CN111881498A - Improved particle swarm algorithm-based frame-shear structure wall layout optimization method - Google Patents
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Abstract
The invention provides a frame-shear structure wall layout optimization method based on an improved particle swarm algorithm, provides a self-adaptive variation strategy and a whole-process dynamic adjustment factor based on population diversity, and improves a standard particle swarm algorithm. The technical scheme adopted by the invention is as follows: the position and the size of the shear wall in the structure are coded in a grading mode, each performance index limit value in the specification is used as a constraint condition, the concrete usage amount after the shear wall bottom tensile stress weighting is considered as a target function, and the shear wall layout is optimized by adopting an improved particle swarm algorithm. The invention has the beneficial effects that: after the improved particle swarm optimization algorithm is adopted, a large number of individuals can be subjected to high-efficiency heuristic search, the analysis efficiency of the arrangement problem of the shear wall is greatly improved, the using amount of wall materials is obviously reduced compared with that of the traditional manual wall arrangement mode, and the optimization result can directly guide engineering design.
Description
Technical Field
The invention belongs to the technical field of design of a frame-shear structure wall, and particularly relates to a frame-shear structure wall layout optimization method based on an improved particle swarm algorithm.
Background
The reinforced concrete frame-shear structure and the frame-cylinder structure are one of the main structural forms of high-rise buildings in China, and are widely applied. When the height of the frame-tube structure exceeds 60m, the shear walls arranged on the periphery of the middle traffic core can present the stress characteristic of the core tube, so that the frame-tube structure can be regarded as a special frame-shear structure, and the two structures are collectively called as a frame-shear structure. Because the shear wall in the frame-shear structure is the first defense line for resisting the lateral force, the layout of the shear wall has direct influence on the lateral force resistance of the structure. Therefore, shear wall layout optimization is a key step in determining the stage of the frame-shear structural solution.
In the prior art, wall limbs in a frame-shear structure have various layout modes such as a single wall, a coupled wall, an L-shaped wall, a T-shaped wall, a cross-shaped wall, a barrel body and the like, so that the position and the length of the single wall and the structural lateral stiffness are in a highly nonlinear relationship. The number of feasible solutions to the problem of shear wall layout optimization increases exponentially with the increase of the number, position and length of wall limbs, and the optimization of the shear wall layout in the traditional design method mainly depends on conceptual design and manual adjustment, so that the working efficiency is low, the shear wall layout is different from person to person, the economy is difficult to guarantee, and a large amount of unnecessary waste is caused. Therefore, aiming at the characteristics of the layout optimization problem of the shear wall, an optimization method for solving the practical engineering problem is researched and developed, and the optimization method has important significance for improving the working efficiency and saving energy and materials in the field.
Disclosure of Invention
The invention aims to provide a frame-shear structure wall layout optimization method based on an improved particle swarm algorithm, so as to improve the design efficiency and achieve the purposes of energy conservation and material conservation. In order to achieve the purpose, the invention adopts the following technical scheme:
a frame-shear structure wall layout optimization method based on an improved particle swarm algorithm comprises the following steps:
step 1: designing a variable vector: constructing a frame-shear structure model, then determining a wall distribution base point of the shear wall, and carrying out parameterization construction on the position coordinates of the base point, the direction of the shear wall and the lengths of wall limbs in all directions;
step 2: designing a first-level code of the position coordinates of each base point and a second-level code of the lengths of the wall limbs in each direction based on a two-level coding method;
and step 3: designing a constraint condition of the length of the wall limb, and then constructing an upper limit value vector according to the sequence of the secondary coding in the step2 based on the two-stage coding method in the step2, so that the upper limit value of the length of the wall limb is in one-to-one correspondence with the secondary coding in the step 2;
and 4, step 4: improving a particle swarm optimization algorithm;
and 5: and (4) inputting the secondary codes in the step (2) into the particle swarm algorithm improved in the step (4), and obtaining the wall limb length vector which can meet the constraint condition in the step (3) and enable the fitness function value in the step (4) to be continuously optimized through iteration.
