CN109815601B - A bridge structure optimization method based on substructure contribution - Google Patents

Abstract

A bridge structure optimization method based on substructure contribution degree provides a concept of substructure contribution degree, a substructure with large contribution degree to an objective function is reserved, the contribution degree is eliminated, the reserved substructure is subjected to scheme combination, the substructure with small contribution degree to the objective function is eliminated again, the required number of elements are directly taken out from the rest substructure set to form design schemes, the objective function of each design scheme is calculated, and a sufficient number of feasible solutions are selected for manual selection. The invention combines the optimization algorithm with subjective judgment, eliminates the worst substructure possibly appearing in the design scheme by calculating the contribution degree of the substructures to the objective function, and reduces the scale of the calculated sample space. And combining the rest optimal substructures, solving a set of feasible solutions of the objective function meeting the design conditions within a certain bandwidth range, and determining the design scheme by manual selection according to factors such as feasibility and aesthetic factors of construction.

Description

A bridge structure optimization method based on substructure contribution

technical field

The invention belongs to the technical field of bridge design and structure optimization, and in particular relates to a bridge structure optimization method based on substructure contribution degrees.

Background technique

Optimal design method is a comprehensive applied engineering technique combining optimization principles with computer technology, and has been widely used in the field of design. With the continuous in-depth research on various complex optimization problems, the bottlenecks faced by traditional research methods are becoming more and more obvious. When traditional optimization methods are used to solve the combined optimization problems of multi-bar structures such as arch bridges and truss bridges, they cannot meet the requirements of practical problems in terms of solution accuracy and convergence speed. The reasons are: (1) traditional optimization methods rely heavily on the initial value; (2) the determination of search direction and step size of traditional optimization methods mostly depends on experience, and it is easy to fall into local minimum; (3) the calculation of combinatorial optimization problems The quantity is very large.

The optimization of the bridge structure has its own characteristics: (1) The main structure is clear, there is a main girder bearing the traffic load, and the alignment of the main girder is determined, and the optimization of the elevation alignment is not allowed, but the section of the main girder can be carried out (2) Sub-structures are diverse and varied, such as the layout of the web members of truss bridges and the suspenders of arch bridges. The quality of the sub-structure layout determines the stress of the entire bridge. Whether it is reasonable or not; (3) Not only the displacement and internal force of the bridge must meet the specification requirements, but also the construction feasibility, project cost and aesthetic requirements must be considered, but the construction feasibility and aesthetic problems cannot be calculated, so it is necessary to introduce artificial subjective judgment factor. Therefore, the goal of bridge structure optimization is to provide the optimal solution that meets the optimization conditions and a large number of suboptimal solutions that can be used for manual selection.

Contents of the invention

The invention provides a bridge structure optimization method based on substructure contribution. Firstly, the structure whose shape has been determined in the bridge structure and does not need to be combined and optimized is defined as the main structure, such as the main girder structure, the main girder and main arch structure in the arch bridge, and the upper and lower main chord structures of the truss bridge; secondly, in In the optimization calculation, the structural members attached to the main structure that need to be changed and adjusted are defined as substructures, such as cables, webs of hanger trusses, etc. When performing finite element calculations, there are n nodes on the main structure that can be connected into m bar-tie substructures, and each group of connection forms constitutes a design scheme, theoretically there will be a different plan. According to each scheme, the value of the objective function is calculated, and the optimal scheme can be found. But when n and m are relatively large, the number of schemes is theoretically very large, far exceeding the computing power. The present invention proposes the concept of substructure contribution degree, which has two levels of meaning: (1) refers to the objective function value obtained when a certain substructure is adopted under the same external force, and the contribution degree of the optimal objective function is the largest; (2) In the combined calculation of substructures, the one with the higher probability of a substructure appearing in the feasible solution set has the greater contribution. In the optimization calculation, the substructure with a large contribution to the objective function is retained, and the substructure with a small contribution is excluded. By analogy, until the number of remaining substructures meets the requirements of the computer's computing power, that is, m substructures can be arbitrarily taken from the remaining n _k substructures for combined calculations, and the optimal solution and the objective function that meets the design conditions can be obtained at a certain bandwidth The set of feasible solutions in the range. The invention has the advantages of combining the optimization algorithm with subjective judgment, eliminating the worst substructure that may appear in the design scheme by calculating the contribution of the substructure to the objective function, and reducing the scale of the calculation sample space. Then combine the remaining optimal substructures to obtain a set of feasible solutions within a certain bandwidth of the objective function that meets the design conditions, and then determine the design scheme through manual selection according to construction feasibility and aesthetics.

