CN115630427B - Comprehensive intelligent optimization method for multiple design variables of cable-stayed bridge in bridge forming state - Google Patents

Comprehensive intelligent optimization method for multiple design variables of cable-stayed bridge in bridge forming state Download PDF

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CN115630427B
CN115630427B CN202211319591.XA CN202211319591A CN115630427B CN 115630427 B CN115630427 B CN 115630427B CN 202211319591 A CN202211319591 A CN 202211319591A CN 115630427 B CN115630427 B CN 115630427B
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张鹤
郭祎晖
孙良凤
薛锟
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Abstract

The invention discloses a comprehensive intelligent optimization method for multiple design variables of a cable-stayed bridge in a bridge forming state, which comprises the following steps: establishing a full-bridge finite element model based on a cable-stayed bridge construction design drawing; determining a global design variable to form an adjustment vector X; determining an optimization target to form a regulated vector Y; determining an influence matrix C of the adjustment vector and the adjustment vector to obtain a corresponding relation of the multiple design variables and the multiple optimization targets as CX=Y; determining constraint conditions; establishing an adaptability function; initializing a design variable; and (5) carrying out optimization iteration by adopting an improved genetic algorithm to finish optimization. According to the bridge formation state optimization method, design variables are selected according to actual conditions in the bridge formation state optimization process, and only bridge formation cable force is not needed to be used as the design variables, so that the optimization space of the bridge formation state is expanded, the related fitness function construction method simplifies the bridge formation state optimization problem of multiple optimization targets and multiple constraint conditions, and the constructed fitness function is reasonable and standard, so that the optimization effect of an intelligent algorithm is improved.

Description

Comprehensive intelligent optimization method for multiple design variables of cable-stayed bridge in bridge forming state
Technical Field
The invention relates to the technical field of bridge engineering, in particular to a comprehensive intelligent optimization method for multiple design variables of a cable-stayed bridge in a bridge forming state.
Background
The cable-stayed bridge is a high-order hyperstatic structure consisting of a bridge tower, a main girder and stay cables, and the reasonable bridge formation state is taken as a target in the design process. The reasonable bridge forming state means that the main girder is under the constant load effect of the bridge forming, the internal force of the bridge tower is uniformly distributed, the bridge is smooth in line shape, and the cable force of the cable-stayed bridge is uniformly changed, so that the safety of the bridge structure is guaranteed, and the economic benefit is improved. Therefore, the optimization of the bridge formation state of the cable-stayed bridge is a critical ring in the design process of the cable-stayed bridge.
It is currently widely accepted that stay cable forces are the primary factor affecting the bridge formation of a cable-stayed bridge given the structural system and constant load distribution. In order to ensure that the cable-stayed bridge reaches a reasonable bridge forming state, the bridge forming force of the cable-stayed bridge is used as a design variable to optimally design the reasonable bridge forming state. However, with increasingly diverse structural forms and construction methods of cable-stayed bridges, other factors besides the bridge-forming forces can also have a great influence on the bridge-forming state. Taking a common cable-stayed bridge with different independent towers as an example, in order to balance the horizontal load of the bridge tower and eliminate the negative reaction force of the side span support, a sufficient amount of concrete weights are usually arranged on the side span, and the weights are sufficient to cause great influence on the internal force of the bridge, and the influence of different load distribution modes on the internal force of the bridge is also quite different. More importantly, the arrangement scheme of the concrete weights can be easily adjusted in the construction process, so that the concrete weights have a large optimization space. The current bridge-forming state optimization methods usually only use bridge-forming cable forces as design variables, and although the principle is concise, the optimization potential of other influencing factors is ignored, so that the calculation result may be difficult for the cable-stayed bridge to reach the most reasonable bridge-forming state.
The optimization problem of the bridge formation state of the cable-stayed bridge is converted into a mathematical optimization model, and an intelligent algorithm is introduced to carry out iterative solution, so that researches and applications to a certain extent are already obtained at present. Compared with the traditional optimization method, the intelligent optimization algorithm directly optimizes the fitness when performing optimization design, and does not need to display specific relations between the expression design variables and the objective functions. The proper fitness function can obviously improve the optimization efficiency of the algorithm and even avoid sinking into a local optimal solution. However, for complex optimization problems, such as multiple types of design variables, multiple optimization objectives, constraints, etc., the problem of constructing fitness functions still needs to be further refined and improved.
The genetic algorithm is a global optimization probability search method formed by simulating natural selection and genetic mechanism, and has many applications in the bridge state optimization problem. However, the conventional genetic algorithm still has the following problems:
(1) Population evolution is typically a probabilistic selection strategy based on individual fitness values, and this single selection strategy results in even the best quality population being likely to be rejected at the beginning of the evolution, resulting in a decrease in the average fitness value of the population, reducing the computational efficiency of the algorithm.
(2) The later quality of the population in the genetic algorithm is greatly influenced by the initial population quality and the earlier population quality, and if the initial population quality is poor or the earlier population is dysplasia, the later quality of the population is difficult to effectively improve, so that the algorithm is easy to fall into local optimum in the later period of evolution.
Disclosure of Invention
The invention provides a comprehensive intelligent optimization method for multiple design variables of a cable-stayed bridge in a bridge forming state, which can take Cheng Qiaosuo force and side span weight load distribution of the cable-stayed bridge as design variables, take minimization of girder bending strain energy and maximization of side span support counter force as optimization targets, establish corresponding relations between different types of design variables and optimization targets through a generalized influence matrix theory, and establish a proper fitness function through a next construction method and a punishment function method. In order to improve algorithm efficiency, genetic algorithm is improved, and a joint selection strategy based on probability selection and excellent individual retention is firstly provided for a selection strategy; then, a method of combining a genetic algorithm and an artificial bee colony algorithm is provided for solving the problem that the genetic algorithm is easy to fall into local optimum in the later stage, and the artificial bee colony algorithm further optimizes the solution set after the first half-path optimization, so that the global searching capability of the algorithm is improved due to the existence of a scout bee random searching mechanism, and the probability of falling into local optimum is reduced. And directly carrying out optimization iteration on the fitness function by using an improved genetic algorithm, and providing a global optimal solution for the reasonable bridge formation state of the cable-stayed bridge.