Preferably, step2 specifically comprises:
step 21: based on a two-stage floating point number coding method, a first-stage code W, a second-stage code X arranged corresponding to a base point in the first-stage code W and a directional vector P corresponding to the second-stage code X one to one are constructed in sequencedDirection number vector Pn；
The primary code W comprises coordinate vectors which are arranged according to a set sequence and can be used for setting base points of the shear wall; the second-level code X is composed of shear wall information vectors S arranged in rowsiComposition is carried out; siThe lengths of the wall limbs corresponding to all directions;
step 22: based on the orientation vector PdRemoving invalid codes which cannot be laid on the wall in the secondary codes X;
step 23: vector P based on number of directionsnDecoding the optimized secondary coding X into a plurality of partitioned shear wall information vectors Si。
Preferably, the constraint conditions in step3 are:
XL＝(xj1,lim,xj2,lim,…,xjd,lim,…,xjD,lim)T；
in the formula, xjd,limIs a length limit value; j is an individual number; d is a dimension value; lim represents a limit.
Preferably, the improvement of the particle group algorithm in the step4 comprises design of an inertia weight factor, design of a learning factor, selection of a fitness function and design of a variation strategy.
Preferably, the inertia weight factor ω and the learning factor c1、c2The models of (a) are respectively:
in the formula, TmaxIs the set maximum iteration number; t is the iteration number;
ω (T) is an inertial weight factor that varies dynamically with the number of iterations T;
ωstartfor a set initial value of the inertial weight factor, ωendSetting the final value of the inertia weight factor after iteration is finished;
k1、k2respectively are regulating factors;
c1、c2is a learning factor that dynamically changes with the number of iterations T;
c1,startis c1An initial value of the iteration; c. C1,endIs c1A final value of the iteration;
c2,startis c2An initial value of the iteration; c. C2,endIs c2The final value of the iteration.
Preferably, the model of the fitness function is:
wherein F is the number of the floor, and F is the total number of the floors;
i is the length grouping number of the shear wall components, and N is the total number of the arrangement numbers of all the shear walls;
Lithe length value of the ith shear wall is obtained;
tfthe thickness value of the shear wall of the f floor is shown, and H is the height value of the floor;
j is the number of the beam member, and M is the total number of all the beam members of the single-storey floor;
Blis the width of the beam section, BwIs a height value of the beam section, Lb,jIs the length value of the jth beam member;
k is the number of the column members, and P is the total number of all the column members of the single-storey floor;
Clis the value of the width of the column section, CwIs a height value of the column section, Lc,kIs the length value of the kth column member;
s is the number of the column or wall member having the wall bottom tensile stress, and S is the total number of the column or wall member having the wall bottom tensile stress;
γsfor conversion ratio of reinforcing bars to concrete, VsThe amount of steel bars needed to be allocated for considering the tensile stress of the wall bottom.
Preferably, the functional model of the mutation strategy is:
in the formula, PmIs the threshold of variation; d is the dimension; dmIs a diversity threshold;
k is a control parameter, 0<K<1 for controlling PmThe degree of smoothness of the curve;
Pm,startis the initial value of the variation; pm,endIs the final value of the variation.
Preferably, the improved particle swarm algorithm in the step4 specifically includes the following steps:
step 1: initializing parameters in a particle swarm algorithm: omegastart、c1,start、c2,startMaximum number of iterations TmaxSetting the historical optimal value of each particle as pbest and the group optimal value as gbest;
step 2: in contemporary evolution, the fitness function of each particle is calculatedNumerical value
Step 3: updating pbest and gbest of the particle;
step 4: updating the speed and position of the particles;
step 5: checking and calculating population diversity: calculating the population diversity of the current generation, if the population diversity is greater than the diversity threshold, skipping Step6, and executing Step 7; if the population diversity is smaller than the diversity threshold, executing Step 6;
step 6: randomly generating variation probability, if the variation probability is greater than a variation threshold, executing variation operation to change the length of the wall limb according to the set probability;
step 7: and (3) iterative calculation: judging whether the maximum iteration number is reached, if not, returning to Step4, and continuing to execute steps 4-Step 6; otherwise, the iteration is terminated, and gbest is output.
