress overrun cubic sum is smaller than or equal to the second construction period stress overrun cubic sum, judging that the first cable force scheme individual and the second cable force scheme individual are in a non-dominant relationship; and on the basis of meeting the non-dominant relationship, if the first operational period eccentricity square sum is smaller than the second operational period eccentricity square sum or the first construction period stress overrun cubic sum is smaller than the second construction period stress overrun cubic sum, determining that the first cable force scheme individual dominates the second cable force scheme individual.
10. The improved second generation genetic algorithm-based anchor line buckling cable force optimization method according to claim 6, wherein the specific implementation manner of the crossing operation is as follows: randomly selecting a first parent binary Gray code sequence and a second parent binary Gray code sequence from the Gray code coding population; acquiring the sequence length of the first parent binary Gray code coding sequence, and generating a random integer as an intersection point in the range of the sequence length; exchanging all gene segments of the first parent binary gray code coding sequence after the intersection with all gene segments of the second parent binary gray code coding sequence after the intersection; And recombining the part of the first parent binary Gray code coding sequence before the intersection with the exchanged second parent gene segment to generate a first child numerical sequence, and recombining the part of the second parent binary Gray code coding sequence before the intersection with the exchanged first parent gene segment to generate a second child numerical sequence.

Description

Anchor buckling cable force optimization method based on improved second-generation genetic algorithm Technical Field The invention relates to the technical field of evolutionary algorithms, in particular to a cable force optimization method of a buckle and anchor cable based on an improved second-generation genetic algorithm. Background The technical field of evolutionary algorithm relates to a calculation method inspired by natural selection and biological evolution. The core matters in the field comprise specific implementations of genetic algorithm, genetic programming, evolution strategy and the like, and the specific implementations are used for iteratively searching the solution by simulating operations such as selection, crossover, variation and the like in the biological evolution process. The technical field is mainly used for solving the complex optimization problem, and particularly searching a feasible solution or an optimal solution in a high-dimensional, nonlinear or multi-peak search space. The traditional anchor cable buckling force optimization method is used for determining the prestress of the anchor cable in the anchoring engineering by the pointer. In conventional practice, cable force optimization typically relies on an established mechanical analytical model or a simplified computational model, and is estimated in conjunction with engineering empirical formulas. Part of the methods also adopt numerical simulation means, such as finite element analysis, to simulate the combined action of the anchor cable and the structure, or use a linear programming algorithm to solve the cable force distribution under the given constraint condition. The existing anchor cable force buckling optimization method is particularly difficult to effectively process nonlinear balance relation between multiple performance indexes in a construction period and an operation period by means of simplifying a mechanical model or linear programming, an optimization target is usually excessively simplified, construction stress control and long-term structure eccentric stress are difficult to be considered, in addition, the traditional estimation method or basic numerical simulation is easily influenced by parameter setting when facing a high-dimensional complex search space, and falls into a local optimal solution, and a sufficiently diversified high-performance cable force scheme set cannot be provided, so that the final selection depends on excessive engineering experience and lacks a global field of view. Disclosure of Invention The invention aims to solve the defects in the prior art, and provides a buckle anchor cable force optimization method based on an improved second-generation genetic algorithm. In order to achieve the purpose, the invention adopts the following technical scheme that the buckle anchor cable force optimization method based on the improved second generation genetic algorithm comprises the following steps: S1, obtaining a maximum tensile stress value in a construction period, a bending moment value in an operation period, an axial force value in the operation period and a reference value of an allowable upper limit of the maximum tensile stress in the construction period of an individual cable force scheme, calculating section eccentricity, obtaining an eccentric distance square sum in the operation period, and calculating an exceeding part of the reference value exceeding the allowable upper limit of the maximum tensile stress in the construction period to obtain an overrun cubic sum of the stress in the construction period; S2, based on the square sum of the eccentricity in the operation period and the overlimit cubic sum of the stress in the construction period, comparing the two-by-two dominance relation of the individual cable force scheme, screening an unordinated individual set as a first grade, and repeating screening until a grade value is given; S3, assigning the grade value to a combined population formed by father cable force scheme individuals and child cable force scheme individuals, filling a new population, when the number of cable force scheme individuals of a certain grade exceeds the number of the remaining space, calling a nuclear density estimation function to obtain a nuclear density estimated value, and screening the lowest nuclear density estimated value to fill the number of the remaining space; S4, executing Gray code coding on the individual with the cable force scheme in the new population, executing cross operation to generate a child numerical sequence, obtaining iteration algebra, calculating self-adaptive mutation rate, and perturbing the child numerical sequence to generate the individual with the cable force scheme. As a further scheme of the invention, the square sum of the eccentricity in the operation period specifically refers to an objective function value representing the eccentricity of a long-term structure in the operation period, the stress overrun c