The invention realizes the aim through the following technical scheme:
a comprehensive intelligent optimization method for multiple design variables of a cable-stayed bridge in a bridge forming state comprises the following steps:
step one: establishing a full-bridge finite element model based on a cable-stayed bridge construction design drawing;
step two: determining a global design variable to form an adjustment vector X; determining an optimization target to form a regulated vector Y;
taking the optimization coefficients of the bridge girder forming force and the compression weight as design variables, and simultaneously taking the constant load of the girder into consideration to obtain the adjustment vector X; taking the bending strain energy of the main beam as a main optimization target, and taking the counter force maximization of the side span support as a secondary optimization target to obtain the bending strain energy of each section of the main beam and the regulated vector Y;
step three: determining an influence matrix C of the adjustment vector and the adjustment vector to obtain a corresponding relation of the multiple design variables and the multiple optimization targets as CX=Y;
step four: determining constraint conditions;
step five: establishing an adaptability function;
the bending strain energy and the support counter force are respectively processed by adopting the following construction method, so that an adaptability sub-function representing the bending strain energy and an adaptability sub-function representing the support counter force are obtained; the fitness function takes the sum of the fitness subfunctions, and introduces the constraint conditions in the fourth step by using a penalty function method to obtain a final fitness function;
step six: initializing a design variable;
calculating to obtain initial bridge forming cable force and initial weight, substituting the initial bridge forming cable force and the initial weight into the finite element model, obtaining initial bending strain energy and initial side span support counter force, and further obtaining an initial value of an fitness function;
step seven: adopting a genetic algorithm to carry out optimization iteration;
and (3) adopting a genetic algorithm, carrying out iterative optimization by taking the maximum fitness function as an optimization target, and finally obtaining a group of solutions to ensure that the cable-stayed bridge reaches a global optimal bridge forming state to finish optimization.
Further, the forming of the adjusted vector X and the adjusted vector Y in the second step is achieved by the following sub-steps:
(2.1) for a cable-stayed bridge considering the weight arrangement, assuming that the full bridge has p or opposite stayed cables, the initial bridging cable force is T i 0 I=1, 2, …, p; the concrete weight on the side span girder is divided into q equal sections along the girder direction, and the initial weight of each section is as follows
Figure BDA0003909772270000031
j=1, 2, …, q; with said bridging cable force and said weightAnd taking the optimization coefficient of the weight as a design variable, and considering the constant load of the main beam, wherein the adjustment vector is as follows:
X n,1 ＝{g 0 ,x 1 ,x 2 ,…,x p ,y 1 ,y 2 ,…,y q } T (1)
x i ＝T i /T i 0 (2)
Figure BDA0003909772270000032
/>
wherein n=1+p+q is the sum of the tuning vector elements; g 0 The constant load coefficient of the main beam is a constant 1, namely the main beam constant load does not participate in optimization iteration; x is x i To optimize the coefficient of the bridge forming cable force, T i The bridge forming cable force is optimized; y is j Optimization coefficient for weight-on-weight, W j Weight is collected for the optimized pressure;
(2.2) taking the bending strain energy of the main girder as a main optimization target and the counter force of the side span support as a secondary optimization target according to the actual condition of the cable-stayed bridge; the girder bending strain energy U is expressed as:
Figure BDA0003909772270000033
wherein r represents the number of key sections taken along the main beam; m is M k Representing the bending moment of the kth section of the main beam, M k+1 Representing the bending moment of the k+1th section of the main beam, l k Representing the length between two adjacent sections E k Represents the modulus of elasticity between adjacent sections, I k Represents the moment of inertia between two adjacent cross-sections, where k=1, 2, …, r;
the regulated vector is:
Y m,1 ＝{M 1 ,M 2 ,…,M r ,R 1 ,R 2 } T (5)
wherein R is 1 Representing the reaction force of a main span transition pier support, R 2 Representing side span transition piersA support counter force; m=r+2, m representing the sum of the tuned vector elements.
Further, the formation of the influence matrix C of the tuning vector-tuning vector in the third step is achieved by the following sub-steps:
applying a unit force of 1 to each or each pair of inhaul cables in turn to obtain girder bending moment response
Figure BDA0003909772270000034
Support reaction response->
Figure BDA0003909772270000041
Thereby constructing an influence matrix C of bridge cable force on the regulated vector x The method comprises the steps of carrying out a first treatment on the surface of the Applying unit weight-collecting "1" to each section of concrete weight in turn to obtain girder bending moment response
Figure BDA0003909772270000042
Support reaction response->
Figure BDA0003909772270000043
And then construct the influence matrix C of the compression weight set weight on the regulated vector y The method comprises the steps of carrying out a first treatment on the surface of the Simultaneously, calculating the girder bending moment response under the action of the girder constant load +.>
Figure BDA0003909772270000044
Support reaction response->
Figure BDA0003909772270000045
Thereby constructing an influence matrix C of the constant load of the main beam on the regulated vector g ；
The influence matrix C of the modulation vector-modulated vector is represented by matrix C g 、C x 、C y The method comprises the following steps:
Figure BDA0003909772270000046
wherein C is m,n Representing the size of the mth structural response caused by the nth applied vector element, the offset vector element being dominantLiang Hengzai or bridge forming cable force or compression weight, wherein the structural response is girder bending moment response or support counter force response;
at this time, the correspondence between the offset vector and the adjusted vector is:
C m,n X n,1 ＝Y m,1 (7)。
further, the constraint includes: the difference between adjacent cable forces is smaller than the allowable value of the non-uniform coefficient of the cable force; the maximum difference of the cable force is smaller than Yu Suoli; each segment weight set is less than a weight set weight allowed value; the support reaction force does not exceed the support bearing capacity limit.