Compared with the prior art, the invention has the advantages that:
(1) the method comprises the steps of determining a performance constraint condition and a geometric dimension constraint condition of a structure according to design conditions such as building functions, site environments and the like, carrying out secondary floating point number coding on coordinates, directions and lengths of nodes of the shear wall in a frame-shear structure, taking the consumption of shear wall concrete weighted by wall bottom tensile stress as a target function, improving a standard particle swarm algorithm by providing a self-adaptive variation strategy and a whole-process dynamic adjustment factor based on population diversity, optimizing by the improved particle swarm algorithm to obtain the optimal layout of the shear wall, and remarkably improving the design efficiency and the economy of design results.
(2) The two-stage coding method is adopted, and the indexes of the positioning vector, the directional vector and the direction number vector of the first-stage coding are utilized to simplify the second-stage coding for optimization as much as possible, so that the optimization workload is greatly reduced.
(3) Geometric constraint conditions such as room division, doors, window openings and the like are introduced, so that the optimization result can adapt to the building layout, and the method is high in practicability.
(4) The concrete consumption of the shear wall after weighted correction of the tensile stress at the bottom of the wall limb is taken as a target function, the stress of the wall limb and the material consumption are considered, and the optimized shear wall is more reasonable in layout.
(5) The variation strategy based on the population diversity is considered, the improved particle swarm algorithm of the dynamic adjustment factors in the whole process is adopted, and the probability that the shear wall layout falls into the local optimal solution is remarkably reduced.
Drawings
Fig. 1 is a flowchart of a particle swarm algorithm in a frame-shear structure wall layout optimization method based on an improved particle swarm algorithm according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating the relationship between the positions and the codes of the base point and the shear wall in step2 according to an embodiment of the present invention;
FIG. 3 is a schematic diagram illustrating a two-level encoding method in step2 according to an embodiment of the present invention;
FIG. 4 is a simplified shear wall information vector S after the two-level code X conversion blocking process in step2 according to an embodiment of the present inventioniA schematic diagram of the conversion of (1);
fig. 5 is a variation curve of a moderate function value when the improved particle swarm algorithm-based frame-shear structure wall layout optimization method is applied in the embodiment of the present invention.
Detailed Description
The present invention will now be described in more detail with reference to the accompanying schematic drawings, in which preferred embodiments of the invention are shown, it being understood that one skilled in the art may modify the invention herein described while still achieving the advantageous effects of the invention. Accordingly, the following description should be construed as broadly as possible to those skilled in the art and not as limiting the invention.
The embodiment provides a frame-shear structure wall layout optimization method based on an improved particle swarm algorithm, which comprises the following steps of 1-5:
step 1: designing a variable vector: and constructing a frame-shear structure model, then determining a wall distribution base point of the shear wall, and carrying out parameterization construction on the position coordinates of the base point, the direction of the shear wall and the lengths of the wall limbs in all directions.
Step 11: according to building functions and field design conditions, the intersection point of the axes of the beam, the column and the wall is used as a wall distribution base point, then base points of a plurality of shear walls are selected, and a coordinate vector of the base point is established. As shown in FIG. 2, the positions of circles 1-6 are the wall laying base points.
Step 12: the direction and size of the shear wall at the base point is determined.
All base points determine 4 directions in a unified way, and correspond to 4 values respectively. As shown in fig. 2, a plurality of base points for arranging the shear walls are selected, and the number of directions in which the shear walls can be arranged on each base point is different. For example, No. 4 and No. 6 base points can be used for arranging the shear walls in 4 directions, No. 2, No. 3 and No. 5 base points can only be used for arranging the shear walls in 3 directions, and No. 1 base points can only be used for arranging the shear walls in 2 directions, and each base point has a corresponding wall limb length value in each direction. Although the number of directions in which the shear walls can be arranged on the base points is different, if the number of the arrangement directions of all the base points is unified to 4, that is, there are 4 directions, each of the base points will have 4 specific values, which respectively represent the length values of the shear walls in the 4 directions. If the shear wall cannot be arranged in a certain direction of a certain base point, the length value in the direction is forced to be 0, and if the shear wall cannot be arranged in two directions in the No. 1 base point in FIG. 2, the length value in the corresponding direction is set to be 0.
