CN109815601B - Bridge structure optimization method based on substructure contribution degree - Google Patents
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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
Technical Field
The invention belongs to the technical field of bridge design and structure optimization, and particularly relates to a bridge structure optimization method based on substructure contribution.
Background
The optimization design method is a comprehensive application engineering technology combining an optimization principle with a computer technology, and is widely applied in the design field. With the continuous and intensive research on various complex optimization problems, the bottleneck faced by the traditional research method is increasingly remarkable. When the traditional optimization method solves the combined optimization problem of multi-rod system structures such as arch bridges, truss bridges and the like, the requirements of practical problems cannot be met in terms of solving precision and convergence speed. The reason for this is that: the traditional optimization method has large dependence on initial values; (2) The search direction and the step length of the traditional optimization method are determined by experience, so that the traditional optimization method is easy to sink into a local minimum value; (3) the computational effort of the combinatorial optimization problem is very large.
The optimization of the bridge structure has the characteristics that: (1) The main structure is clear, the main beam for bearing traffic load is arranged, the shape of the main beam is definite, the optimization of the shape of the vertical face is not allowed, but the shape and the size of the section of the main beam can be optimized; (2) The form of the substructure is various and rich in variation, such as the arrangement mode of web members of truss bridge and the arrangement mode of arch bridge suspenders, and the advantages and disadvantages of the arrangement mode of the substructure determine whether the stress of the whole bridge is reasonable or not; (3) The bridge not only meets the standard requirements on displacement and internal force, but also considers the feasibility of construction, engineering cost and aesthetic requirements, but the feasibility of construction and aesthetic problems cannot be calculated, so that artificial subjective judgment factors must be introduced. Therefore, the goal of bridge structure optimization is to provide an optimal solution that satisfies the optimization conditions and a large number of sub-optimal solutions that can be used for manual selection.
Disclosure of Invention
The invention provides a bridge structure optimization method based on substructure contribution. Firstly, defining a structure which has determined a shape and does not need to be combined and optimized in a bridge structure as a main structure, such as a main girder structure, a main girder and main arch structure in an arch bridge and an upper main chord structure and a lower main chord structure of the truss bridge; secondly, in the optimization calculation, structural members which are attached to the main structure and need to be changed and adjusted are defined as substructures, such as cables, web members of a boom truss and the like. When finite element calculation is performed, n nodes on the main structure can be connected into m rod system substructures, each group of connection modes forms a design scheme, and theoretically, the method has the following steps ofDifferent schemes. And calculating the value of the objective function according to each scheme, so that the optimal scheme can be found out. However, when n and m are relatively large, the number of schemes is theoretically very large, far beyond the computational capability. The invention provides a concept of contribution degree of a substructure, which has two levels of meaning: (1) The objective function value obtained when a certain substructure is adopted under the action of the same external force is indicated, and the contribution degree of the optimum person of the objective function is the maximum; (2) In the computation of the sub-structure combination, the contribution degree of the probability that a certain sub-structure appears in the feasible solution set is large. In the optimization calculation, the substructure with large contribution to the objective function is reserved, and the substructure with small contribution is eliminatedScheme combining the reserved substructures, removing the substructures with small contribution to the objective function again, and so on until the number of the remaining substructures meets the requirement of the computing power of the computer, namely, the remaining substructures can be removed from the remaining n k And randomly taking out m substructures from the substructures, and carrying out combination calculation to obtain an optimal solution and a set of feasible solutions of the objective function meeting the design condition within a certain bandwidth range. The invention has the advantages that the optimization algorithm is combined with subjective judgment, the worst substructure possibly occurring in the design scheme is eliminated by calculating the contribution degree of the substructures to the objective function, and the scale of the calculated sample space is reduced. 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.