Further, the fifth step is specifically implemented by the following substeps:
the bending strain energy U and the support counter force R are respectively processed by adopting the following construction method, and the support counter force R comprises a main span transition pier support counter force R 1 And side span transition pier support counter force R 2 ：
Figure BDA0003909772270000047
Figure BDA0003909772270000048
Wherein f U A fitness sub-function for characterizing the bending strain energy U; f (f) R To characterize the reaction force R of the main span transition pier support 1 Or the reaction force R of the side span transition pier support 2 Is a fitness sub-function of (1); -c 1 Is the lower bound of U, -c 2 For the lower bound of R, there is U.gtoreq.0, R.gtoreq.0, and thus c for the bending strain energy U and the support reaction R 1 ＝c 2 =0; said f U And f R The value ranges of (2) are all within the range of (0, 1);
the fitness function fitness is the sum of fitness subfunctions; for constraint conditions, introducing each constraint condition into a fitness function by adopting a penalty function method; the fitness function fitness is expressed as:
Figure BDA0003909772270000051
wherein K is a constraint condition penalty function, and is determined by each penalty function subitem;
Figure BDA0003909772270000052
wherein N represents the constraint number; k (K) c Is a sub-term of a penalty function, determined by a state variable, K c The specific expression of (2) is:
Figure BDA0003909772270000053
Figure BDA0003909772270000054
in delta c Is the state variable of the c-th constraint, S c Is the structural response of the c-th constraint, [ S ] c ]Is a structural response allowable value.
Further, the genetic algorithm adopted in the step seven is an improved genetic algorithm, and is specifically realized through the following substeps:
(7.1) at the initial bridle force T i 0 And initial pressure weight set weight
Figure BDA0003909772270000055
Performing random search around to form initial population, wherein the total number of population individuals is N pop ；
(7.2) calculating fitness function values of each individual in the population;
(7.3) performing replication, crossover and mutation operations on individuals of the population to form a new offspring population; wherein the mathematical expression of the selection strategy of the copy operation is as follows:
if the individual fitness function value meets the formula (14), directly taking the individual fitness function value as a new offspring population individual;
fitness u ≥fitness max -0.1×(fitness max -fitness min ) (14)
in the field of u (u＝1,2,…,N pop ) Representing individual fitness function values, fitness max Fitness function value representing the best quality individuals in this generation of population min The fitness function value of the individual with the worst quality in the first generation population is represented;
if the individual fitness function value does not satisfy equation (14), calculating the probability P that the individual is selected si Expressed as:
Figure BDA0003909772270000056
randomly generating a number g between 0 and 1, if P u If the weight is more than or equal to g, the individual is reserved, otherwise, the individual is eliminated;
(7.4) judging whether the iteration times are met, if the iteration times are not met, repeating the steps (7.2) and (7.3), and increasing the iteration times once; if the iteration times are met, entering a section of the artificial bee colony algorithm;
(7.5) optimizing the population by the former half-way algorithm to be used as an initial honey source of the artificial bee colony algorithm, and increasing the algorithm convergence difficulty when setting the parameters of the artificial bee colony algorithm due to the fact that the population is greatly optimized, and improving the generation probability of the scout bee so as to enhance the global searching capability; meanwhile, the number of honey sources of the artificial bee colony algorithm is the same as the number of population individuals of the genetic algorithm;
(7.6) carrying out neighborhood search on honey sources by bees, wherein the expression of the new honey sources is as follows:
Figure BDA0003909772270000061
in the method, in the process of the invention,
Figure BDA0003909772270000062
the v-th element (v=1, 2, …, n) representing the u-th old honey source and u' notequ; delta u,v A random number between 0 and 1;
then greedy selection is carried out, namely the fitness function values of the new honey source and the old honey source are compared, and the higher one is selected;
(7.7) observing the roulette to select honey sources, namely calculating fitness function values of the honey sources, performing probability selection according to the fitness function values by the observed bees according to a formula (15), and then performing neighborhood search and greedy selection according to a formula (16) near the honey sources;
(7.8) if the fitness function value of a honey source is not obviously improved under the condition of multiple updating, discarding the honey source, and generating a new honey source for random search of the scout bees to replace; simultaneously recording a solution set with the highest fitness function value in the current honey source as an optimal solution;
(7.9) judging whether the iteration times are met, if not, repeating the steps (7.6), (7.7) and (7.8), and increasing the iteration times once; if the iteration times are met, outputting the current recorded optimal solution as a global optimal solution, and completing optimization.
The beneficial effects of the invention are as follows:
(1) The comprehensive intelligent optimization method for the multiple design variables of the bridge formation state of the cable-stayed bridge can consider optimization of the multiple design variables, so that the design variables can be selected according to actual conditions in the optimization process of the bridge formation state without taking the bridge formation cable force as the design variables, the optimization space of the bridge formation state is expanded, and the probability of obtaining a global optimal solution is indirectly improved.
(2) In the optimization method, the provided fitness function construction method simplifies the multi-optimization target and multi-optimization condition optimization problem into the unconstrained single-optimization target optimization problem, and the constructed fitness function can be well combined with various intelligent algorithms to treat the bridging state optimization problem of the multi-optimization target and the constrained condition.
(3) The invention improves the selection strategy of the genetic algorithm, and increases the iterative speed of the algorithm in the early stage; and a combined genetic algorithm and an artificial bee colony algorithm are provided, so that the global optimizing capability of the algorithm in the latter half of calculation is improved. The improved genetic algorithm has the characteristics of high early iteration speed and high later global searching capability, and is excellent in the bridge state optimization problem of processing multiple types of design variables.
Drawings
FIG. 1 is a flow chart of a method for comprehensively and intelligently optimizing multiple design variables in a bridge formation state of a cable-stayed bridge.
Fig. 2 is a general layout of a cable-stayed bridge.
Fig. 3 is a full-bridge finite element model of a cable-stayed bridge.
Fig. 4 is a graph showing the displacement comparison of the main beams before and after optimization of a cable-stayed bridge.
Fig. 5 is a graph showing a comparison of bending moments of the main beams before and after optimization of a cable-stayed bridge.
Fig. 6 is a comparison of algorithm iterations.
Detailed Description
The objects and effects of the present invention will become more apparent from the following detailed description of the preferred embodiments and the accompanying drawings, in which the present invention is further described in detail. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
As shown in FIG. 1, the multi-design-variable comprehensive intelligent optimization method for the bridge formation state of the cable-stayed bridge comprises the following steps:
step one: and establishing a full-bridge finite element three-dimensional numerical simulation model.
Based on a cable-stayed bridge construction design drawing, a refined finite element model of the full-bridge structure is established by adopting finite element software. Calculating to obtain initial bridge forming cable force T by adopting zero displacement method i 0 。
Step two: determining a global design variable to form an adjustment vector X; an optimization objective is determined to form a tuned vector Y.