Step 13: and determining a shear wall information matrix.
In order to facilitate the subsequent parameterization process, the length values correspond to the directions one by one, and the following regulations are made for each direction of the shear wall: the forward direction (i.e. the length value increasing direction) of the X direction of the floor plan is taken as the 1 st direction, the other directions are counted in turn in the anticlockwise direction, and if the forward direction of the Y direction is the 2 nd direction, the rest is done in turn. Taking the reference point No. 6 in fig. 2 as an example, a wall limb with a length of 4.5m corresponds to the 1 st direction, a wall limb with a length of 4m corresponds to the 2 nd direction, a wall limb with a length of 4.2m corresponds to the 3 rd direction, a wall limb with a length of 3.2m corresponds to the 4 th direction, and the rest of the reference points are analogized. The length values of the shear walls in the 4 directions of each base point correspond to 4 values, and the 4 values are arranged according to the sequence of the 1-4 directions to form a vector. The vectors of a plurality of base points are combined to form a shear wall information matrix. Therefore, the position coordinates of the shear wall base points, the direction of the shear wall and the length information of the wall limbs in the frame-shear structure are all converted into a rectangular form, and the parameterization processing of the shear wall is realized.
Step 2: based on a two-stage coding method, a primary coding of the position coordinates of each base point and a secondary coding of the lengths of the wall limbs in each direction are designed. On the basis of floating-point number coding, a two-stage coding method is provided. The two-stage coding method is divided into 2 steps: firstly, determining base points for arranging the shear wall according to building functions and limiting conditions, sequencing coordinates of the base points according to a certain number to obtain codes, and then sequentially distributing length values in four directions of each base point according to a floating point number coding method.
Step 21: based on a two-stage floating point number coding method, a first-stage code W, a second-stage code X arranged corresponding to a base point in the first-stage code W and a directional vector P corresponding to the second-stage code X one to one are constructed in sequencedDirection number vector Pn(ii) a The primary code W comprises coordinate vectors which are arranged according to a set sequence and can be used for setting base points of the shear wall; the second-level code X is composed of shear wall information vectors S arranged in rowsiComposition is carried out; siThe lengths of the wall limbs corresponding to all directions.
In the present embodiment, as shown in fig. 2 to 4, the coordinates of the base points No. 1 to 6 are (0, 0), (0, 8), (8, 0), (24, 0), (24, 32), respectively, and the other positions are considered to be limited by the building and not to allow the arrangement of the shear wall. The first-level coding is to put 6 base points into a coordinate vector according to a self-defined sequence, and to clarify the sequence of each base point so as to correspond to the next second-level coding, the first-level coding is as follows:
W＝((0，0),(0，8)，(8，0)，(8，8)，(24，0)，(24，32))T；
and the specification of the length of each wall limb is completed by adopting a floating point coding method. The vectors at the base points are respectively S1＝(3，3，0，0)T，S2＝(3，0，0，3)T，S3＝(0，3，3，0)T，S4＝(0，0，3，3)T，S5＝(4.8，4，4.2，0)T，S6＝(4.5，4，4.2，3.2)TThen the above 6 vectors are groupedSynthesizing a shear wall information matrix with 4 rows and 6 columns, namely:
X＝[S1，S2，S3，S4，S5，S6]
each row of X represents the length value of all base points in the same direction, and each column represents the length value of a point in all directions. In order to be consistent with the form of particle swarm optimization, the matrix needs to be converted into a position vector, and the conversion method is as follows: changing the matrix to a vector by changing 6 columns of the matrix to 1, i.e., placing the 2 nd column vector of the matrix below the first column vector, and then placing the row vector of the 2 nd column immediately below, and so on, until all column vectors have been converted to column vectors of only 1 column, at which point the matrix is changed to a vector, with the position variable X ═ 3, 3, 0, 0, 3, 0, 0, 3, 3, 4.8, 4, 4.2, 0, 4.5, 4, 4.2, 3.2)T。
Step 22: based on the orientation vector PdAnd removing invalid codes which cannot be subjected to wall laying in the secondary codes X. During the shear wall parameterization process (step 12), some base points cannot be arranged with the shear wall in some directions due to building limitations and are forced to be set to 0, so that elements which do not change exist in the matrix, and the elements do not accord with the concept of design variables, and the dimension value D is increased. Therefore, the original position vector X needs to be correctedt iRemoving the redundant 0 elements in the vector, and not removing the elements which are not 0 due to the construction limitation so as to ensure that all elements in the vector are variable, wherein the specific improvement thought is as follows: on the basis of one-level coding in a two-level coding method, improvement is carried out, a direction constraint condition is introduced, a directional vector is set, and all values in the directional vector correspond to position vectors one by one.