Technical scheme of the present invention:

A truss optimization method based on substructure contribution, comprising the following steps:

S1: Determine the quantity of the main structure, the position and number of possible connection nodes of the substructure on the main structure;

S2: Determine the alternative substructure, the substructure is all possible ways of connecting members that only connect one member between the nodes of the main structure, and the upper limit of the number n ₁ is: if there are connections between two main structures, with p nodes on the first main structure and q nodes on the second main structure, the number of substructures is reduced to p×q; the finite element method is used to calculate each an objective function for a substructure;

S3: Sort the substructures according to the contribution degree from large to small, and divide n ₁ substructures into sets A, B, and C according to the contribution degree from large to small, and the number of elements in the three sets each accounts for 1/3;

S4: Randomly select two elements from the substructure set of n ₁ elements to form a second-order substructure combination. The total number n ₂ of second-order substructure combinations is: , calculate the objective function of each second-order substructure combination;

S5: Find the contribution degree of each element in the substructure set A, B, C in the second-order substructure combination, and the contribution degree is greater for the probability of a certain substructure appearing in the feasible solution set;

S6: According to the calculation result of S5, the 20% elements with the smallest substructure contribution are excluded, and the remaining elements form a new set D;

Specifically, do the following two operations:

S6.1: Keep all the elements in the set A;

S6.2: Exclude 20% of the elements in the set B∪C according to the principle of the least substructure contribution, and exclude substructures that are considered to be very bad in terms of construction feasibility and aesthetics, and finally keep k ₁ The elements form a new set D;

S7: Judgment Whether the scheme satisfies the computing power of the computer, if so, directly select m elements from the substructure set of k ₁ elements to form the design scheme, and there are total Design schemes, calculate the objective function of each design scheme, and select a sufficient number of feasible solutions for manual selection.

S8: If not satisfied, randomly select three elements from the substructure set of k ₁ elements in the set D to form a third-order substructure combination, and calculate the objective function of each substructure combination. Return to S6, in this loop, increase the order of a substructure each time.

Effect and benefit of the present invention are:

1) Eliminate the worst substructure that may appear in the design scheme by calculating the contribution of the substructure to the objective function, and reduce the scale of the calculation sample space.

2) Compared with the traditional optimization method, it requires less computer and takes less time.

3) Combining the optimization algorithm with subjective judgment, find out the set of feasible solutions of the objective function satisfying the design conditions within a certain bandwidth range, and then determine the design scheme through manual selection according to construction feasibility, aesthetics and other factors.

Description of drawings

Fig. 1 is a flowchart of a bridge structure optimization method based on substructure contribution.

Figure 2 is a schematic diagram of a specific implementation example.

In the figure: 1 main structure; 2 substructure.

Detailed ways

The specific embodiments of the present invention will be described in detail below in conjunction with the technical solutions and accompanying drawings.

A cantilever truss beam with a truss length of 30m and an upper and lower truss height of 10m. The upper and lower trusses are each divided into 7 nodes, as shown in Figure 2. The truss is subjected to a concentrated force of 360kN at three vertical nodes.

S1: Establish a cantilever truss model, the upper and lower trusses are the main structure, and k=7 nodes are evenly arranged, as shown in Figure 2.

S2: Determine the alternative substructure. There are two main structures in this calculation example. There are 7 nodes on the first main structure and 7 nodes on the second main structure, so the number of substructures is 49. The finite element method is used to calculate the objective function of each substructure, and the vertical average displacement at the action points of the three concentrated forces is taken as the objective function.