(1) A misalignment vector X is constructed.
For a cable-stayed bridge considering weight arrangement, the full bridge is assumed to have p (pairs of) stay cables, and the initial bridge-forming cable force is T i 0, i=1, 2, …, p. The concrete weight on the side span girder is divided into q equal sections along the girder direction, and the initial weight of each section is that
Figure BDA0003909772270000071
j=1, 2, …, q. Taking the optimization coefficient of each optimization parameter as a design variable, and simultaneously considering the constant load of the main beam, the adjustment vector X is:
X n,1 ＝{g 0 ,x 1 ,x 2 ,…,x p ,y 1 ,y 2 ,…,y q } T (1)
x i ＝T i /T i 0 (2)
Figure BDA0003909772270000072
wherein n=1+p+q is the sum of the tuning vector elements; g 0 The constant load coefficient of the main beam is a constant 1, namely the main beam constant load does not participate in optimization iteration; x is x i Is the optimization coefficient of the cable force, namely the optimized bridge cable force T i With initial bridging cable force T i 0 Ratio of; y is j For optimizing the coefficient of weight-heavy, i.e. weight-heavy-W after optimization j With the initial set weight
Figure BDA0003909772270000073
Ratio of the two components.
(2) Building a regulated vector Y.
According to the actual condition of the cable-stayed bridge, the main girder bending strain energy is minimized as a main optimization target, and the side span support counter force is maximized as a secondary optimization target. Wherein the girder bending strain energy U can be expressed by bending moment of each section of the girder as follows:
Figure BDA0003909772270000074
wherein r represents the number of key sections taken along the main beam; m is M k Representing the bending moment of the kth section of the main beam, M k+1 Representing the bending moment of the k+1th section of the main beam, l k Representing the length between two adjacent sections E k Represents the modulus of elasticity between adjacent sections, I k Represents the moment of inertia between two adjacent cross-sections, where k=1, 2, …, r.
Thus, the modulated vector Y can be expressed as:
Y m,1 ＝{M 1 ,M 2 ,…,M r ,R 1 ,R 2 } T (5)
wherein R is 1 Representing the reaction force of a main span transition pier support, R 2 Representing the counter force of the side span transition pier support; m=r+2, m representing the sum of the tuned vector elements.
Step three: an influence matrix C of the steering vector-the steering vector is determined.
For the cable-stayed bridge in the normal use stage, the structure is in the elastic range, the bridge response meets the linear superposition principle, and then the adjustment vector and the adjusted vector meet the following relation:
CX＝Y (6)
where C is the influence matrix of the steering vector-the steering vector.
The solution method of the influence matrix C of the applied vector-modulated vector is as follows:
applying a unit force '1' to each inhaul cable in sequence by means of a full-bridge finite element three-dimensional numerical simulation model to obtain girder bending moment response
Figure BDA0003909772270000081
Support reaction response->
Figure BDA0003909772270000082
Constructing an influence matrix C of bridge cable force on the regulated vector x The method comprises the steps of carrying out a first treatment on the surface of the Applying unit weight-collecting "1" to each section of concrete weight in turn to obtain girder bending moment response
Figure BDA0003909772270000083
Support reaction response->
Figure BDA0003909772270000084
Constructing an influence matrix C of the compression weight set on the regulated vector y The method comprises the steps of carrying out a first treatment on the surface of the Simultaneously, calculating the girder bending moment response under the action of the girder constant load +.>
Figure BDA0003909772270000085
Support reaction response
Figure BDA0003909772270000086
Constructing an influence matrix C of girder constant load on the regulated vector g . The influence matrix C of the applied vector on the modulated vector may be formed by a blocking matrix C g ,C x ,C y And (3) forming:
Figure BDA0003909772270000087
in the formula, the vector of modulation is applied to an influence matrix C of the vector of modulation m×n Element C of (3) m,n Representing the response size (corresponding to the bending moment of the main beam or the counter force of the support) of the mth structure caused by the nth applied vector element (corresponding to the constant load of the main beam or the bridge forming cable force or the weight of the pressing weight).
So far, in the optimization problem of the bridge formation state of the cable-stayed bridge, the corresponding relation between the multiple design variables and the multiple optimization targets can be expressed as follows:
C m,n X n,1 ＝Y m,1 (8)
step four: constraint conditions are determined.
For the bridge formation state optimization problem considering multiple design variables, constraint indexes are set according to other optimization parameters besides constraint on cable force:
(1) The difference between adjacent cable forces is not proper to be too large. For this purpose, the cable forces of the adjacent three cables are respectively T i-1 、T i And T i+1 Defining adjacent cable force non-uniformity coefficients as:
Figure BDA0003909772270000091
wherein [ alpha ] is a permissible value of a cable force non-uniformity coefficient, i=1, 2, …, n-1.
(2) The maximum difference of the cable force should not be too large. The maximum difference of the cable force is as follows:
β＝T max -T min ≤[β] (10)
in the formula [ beta ]]Is the cable forceAllowable difference value, T max Represents the maximum cable force among all cable forces, T min Representing the minimum of all cable forces.
(3) Due to the limited capacity of the box girder, each segment should be ensured to press the weight W j Within a reasonable range:
W j ≤[W] (11)
wherein [ W ] is a weight-set weight allowable value.
(4) The counter force of the support should not exceed the bearing capacity limit of the support, and the counter force R of the support of the main-span transition pier 1 Reaction force R of side span transition pier support 2 Satisfies the following formula:
R 1 ≤[R] (12)
R 2 ≤[R] (13)
wherein [ R ] is the bearing capacity limit of the support.
Step five: and establishing an fitness function fitness.
Aiming at the problem that the numerical value between different types of optimization targets is possibly larger, so that the participation degree of the optimization targets with smaller numerical value in the optimization process is too low, the bending strain energy U and the support counter force R are respectively processed by adopting the following construction method, wherein the support counter force R refers to the support counter force R of the side span transition pier 2 。
Figure BDA0003909772270000092
Figure BDA0003909772270000093
Wherein f U A fitness sub-function for characterizing the bending strain energy U; f (f) R To characterize the reaction force R of the support of the side-span transition pier 2 Is a fitness sub-function of (1); -c 1 Is the lower bound of the bending strain energy U, -c 2 For the lower boundary of the support counter-force R, U is more than or equal to 0 and R is more than or equal to 0 for the bending strain energy U and the support counter-force R, so c is present 1 ＝c 2 =0; after treatment, f as the bending strain energy U decreases U Rise, with the rise of the support reaction force R, f R Descend and f U And f R The value ranges of (2) are all within the (0, 1) range.