As shown in FIG. 3, an orientation vector, P, is addedd＝((1，2)，(1，4)，(2，3)，(3，4)，(1，2，3)，(1，2，3，4))TThe direction represented by the number in the orientation vector also corresponds to the new position variable one by one, and the improved position variable X is (3, 3, 3, 3, 3, 3, 3, 4.8, 4, 4.2, 4.5, 4, 4.2, 3.2)T. It can be seen that the 1 direction and the 2 direction of the base point No. 1 are both 3 in the position vector X, and the base point No. 6 also corresponds to 4.5, 4, 4.2, and 3.2 in the four directions, respectively, consistent with the actual arrangement.
Step 23: as shown in fig. 4, vector P is based on the number of directionsnDecoding the optimized secondary coding X into a plurality of partitioned shear wall information vectors Si。
Due to the simplified operation, the individual position vector generated by each iteration in the particle swarm algorithm cannot directly guide the parametric modeling process of the shear wall, and the position vector generated by the two-stage encoding method must be decoded to convert the individual position into the form of a shear wall information matrix or vector.
Pd＝(d1，d2，…，di)T，diA direction array of shear walls can be arranged at the ith base point;
Pn＝(k1，k2，…，ki)T，kithe number of directions in which the shear wall can be arranged at the ith base point.
As shown in FIG. 2, there are 3 directions in which the shear wall can be arranged at the base point 5, namely, the first, second and third directions, i.e., d5＝(1，2，3)；k5When the result is 3, then Pd＝((1，2)，(1，4)，(2，3)，(3，4)，(1，2，3)，(1，2，3，4))T，Pn＝(2，2，2，2，3，4)T。
And step 3: and (3) designing a constraint condition of the length of the wall limb, and then constructing an upper limit value vector according to the sequence of the secondary coding in the step2 based on the two-stage coding method in the step2, so that the upper limit value of the length of the wall limb is in one-to-one correspondence with the secondary coding in the step 2.
During the parameterization processing of the shear wall, a certain length of the shear wall can be arranged in the direction allowing the arrangement of the shear wall. As shown in fig. 2, the maximum length of the shear wall of the base point No. 5 in the 3 direction is 8 m. In the base point No. 1 and the base point No. 2, since the No. 2 direction of the base point No. 1 is opposite to the No. 4 direction of the base point No. 2, the sum of the two values in the two directions can not exceed the two base pointsThe maximum value of the length of the shear wall in both directions of the two base points is taken to be half of the span, i.e., Li,2∈[0，l/2]Wherein L isi,2The limb length in the 2 nd direction for the ith base point; l is the span between two base points.