The technical scheme of the invention is as follows:
a truss optimization method based on substructure contribution degree comprises the following steps:
s1: determining the number of main structures, the positions and the number of nodes possibly connected by the sub-structures on the main structures;
s2: alternative substructures are determined, the substructures being all possible ways of connecting the bars between the nodes of the main structure by connecting only one bar, the number n 1 The upper limit of (2) is:a plurality of; if there are p nodes on the first main structure and q nodes on the second main structure, the number of substructures is reduced to p x q; calculating an objective function of each substructure by adopting a finite element method;
s3: ordering the substructures from big to small according to the contribution degree, and n is selected from the following steps of 1 The sub-structures are divided into sets A, B, C from large to small according to the contribution degree, and the number of elements in the three sets is 1/3;
s4: from n 1 Two elements are arbitrarily taken from the substructures of the individual elements to form a second-order substructures combination, and the number n of the second-order substructures combination is shared 2 The method comprises the following steps:calculating an objective function of each second-order substructure combination;
s5: the contribution degree of each element in the substructures set A, B, C in the second-order substructures combination is calculated, and the contribution degree of the probability that a certain substructures appears in the feasible solution set is large;
s6: according to the calculation result of S5, removing 20% of elements with minimum contribution of the substructures, and forming a new set D by the rest elements;
the method specifically comprises the following two operations:
s6.1: reserving all elements in the set A;
s6.2: the elements in the set B U C are removed by 20 percent according to the principle of minimum contribution degree of the substructure, the substructure which is considered to be very bad from the aspects of construction feasibility and aesthetic aspect is removed, and k is finally reserved 1 The individual elements form a new set D;
s7: judgingWhether the scheme satisfies the computing power of the computer or not, if so, directly from k 1 M elements are arbitrarily selected from the substructure set of the elements to form a design scheme, which is shared by +.>The objective function of each design is calculated, and a sufficient number of feasible solutions are selected for manual selection.
S8: if not, k is from set D 1 And (3) arbitrarily taking three elements from the substructures of the individual elements to form a third-order substructures combination, and calculating an objective function of each substructures combination. Returning to S6, in this loop, the order of the substructures is increased one at a time.
The invention has the following effects and benefits:
1) The worst substructure possibly occurring in the design scheme is eliminated by calculating the contribution degree of the substructures to the objective function, so that the scale of the calculated sample space is reduced.
2) Compared with the traditional optimization method, the method has low requirement on a computer and less time consumption.
3) Combining an optimization algorithm with subjective judgment, solving a set of feasible solutions of an objective function meeting design conditions within a certain bandwidth range, and determining a design scheme through manual selection according to factors such as feasibility and aesthetic factors of construction.
Drawings
FIG. 1 is a flow chart of a bridge structure optimization method based on substructure contribution.
The embodiment of fig. 2 is shown schematically.
In the figure: 1 a main structure; 2 substructures.
Detailed Description
The following describes the embodiments of the present invention in detail with reference to the technical scheme and the accompanying drawings.
The cantilever truss girder is 30m long, the upper truss is 10m high, the lower truss is divided into 7 nodes, and the truss is subjected to 360kN of concentrated force by three vertical nodes in the figure 2.
S1: a cantilever truss model is built, wherein upper and lower truss rods are main structures, and k=7 nodes are uniformly arranged, as shown in fig. 2.
S2: an alternative substructure is determined, in this example two main structures, 7 nodes on the first main structure and 7 nodes on the second main structure, the number of substructures being 49. And calculating an objective function of each substructure by adopting a finite element method, and taking the vertical average displacement at the action points of the three concentrated forces as the objective function.
S3: the substructures are ordered from big to small according to the contribution degree, 49 substructures are divided into sets A, B, C from big to small according to the contribution degree, and the number of elements in the three sets is about 1/3. The contribution of the elements in set A is the largest, set B is the next smallest, and set C is the smallest. The substructures are numbered according to the contribution degree:
{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: two elements are arbitrarily taken from the sub-structure set of 49 elements to form second-order sub-structure combinations, the number of the shared second-order sub-structure combinations is 1176, and an objective function of each second-order sub-structure combination is calculated.