The fitness function fitness takes the sum of the fitness subfunctions. And for constraint conditions, introducing each constraint condition into the fitness function by adopting a penalty function method. The fitness function fitness can be expressed as:
Figure BDA0003909772270000101
wherein Q is the number of fitness subfunctions. K is a constraint condition penalty function, and is determined by each penalty function subitem, and the relation between the two can be expressed as follows:
Figure BDA0003909772270000102
wherein N represents the constraint number; k (K) c Is a penalty function sub-term, defined by the state variable delta c Determining K c The specific expression of (2) is:
Figure BDA0003909772270000103
Figure BDA0003909772270000104
in delta c Is the state variable of the c-th constraint, S c Is the structural response of the c-th constraint, [ S ] c ]Is a structural response allowable value.
Step six: the design variables are initialized.
The initial bridge forming cable force T calculated by the zero displacement method i 0 And initial pressure weight set weight
Figure BDA0003909772270000105
Substituting into a finite element model to solve the initial bending strain energy U 0 And initial side span support reaction->
Figure BDA0003909772270000106
Thereby obtaining the initial value fitness of the fitness function 0 。
Step seven: and adopting an improved genetic algorithm to carry out optimization iteration.
In genetic algorithms, the evolution process of a population is driven by selection operations by replication operators based on individual fitness values. The selection strategy of the replication operator on the individuals determines the optimization effect and convergence speed of the algorithm, the invention adopts a combined strategy of probability selection and excellent individual retention, and when the individuals are excellent enough, the individuals are directly retained to the next generation population so as not to be eliminated, and the population evolution process is accelerated. The genetic algorithm is easy to fall into local optimum in the latter half of evolution under the influence of initial population quality and early population quality, the latter half of the algorithm is converted into an artificial bee colony algorithm for increasing global searching capability, and a solution set after the former half of optimization is further optimized based on a global optimizing mechanism of bee-picking neighborhood searching, observed bee probability selecting and spying bee random searching, so that the optimizing effect is improved. The improved genetic algorithm has the characteristics of quicker convergence in the early calculation stage and difficult sinking into local optimum in the later calculation stage. The improved genetic algorithm comprises the following specific steps:
(1) At the initial bridging cable force T i 0 And initial pressure weight set weight
Figure BDA0003909772270000111
Performing random search around to form initial population, wherein the total number of population individuals is N pop 。
(2) And calculating the fitness function value of each individual in the population.
(3) And (3) carrying out copying, crossing and mutation operations on the population individuals to form a new offspring population. The selection strategy for the replication operation is improved, and in order to avoid that part of good individuals are eliminated in the evolution process, a joint strategy of probability selection and excellent individual retention is introduced: when the individual quality is sufficiently good in this generation population, it is retained directly to the next generation population. Otherwise, participate in the probability selection. The mathematical expression is as follows:
if the individual fitness function value satisfies the formula (20), the new offspring population individuals are directly used.
fitness u ≥fitness max -0.1×(fitness max -fitness min ) (20)
In the field of u (u＝1,2,…,N pop ) Representing individual fitness function values, fitness max Fitness function value representing the best quality individuals in this generation of population min And the fitness function value of the individual with the worst quality in the first generation of population is represented.
If the individual fitness function value does not satisfy the formula (20), calculating the probability P that the individual is selected u This can be expressed as:
Figure BDA0003909772270000112
randomly generating a number g between 0 and 1, if P u And if the weight is more than or equal to g, the individual is reserved, otherwise, the individual is eliminated.
(4) Judging whether the iteration times are met, if the iteration times are not met, repeating the steps (2) and (3), and increasing the iteration times for one time; and if the iteration times are met, entering a section of the artificial bee colony algorithm.
(5) The optimized population of the former half-way algorithm is used as an initial honey source of the artificial bee colony algorithm, and the algorithm convergence difficulty is properly increased when parameters of the artificial bee colony algorithm are set due to the fact that the initial honey source is greatly optimized, so that the generation probability of the spyware is improved, and the global searching capability is enhanced. Meanwhile, the number of honey sources of the artificial bee colony algorithm is the same as the number of population individuals of the genetic algorithm, and the number is N pop 。
(6) The bee-collecting carries out neighborhood search on honey sources, and new honey sources V new The expression of (2) is as follows:
Figure BDA0003909772270000113
in the method, in the process of the invention,
Figure BDA0003909772270000114
the v-th element (v=1, 2, …, n) representing the u-th old honey source, and>
Figure BDA0003909772270000115
the v element representing the u 'th old honey source, and u' notequ. Delta u,v Is a random number between 0 and 1.
Then greedy selection is performed, i.e. the fitness function values of the new and old honey sources are compared and the higher one is selected.
(7) Observing the roulette to select honey sources, namely calculating fitness function values of the honey sources, performing probability selection according to the fitness function values by the observed bees according to a formula (21), and then performing neighborhood search and greedy selection according to a formula (22) near the honey sources.
(8) If the fitness function value of a honey source is not obviously improved under multiple updating, discarding the honey source, and generating a new honey source for random search of the scout bees to replace; and simultaneously recording the solution set with the highest fitness function value in the current honey source as the optimal solution.
(9) Judging whether the iteration times are met, if not, repeating the steps (6), (7) and (8), and increasing the iteration times for one time; and if the iteration times are met, outputting the currently recorded optimal solution as a global optimal solution.
The following describes the advantageous effects of the optimization method proposed by the present invention based on specific examples.