S3: Sort the substructures according to the contribution degree from large to small, and divide the 49 substructures into sets A, B, and C according to the contribution degree from large to small. The number of elements in the three sets each accounts for about 1/3. The contribution of elements in set A is the largest, followed by set B, and set C is the smallest. Substructures are numbered by contribution:

{1,2,3,4,5,6,7,8,9,10,11,12,13,15,15,16,17}∈A

{18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33}∈B

{34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49}∈C

S4: Randomly select two elements from the 49-element substructure set to form a second-order substructure combination. There are 1176 second-order substructure combinations in total, and calculate the objective function of each second-order substructure combination.

S5: Find the contribution degree of each element in the substructure set A, B, C in the second-order substructure combination, given the threshold of the objective function -0.767m, after filtering, 425 solutions with the smallest contribution degree are obtained, and The probability of occurrence of the substructure with the smallest contribution.

S6: According to the calculation result of S5, the 9 elements with the smallest substructure contribution are excluded, and the remaining elements form a new set D. Specifically, do the following two operations:

S6.1: Keep all the elements in the set A;

S6.2: Exclude 9 elements in the set B∪C according to the principle of the least substructure contribution, and finally retain 40 elements to form a new set D. Removed substructure numbers:

{34,39,41,42,43,46,47,48,49}

S7: Randomly select three elements from the substructure set of 40 elements in the set D to form a third-order substructure combination. There are 9880 third-order substructure combinations in total, and calculate the objective function of each third-order substructure combination .

S8: According to the calculation result of S7, exclude the 20% elements with the least substructure contribution, and exclude the substructures that are considered to be very bad in terms of construction feasibility and aesthetics, and the remaining 28 elements form a new set D . The elements in D are taken from the sets A, B, and C respectively as follows:

{1,2,3,4,5,6,7,8,9,10,11,12,13,15,15,16,17}∈A

{25,27,28,29,30,31,33}∈B

{36,38,40,44}∈C

S9: During the process of repeating S7 and S8, it is found that 5 elements are arbitrarily selected from the substructure set D of 28 elements to form a design scheme, and there are 98280 design schemes in total. These programs already meet the computing power requirements of the computer.

S10: directly select 5 elements from the 28-element substructure set D to form 98280 design schemes, calculate the objective function of each design scheme, and select a sufficient number of feasible solutions for manual selection. The final 5 sets of optimal solutions output are as follows:

Claims (1)

1. A bridge structure optimization method based on substructure contribution, characterized in that the steps are as follows: S1: Determine the quantity of the main structure, the position and number of possible connection nodes of the substructure on the main structure; S2: Determine the alternative substructure, the substructure is all possible ways of connecting members that only connect one member between the nodes of the main structure, and the upper limit of the number n ₁ is: if there are connections between two main structures, with p nodes on the first main structure and q nodes on the second main structure, the number of substructures is reduced to p×q; the finite element method is used to calculate each an objective function for a substructure; S3: Sort the substructures according to the contribution degree from large to small, and divide n ₁ substructures into sets A, B, and C according to the contribution degree from large to small, and the number of elements in the three sets each accounts for 1/3; S4: Randomly select two elements from the substructure set of n ₁ elements to form a second-order substructure combination. The total number n ₂ of second-order substructure combinations is: , calculate the objective function of each second-order substructure combination; S5: Find the contribution degree of each element in the substructure set A, B, C in the second-order substructure combination, and the contribution degree is greater for the probability of a certain substructure appearing in the feasible solution set; S6: According to the calculation result of S5, the 20% elements with the smallest substructure contribution are excluded, and the remaining elements form a new set D; Specifically, do the following two operations: S6.1: Keep all the elements in the set A; S6.2: Exclude 20% of the elements in the set B∪C according to the principle of the least substructure contribution, and exclude substructures that are considered to be very bad in terms of construction feasibility and aesthetics, and finally keep k ₁ The elements form a new set D; S7: Judgment Whether the scheme satisfies the computing power of the computer, if so, directly select m elements from the substructure set of k ₁ elements to form the design scheme, and there are total Design schemes, calculate the objective function of each design scheme, and select a sufficient number of feasible solutions for manual selection; S8: If not satisfied, randomly select three elements from the substructure set of k ₁ elements in the set D to form a third-order substructure combination, and calculate the objective function of each substructure combination; return to S6, in this loop, The order of the substructure is raised one at a time.