S5: and calculating the contribution degree of each element in the substructures A, B, C in the second-order substructures combination, giving a threshold value of an objective function of-0.767 m, and filtering to obtain 425 solutions with the smallest contribution degree and the probability of occurrence of the substructures with the smallest contribution degree.
S6: and according to the calculation result of S5, excluding 9 elements with the minimum contribution degree of the substructures, and forming a new set D by the rest elements. The method specifically comprises the following two operations:
s6.1: reserving all elements in the set A;
s6.2: and removing 9 elements in the set B U C according to the principle of minimum contribution of the substructures, and finally reserving 40 elements to form a new set D. Removed substructures number:
{34,39,41,42,43,46,47,48,49}
s7: three elements are arbitrarily taken from the substructures of 40 elements in the set D to form three-order substructures, the total number of the three-order substructures is 9880, and the objective function of each three-order substructures is calculated.
S8: according to the calculation result of S7, the element with the smallest contribution of the substructure is excluded by 20%, and the substructure considered very bad from the viewpoint of construction feasibility, aesthetics is excluded, and the remaining 28 elements form a new set D. The elements in D are taken from the sets A, B, 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: in the process of repeating S7 and S8, 5 elements are arbitrarily taken from the substructure set D of 28 elements to form a design scheme, and 98280 design schemes are taken. These schemes have met the computational power requirements of computers.
S10: directly taking 5 elements from the substructures set D of 28 elements to form 98280 design schemes, calculating an objective function of each design scheme, and selecting a sufficient number of feasible solutions for manual selection. The 5 sets of optimal solutions for the final output are as follows:
Claims (1)
1. the bridge structure optimization method based on the substructure contribution degree is characterized by comprising the following steps:
s1: determining the number of main structures, the positions and the number of nodes possibly connected by the sub-structures on the main structures;
s2: alternative substructures are determined, the substructures being all possible ways of connecting the bars between the nodes of the main structure by connecting only one bar, the number n 1 The upper limit of (2) is:a plurality of; if there are p nodes on the first main structure and q nodes on the second main structure, the number of substructures is reduced to p x q; calculating an objective function of each substructure by adopting a finite element method;
s3: ordering the substructures from big to small according to the contribution degree, and n is selected from the following steps of 1 The sub-structures are divided into sets A, B, C from large to small according to the contribution degree, and the number of elements in the three sets is 1/3;
s4: from n 1 Two elements are arbitrarily taken from the substructures of the individual elements to form a second-order substructures combination, and the number n of the second-order substructures combination is shared 2 The method comprises the following steps:calculating an objective function of each second-order substructure combination;
s5: the contribution degree of each element in the substructures set A, B, C in the second-order substructures combination is calculated, and the contribution degree of the probability that a certain substructures appears in the feasible solution set is large;
s6: according to the calculation result of S5, removing 20% of elements with minimum contribution of the substructures, and forming a new set D by the rest elements;
the method specifically comprises the following two operations:
s6.1: reserving all elements in the set A;
s6.2: the elements in the set B U C are removed by 20 percent according to the principle of minimum contribution degree of the substructure, the substructure which is considered to be very bad from the aspects of construction feasibility and aesthetic aspect is removed, and k is finally reserved 1 The individual elements form a new set D;
s7: judgingWhether the scheme satisfies the computing power of the computer or not, if so, directly from k 1 M elements are arbitrarily selected from the substructure set of the elements to form a design scheme, which is shared by +.>Calculating an objective function of each design scheme, and selecting a sufficient number of feasible solutions for manual selection;
s8: if not, k is from set D 1 Three elements are arbitrarily taken from the substructures of the individual elements to form a third-order substructures combination, and the objective function of each substructures combination is calculated; returning to S6, in this loop, the order of the substructures is increased one at a time.
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