As shown in FIG. 2, the overall layout of the cable-stayed bridge with different spans is shown as (120+105) m, the bridge width is 28m, the main beam is a single-box multi-chamber concrete box beam, the beam height is 3.2m, the bridge tower is a hollow cylindrical cable tower, the tower height above the bridge deck is 52m, the tower height below the bridge deck is 28m, and the main beam and the cable tower are all made of C50 concrete. The stay cables are single cable surfaces, 16 pairs of stay cables are arranged on two sides of a cable tower respectively, a steel strand with standard tensile strength of 1860MPa is adopted, the basic cable distance is 6.5m, the cable moment of a side span tail cable area is 4.2m, the cable distance on the cable tower is 2.0m, and two parallel cables are equivalent to one cable in calculation. The main girder box girder with the iron sand concrete within the range of about 24m from the center line of the side pier is designed to carry out weight, and the weight concentration degree is 230kN/m.
The bridge-forming state optimization design is carried out according to the flow shown in fig. 1, and the specific steps are as follows:
(1) A finite element model as shown in fig. 3 is built based on the above information. Calculating initial bridge forming cable force T by adopting zero displacement method i 0 。
(2) The total bridge is provided with 32 pairs of stay cables, and the cable force of each pair of stay cables is T i (i=1, 2, …, 32), the cable force optimization coefficient is x i The method comprises the steps of carrying out a first treatment on the surface of the Dividing each 2m of the side span weight range into 12 segments, wherein the weight of each segment is W j (j=1, 2, …, 12), the initial pressure weight set is again valued as designed, i.e
Figure BDA0003909772270000121
The weight optimization coefficient is y j . Constructing an adjusting variable X by considering constant load of a main beam 45,1 ＝{1,x 1 ,x 2 ,…,x 32 ,y 1 ,y 2 ,…,y 12 } T 。
In the optimization process, the minimization of the bending strain energy of the main beam and the maximization of the counter force of the side span support are taken as optimization targets, 106 key sections are taken along the main beam, and the bending moment of the kth section of the main beam is M k (k=1, 2, …, 106), the support reaction forces at the two ends of the main beam are R 1 、R 2 And (3) calculating the bending strain energy U of the main beam through a formula (4). Construction of the modulated variable Y 108,1 ＝{M 1 ,M 2 ,…,M 106 ,R 1 ,R 2 } T 。
(3) Applying unit force '1' to each pair of inhaul cables in turn, and extracting a cable force-regulated vector influence matrix
Figure BDA0003909772270000122
Applying unit concentration of 1 to each section of weight in turn, and extracting a weight load-regulated vector influence matrix +.>
Figure BDA0003909772270000123
Simultaneously calculating a main beam constant load-regulated vector influence matrix +.>
Figure BDA0003909772270000124
FinallyForming a steering vector-affected matrix
Figure BDA0003909772270000131
(4) To ensure the rationality of the optimization result, constraining the cable force uniformity and the cable force maximum difference value, and taking [ alpha ] =200, [ beta ] =5000 kN; constraining the weight of the pressure weight set, and taking [ W ] =450 kN/m; and restraining the counter force of the support, and taking [ R ] =7000 kN.
(5) And constructing an fitness function fitness.
(6) Initial bridging cable force T calculated by zero displacement method i 0 As shown in table 1.
TABLE 1 initial bridle force
Cable number Initial cable force (kN) Cable number Initial cable force (kN)
T 1 9967.30 T 17 5085.32
T 2 9689.02 T 18 5302.95
T 3 9514.72 T 19 6027.62
T 4 9314.54 T 20 6759.15
T 5 9148.41 T 21 7156.82
T 6 9002.34 T 22 7540.59
T 7 8930.35 T 23 7748.05
T 8 8626.48 T 24 8035.38
T 9 8354.71 T 25 8294.39
T 10 8015.16 T 26 8431.30
T 11 7629.90 T 27 9474.01
T 12 7278.65 T 28 9562.16
T 13 6793.88 T 29 9580.22
T 14 6207.64 T 30 9572.19
T 15 5565.78 T 31 9496.05
T 16 5397.15 T 32 9372.04
The initial pressure weight is re-valued according to the design value, namely
Figure BDA0003909772270000132
Calculating the fitness function value as fitness in the initial state 0 ＝0.075。
(7) The improved genetic algorithm is adopted to optimize iteration to the design variable with the aim of maximizing the fitness function fitness, and related parameters are shown in table 2.
Table 2 improved genetic algorithm parameters
Figure BDA0003909772270000141
The optimal bridging forces after iterative optimization are shown in table 3 below.
TABLE 3 optimized bridle force
Cable number Bridge forming rope force (kN) Cable number Bridge forming rope force (kN)
T 1 9253.92 T 17 5438.72
T 2 9190.69 T 18 5608.59
T 3 9126.06 T 19 6615.08
T 4 8930.15 T 20 7082.03
T 5 8858.97 T 21 7653.37
T 6 8710.17 T 22 8000.78
T 7 8547.32 T 23 8159.50
T 8 8594.16 T 24 8478.11
T 9 8484.36 T 25 8766.37
T 10 8282.69 T 26 8756.59
T 11 8093.72 T 27 8781.28
T 12 7866.07 T 28 8674.87
T 13 7333.71 T 29 8796.13
T 14 7008.62 T 30 8794.47
T 15 6574.81 T 31 8827.05
T 16 6081.29 T 32 9010.27
The optimal pressure re-set redistribution is shown in table 4 below.
Table 4 optimized pressure weight redistribution
Segment numbering Weight-set weight (kN/m) Segment numbering Weight-set weight (kN/m)
W 1 415.52 W 7 350.87
W 2 227.33 W 8 276.00
W 3 207.69 W 9 248.72
W 4 162.58 W 10 239.19
W 5 204.32 W 11 114.99
W 6 235.32 W 12 248.99
In conclusion, after optimization, cheng Qiaosuo force changes are more uniform, the maximum difference value of the cable force is reduced from 4882.0kN to 3815.2kN, and the weight are in a reasonable range and are distributed uniformly.
In order to conveniently embody the optimization effect of the invention by considering the weight, three working conditions are set:
working condition 1: and calculating the obtained initial bridge formation state by adopting a zero displacement method.
Working condition 2: the bridge formation state of the weight optimization is not considered, namely the weight is set according to the design value.
Working condition 3: consider the bridge formation state of weight optimization.
As can be seen from fig. 4, after optimization (working condition 3), the maximum deflection of the main beam is reduced by 47%, compared with working condition 2, it can be found that the main beam of working condition 3 has smoother line shape, i.e. the vertical displacement of the side span main beam is greatly optimized by considering the weight.