Geometric constraint of the base point in each direction requires factors such as a sum span value and architectural arrangement limits of doors, windows, holes and the like, and takes a smaller value, namely
The constraint conditions are as follows:
L1＝{L1,1,L2,1,L3,1,…,LN,1},
and L isi,1∈[0,li,1,limit]；
L2＝{L1,2,L2,2,L3,2,…,LN,2},
And L isi,2∈[0,li,2,limit]；
L3＝{L1,3,L2,3,L3,3,…,LN,3},
And L isi,3∈[0,li,3,limit]；
L4＝{L1,4,L2,4,L3,4,…,LN,4},
And L isi,4∈[0,li,4,limit]；
In the formula, Li,1,limit，Li,2,limit，Li,3,limit，Li,4,limitRespectively, the geometric maximum value of the ith base point in 4 directions due to construction limitations.
Because the vector expression in four directions exists, the vector expression is inconsistent with the expression form of an individual in the particle swarm optimization and is not squareThe particle swarm algorithm is executed. Therefore, the shear wall information vectors are converted into a plurality of shear wall information vectors, the shear wall information vectors are respectively provided with upper limit values, then the shear wall information vectors are converted into a special position vector according to a two-stage coding method, and the position vector is an upper line value vector of a solution space, namely XL：
XL＝(xj1,lim,xj2,lim,…,xjd,lim,…,xjD,lim)T
Wherein x isj1,limIs a length limit value and is unchanged; d is the dimension; j is an individual number; d is a dimension value; lim represents a limit.
And 4, step 4: and improving a particle swarm optimization algorithm. The improvement of the particle swarm optimization comprises the design of an inertia weight factor, the design of a learning factor, the selection of a fitness function and the design of a variation strategy.
(1) Inertia weight factor omega, learning factor c1、c2The models of (a) are respectively:
in the formula, TmaxIs the set maximum iteration number; t is the iteration number;
ω (T) is an inertial weight factor that varies dynamically with the number of iterations T;
ωstartfor a set initial value of the inertial weight factor, ωendSetting the final value of the inertia weight factor after iteration is finished;
k1、k2respectively are regulating factors; k is a radical of1Mainly controlling the variation of omega (T) between 0.4 and 0.9, k2Mainly controlling the smoothness of a variation curve of omega (T) and T;
c1、c2is a learning factor that dynamically changes with the number of iterations T;
c1,startis c1The initial value of iteration is 2.75; c. C1,endIs c1Taking the final value of iteration to be 1.25;
c2,startis c2Taking 0.5 as an initial value of iteration; c. C2,endIs c2The final value of the iteration was taken to be 2.25.
The main purpose of improving the inertial weighting factor ω is to balance the local and global search capabilities when 0 < k2When the number of the iteration times is less than 1, the algorithm has a larger inertia weight factor at the early stage, but the inertia weight factor is rapidly reduced along with the increase of the iteration times, namely the search of the whole space is rapidly completed, and then the search is continuously completed by using a smaller inertia weight factor, so that the local search capability is enhanced, the convergence of the algorithm is improved, and the local optimal solution is effectively avoided; when k is2When the inertial weight factor is more than 1, the descending speed of the inertial weight factor in the early stage of the algorithm is lower, and the descending speed in the later stage is higher, so that the algorithm can fully ensure the global searching capability in the early stage, and simultaneously has a larger inertial weight factor in the later stage, and can effectively avoid trapping in a local optimal solution on the basis of ensuring the convergence.
Improved learning factor c1、c2The purpose of (1) is as follows: early algorithm pass delay c1And acceleration c2The algorithm slowly enters local search, the global search capability is enhanced, so that the local optimal solution is effectively avoided from being trapped, and more ideal c than a linear change strategy is set at the later stage of the algorithm1、c2By acceleration of c1And delay c2To accelerate convergence to a certain extent, thereby ensuring the convergence of the algorithm.
(2) The model of the fitness function is:
wherein F is the number of the floor, and F is the total number of the floors;
i is the length grouping number of the shear wall components, and N is the total number of the arrangement numbers of all the shear walls;
Lithe length value of the ith shear wall is obtained;
tfthe thickness value of the shear wall of the f floor is shown, and H is the height value of the floor;
j is the number of the beam member, and M is the total number of all the beam members of the single-storey floor;
Blis the width of the beam section, BwIs a height value of the beam section, Lb,jIs the length value of the jth beam member;
k is the number of the column members, and P is the total number of all the column members of the single-storey floor;
Clis the value of the width of the column section, CwIs a height value of the column section, Lc,kIs the length value of the kth column member;
s is the number of the column or wall member having the wall bottom tensile stress, and S is the total number of the column or wall member having the wall bottom tensile stress;
γsfor conversion ratio of reinforcing bars to concrete, VsThe amount of steel bars needed to be allocated for considering the tensile stress of the wall bottom.