As can be seen from FIG. 5, the maximum bending moment of the main beam is reduced from 90568 kN.m to 72674 kN.m by 19% after optimization (working condition 3).
The optimized result of the pier support counter force is shown in table 5, and it can be seen that after optimization, the pier support counter force of the working condition 3 is improved by 24.8%, and the pier support pressure reserve is effectively improved; the reaction force of the side pier support in the working condition 2 is improved by 19.8%, and compared with the working condition 2 and the working condition 3, the side pier support reaction force can be further improved by considering the weight distribution design.
TABLE 5 optimization results of side pier support counter force
Project Working condition 1 Working condition 2 Working condition 3
R 2 4737.3 5676.6 5913.7
In order to explore the superiority of the improved genetic algorithm in the calculation efficiency, iterative calculation is carried out by adopting the improved genetic algorithm and the conventional genetic algorithm, and the comparison result is shown in fig. 6. Compared with the conventional genetic algorithm, the calculation efficiency of the first half process is not very different, and the fitness function is about 0.036 in half process. The improved genetic algorithm has excellent global searching capability in the latter half, and under the same iteration times, the fitness function finally converges to 0.044, while the conventional genetic algorithm falls into local optimum in the latter half of calculation and finally converges to 0.039.
In conclusion, the method can effectively and efficiently realize the optimization design of the bridge-forming state of the cable-stayed bridge with various design variables.
It will be appreciated by persons skilled in the art that the foregoing description is a preferred embodiment of the invention, and is not intended to limit the invention, but rather to limit the invention to the specific embodiments described, and that modifications may be made to the technical solutions described in the foregoing embodiments, or equivalents may be substituted for elements thereof, for the purposes of those skilled in the art. Modifications, equivalents, and alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (6)

1. A comprehensive intelligent optimization method for multiple design variables of a cable-stayed bridge in a bridge forming state is characterized by comprising the following steps:
step one: establishing a full-bridge finite element model based on a cable-stayed bridge construction design drawing;
step two: determining a global design variable to form an adjustment vector X; determining an optimization target to form a regulated vector Y;
taking the optimization coefficients of the bridge girder forming force and the compression weight as design variables, and simultaneously taking the constant load of the girder into consideration to obtain the adjustment vector X; taking the bending strain energy of the main beam as a main optimization target, and taking the counter force maximization of the side span support as a secondary optimization target to obtain the bending strain energy of each section of the main beam and the regulated vector Y;
step three: determining an influence matrix C of the adjustment vector and the adjustment vector to obtain a corresponding relation of the multiple design variables and the multiple optimization targets as CX=Y;
step four: determining constraint conditions;
step five: establishing an adaptability function;
the bending strain energy and the support counter force are respectively processed by adopting the following construction method, so that an adaptability sub-function representing the bending strain energy and an adaptability sub-function representing the support counter force are obtained; the fitness function takes the sum of the fitness subfunctions, and a penalty function method is adopted to introduce the constraint condition in the fourth step, so that a final fitness function is obtained;
step six: initializing a design variable;
calculating to obtain initial bridge forming cable force and initial weight, substituting the initial bridge forming cable force and the initial weight into the finite element model, obtaining initial bending strain energy and initial side span support counter force, and further obtaining an initial value of an fitness function;
step seven: adopting a genetic algorithm to carry out optimization iteration;
and (3) adopting a genetic algorithm, carrying out iterative optimization by taking the maximum fitness function as an optimization target, and finally obtaining a group of solutions to ensure that the cable-stayed bridge reaches a global optimal bridge forming state to finish optimization.
2. The method for the integrated intelligent optimization of multiple design variables for the bridge formation of a cable-stayed bridge according to claim 1, wherein the formation of the adjusted vector X and the adjusted vector Y in the second step is achieved by the following substeps:
(2.1) for a cable-stayed bridge considering the weight arrangement, assuming that the full bridge has p or opposite stayed cables, the initial bridging cable force is T i 0 I=1, 2, …, p; the concrete weight on the side span girder is divided into q equal sections along the girder direction, and the initial weight of each section is as follows
Figure FDA0004188972730000011
Taking the optimization coefficients of the bridge girder forming force and the compression weight as design variables, and considering the constant load of the girder, the adjustment vector is:
X n,1 ＝{g 0 ,x 1 ,x 2 ,…,x p ,y 1 ,y 2 ,…,y q } T (1)
x i ＝T i /T i 0 (2)
Figure FDA0004188972730000021
wherein n=1+p+q is the sum of the tuning vector elements; g 0 The constant load coefficient of the main beam is a constant 1, namely the main beam constant load does not participate in optimization iteration; x is x i To optimize the coefficient of the bridge forming cable force, T i The bridge forming cable force is optimized; y is j Optimization coefficient for weight-on-weight, W j Weight is collected for the optimized pressure;
(2.2) taking the bending strain energy of the main girder as a main optimization target and the counter force of the side span support as a secondary optimization target according to the actual condition of the cable-stayed bridge; the girder bending strain energy U is expressed as:
Figure FDA0004188972730000022
wherein r represents the number of key sections taken along the main beam; m is M k Representing the bending moment of the kth section of the main beam, M k+1 Representing the bending moment of the k+1th section of the main beam, l k Representing the length between two adjacent sections E k Represents the modulus of elasticity between adjacent sections, I k Represents the moment of inertia between two adjacent cross-sections, where k=1, 2, …, r;
the regulated vector is:
Y m,1 ＝{M 1 ,M 2 ,…,M r ,R 1 ,R 2 } T (5)
wherein R is 1 Representing the reaction force of a main span transition pier support, R 2 Representing the counter force of the side span transition pier support; m=r+2, m representing the sum of the tuned vector elements.
3. The method for the integrated intelligent optimization of the multiple design variables of the bridge formation state of the cable-stayed bridge according to claim 2, wherein the formation of the influence matrix C of the tuning vector-tuning vector in the third step is realized by the following substeps:
applying a unit force of 1 to each or each pair of inhaul cables in turn to obtain girder bending moment response
Figure FDA0004188972730000023
Support reaction response->
Figure FDA0004188972730000024
Thereby constructing an influence matrix C of bridge cable force on the regulated vector x The method comprises the steps of carrying out a first treatment on the surface of the Applying unit weight-collecting "1" to each section of concrete weight in turn to obtain main beamMoment response->
Figure FDA0004188972730000025
Support reaction response->
Figure FDA0004188972730000026
And then construct the influence matrix C of the compression weight set weight on the regulated vector y The method comprises the steps of carrying out a first treatment on the surface of the Simultaneously, calculating the girder bending moment response under the action of the girder constant load +.>
Figure FDA0004188972730000027
Support reaction response->
Figure FDA0004188972730000028
Thereby constructing an influence matrix C of the constant load of the main beam on the regulated vector g ；
The influence matrix C of the modulation vector-modulated vector is represented by matrix C g 、C x 、C y The method comprises the following steps:
Figure FDA0004188972730000029
wherein C is m,n Representing the size of an mth structural response caused by an nth regulating vector element, wherein the regulating vector element is a main beam constant load or a bridge forming cable force or a pressing weight, and the structural response is a main beam bending moment response or a support counter force response;
at this time, the correspondence between the tuning vector and the tuning vector is:
C m,n X n,1 ＝Y m,1 (7)。
4. the method for comprehensively and intelligently optimizing the multiple design variables of the bridge formation state of the cable-stayed bridge according to claim 1, wherein the constraint conditions comprise: the difference between adjacent cable forces is smaller than the allowable value of the non-uniform coefficient of the cable force; the maximum difference of the cable force is smaller than Yu Suoli; each segment weight set is less than a weight set weight allowed value; the support reaction force does not exceed the support bearing capacity limit.
5. A method for the integrated intelligent optimization of multiple design variables for the bridge formation state of a cable-stayed bridge according to claim 3, wherein the fifth step is specifically realized by the following substeps:
the bending strain energy U and the support counter force R are respectively processed by adopting the following construction method, and the support counter force R comprises a main span transition pier support counter force R 1 And side span transition pier support counter force R 2 ：
Figure FDA0004188972730000031
Figure FDA0004188972730000032
Wherein f U A fitness sub-function for characterizing the bending strain energy U; f (f) R To characterize the reaction force R of the main span transition pier support 1 Or the reaction force R of the side span transition pier support 2 Is a fitness sub-function of (1); -c 1 Is the lower bound of U, -c 2 For the lower bound of R, there is U.gtoreq.0, R.gtoreq.0, and thus c for the bending strain energy U and the support reaction R 1 ＝c 2 =0; said f U And f R The value ranges of (2) are all within the range of (0, 1);
the fitness function fitness is the sum of fitness subfunctions; for constraint conditions, introducing each constraint condition into a fitness function by adopting a penalty function method; the fitness function fitness is expressed as:
Figure FDA0004188972730000033
wherein K is a constraint condition penalty function, and is determined by each penalty function subitem;
Figure FDA0004188972730000034
wherein N represents the constraint number; k (K) c Is a sub-term of a penalty function, determined by a state variable, K c The specific expression of (2) is:
Figure FDA0004188972730000041
Figure FDA0004188972730000042
in delta c Is the state variable of the c-th constraint, S c Is the structural response of the c-th constraint, [ S ] c ]Is a structural response allowable value.
6. The method for intelligently optimizing the multiple design variables of the bridge formation state of the cable-stayed bridge according to claim 2, wherein the genetic algorithm adopted in the step seven is an improved genetic algorithm, and is specifically realized by the following substeps:
(7.1) at the initial bridle force T i 0 And initial pressure weight set weight
Figure FDA0004188972730000043
Performing random search around to form initial population, wherein the total number of population individuals is N pop ；
(7.2) calculating fitness function values of each individual in the population;
(7.3) performing replication, crossover and mutation operations on individuals of the population to form a new offspring population; wherein the mathematical expression of the selection strategy of the copy operation is as follows:
if the individual fitness function value meets the formula (14), directly taking the individual fitness function value as a new offspring population individual;
fitness u ≥fitness max -0.1×(fitness max -fitness min ) (14)
in the field of u Represents an individual fitness function value, u=1, 2, …, N pop ，fitness max Fitness function value representing the best quality individuals in this generation of population min The fitness function value of the individual with the worst quality in the first generation population is represented;
if the individual fitness function value does not satisfy equation (14), calculating the probability P that the individual is selected u Expressed as:
Figure FDA0004188972730000044
randomly generating a number g between 0 and 1, if P u If the weight is more than or equal to g, the individual is reserved, otherwise, the individual is eliminated;
(7.4) judging whether the iteration times are met, if the iteration times are not met, repeating the steps (7.2) and (7.3), and increasing the iteration times once; if the iteration times are met, entering a section of the artificial bee colony algorithm;
(7.5) optimizing the population by the former half-way algorithm to be used as an initial honey source of the artificial bee colony algorithm, and increasing the algorithm convergence difficulty when setting the parameters of the artificial bee colony algorithm due to the fact that the population is greatly optimized, and improving the generation probability of the scout bee so as to enhance the global searching capability; meanwhile, the number of honey sources of the artificial bee colony algorithm is the same as the number of population individuals of the genetic algorithm;
(7.6) carrying out neighborhood search on honey sources by bees, wherein the expression of the new honey sources is as follows:
Figure FDA0004188972730000045
/>
in the method, in the process of the invention,
Figure FDA0004188972730000051
v element representing the u-th old honey source, v=1, 2, …, n, and u' notequ; delta u,v A random number between 0 and 1;
then greedy selection is carried out, namely the fitness function values of the new honey source and the old honey source are compared, and the higher one is selected;
(7.7) observing the roulette to select honey sources, namely calculating fitness function values of the honey sources, performing probability selection according to the fitness function values by the observed bees according to a formula (15), and then performing neighborhood search and greedy selection according to a formula (16) near the honey sources;
(7.8) if the fitness function value of a honey source is not obviously improved under the condition of multiple updating, discarding the honey source, and generating a new honey source for random search of the scout bees to replace; simultaneously recording a solution set with the highest fitness function value in the current honey source as an optimal solution;
(7.9) judging whether the iteration times are met, if not, repeating the steps (7.6), (7.7) and (7.8), and increasing the iteration times once; if the iteration times are met, outputting the current recorded optimal solution as a global optimal solution, and completing optimization.
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