In actual engineering, the shear wall bears most of earthquake substrate shear, meanwhile, earthquake overturning moment can also generate tensile stress on the section of the bottom of a wall limb, and after the wall limb is cracked due to the tensile stress, the shear-resistant bearing capacity of the shear wall can be greatly reduced. Therefore, if the number of the wall limbs can meet various index requirements according to the elasticity analysis result, but the tensile stress at the bottom of the wall limbs is greater than the tensile strength of concrete, the shear-resistant bearing capacity of the shear wall needs to be reinforced by measures such as configuration of section steel and the like, and the analysis result shows that the arrangement of the shear wall is less and is not the optimal scheme. Therefore, it is necessary to introduce the tensile stress at the bottom of the wall limb into the objective function, and the specific conversion equation is weighted by the amount of steel. Assuming that all the tensile stress generated at the bottom of the shear wall is borne by the steel bars, the additional steel bar manufacturing cost generated due to the tensile stress is converted into equal-value concrete according to the price, and the material consumption of the steel bars is converted into the material consumption of the concrete, so that the material consumption of the objective function-integral structure concrete is kept unchanged at a minimum. Therefore, the above objective function (fitness function) actually consists of two parts: one part does not consider the material dosage under the condition of wall bottom tensile stress (total concrete volume of beam-column wall), and the other part considers the material dosage under the condition of wall bottom tensile stress (obtained by conversion of values such as reinforcing steel bar dosage).
(3) The function model of the mutation strategy is:
in the formula, PmIs the threshold of variation;
k is a control parameter, 0<K<1, take 0.5, for controlling PmThe smoothness of the curve and the change curve of D;
Pm,starttaking 0.8 as the initial value of variation; pm,endThe final value of the variation was 0.3.
The parameters associated with the algorithm take the following values: the population size N is 25-40, and the diversity threshold value DmTaking the value of 2.25; the fine search coefficient takes 0.3, and the maximum speed proportionality coefficient takes 0.4.
And 5: and (4) inputting the secondary codes in the step (2) into the particle swarm algorithm improved in the step (4), and obtaining the wall limb length vector which can meet the constraint condition in the step (3) and enables the fitness function value to be continuously optimized through iteration. As shown in particular in figure 1.
Step 1: initializing parameters in a particle swarm algorithm: omegastart、c1,start、c2,startMaximum number of iterations TmaxSetting the historical optimal value of each particle as pbest and the group optimal value as gbest;
step 2: in contemporary evolution, the fitness function value of each particle is calculated
Screening out the present pbest and gbest from the individuals; the individual optimal position variables for each generation are set as:
the global optimal position variable for each generation is set as:
step 3: the pbest and gbest of the particle are updated.
Step 4: and updating the speed and the position of the particle, wherein the updating formula of the particle is as follows:
position variable
Speed variable
Wherein the content of the first and second substances,
a d-dimension position variable for the ith individual of the t generation;
d-dimension speed variable of ith individual for t generation;
the d-dimension individual historical optimal position of the ith individual of the t generation;
is the global optimum position of the d-th dimension of the t generation;
r1，r2is a random number uniformly distributed in the interval of (0, 1); c. C1，c2Is a learning factor.
Step 5: checking and calculating population diversity: calculating the population diversity of the current generation, if the population diversity is greater than the diversity threshold, skipping Step6, and executing Step 7; if the population diversity is less than the diversity threshold, Step6 is performed.
Wherein, the calculation formula of the population diversity is as follows:
m is the total number x of particlesiIs a position variable of the particle, pcD is the diversity of the particle population, is the position variable of the particle in the central position of the particle population.
Step 6: and randomly generating variation probability, and if the variation probability is greater than a variation threshold, executing variation operation to change the length of the wall limb according to the set probability.
(1) Randomly generating variation probability by each particle, triggering a variation mechanism if the variation probability is larger than a variation threshold, and updating the position variable of the particle according to the following formula
And checking whether the position variable is out of range, and if so, setting the position value smaller than the minimum value and the position value larger than the maximum value as a preset position minimum value and a preset position maximum value respectively.
In the above formula, xidIs the position variable of the ith particle in the d dimension;
r is a random number between intervals [ -1,1], the sign of which represents the direction of particle variation;
lmax、lminrepresents the upper limit and the lower limit of the position variable of the particle in the d-dimension;
p is the probability of the current mutation;Pmis the threshold of variation.
K is a control parameter and must satisfy 0<K<1, for controlling PmSmoothing of the curve of variation with D, Pm,start、Pm,endRespectively referring to the initial value and the final value of the variation, and taking Pm,start＝0.8，Pm,end＝0.3。
The inequality on the right side of the above equation indicates that the left equation can only be executed when the probability P of the current occurrence of the mutation is greater than the mutation threshold. Until a maximum number of iterations is reached.
(2) If the mutation probability is not greater than the mutation threshold, the mutation mechanism is not triggered. The variation threshold varies with population diversity.
Step 7: and (3) iterative calculation: judging whether the maximum iteration number is reached, if not, returning to Step4, and continuing to execute steps 4-Step 6; otherwise, the iteration is terminated, and gbest is output.
The method of the invention is verified by combining a built project case as follows: 13 layers above the main floor of a certain project, 3 layers below the ground, and 57.85m from the outdoor ground to the main roof, and belongs to an A-level high-rise reinforced concrete building structure. The project is regular in plane arrangement, the length along the X direction is 67.20m, the length along the Y direction is 31.50m, and the main structure is a frame-shear wall structure. The service life of the project structural design is 50 years, the safety level of the main structure of the building is two levels, and the corresponding structural design importance coefficient gamma iso1.0, the seismic fortification intensity of the location is 7 degrees, the designed basic seismic acceleration is 0.15g, the designed earthquake group is a second group, the seismic fortification category is class C, the site category is class III, the site characteristic period is 0.55s, and the horizontal earthquake influence coefficient is 0.12. In the area, the basic wind pressure omega is 0.45kN/m, the basic snow pressure s is 0.4kN/m, the wind carrier type coefficient is 1.3, and the ground roughness is B type. The floor constant load design is 4.5kN/m2(constant load takes the weight of floor slabs, surface layers, suspended ceilings, partition walls and the like into consideration, wherein the thickness of the floor slabs is calculated according to 120 mm), and the live load design of the roof is 3.5kN/m2. The reinforced concrete has the strength grade of C40, the designed value of the compressive strength of 19.1MPa and the elastic modulus of 3.25 multiplied by 104MPa, Poisson's ratio of 0.2. Principal in the modelThe material dimensions were as follows: 700mm is multiplied by 700mm for columns, 400mm is multiplied by 700mm for beams, 400mm is multiplied by 600mm for secondary beams, and 400mm is multiplied by 600mm for shear wall thickness. Considering the design value of the axial pressure of the earthquake action combination according to the load working condition which plays a role in controlling the bearing capacity, namely: 1.2 times (dead load +0.5 live load) +1.4 times seismic action. And considering the pressure design value of the shear wall according to the pressure design value born by the wall limb under the action of the gravity load representative value. In addition, the indexes are calculated according to standard values under the action of multi-earthquake. Horizontal seismic action is applied using reaction spectroscopy. FIG. 2 is a plan view of the standard layer structure of the process. And (3) carrying out secondary development on the general finite element program by adopting Python language and taking the node and length values of the shear wall as optimization variables and the minimum material consumption as an optimization target under the limitation of constraint conditions, and carrying out optimization iteration through the developed program. FIG. 5 is a diagram of a shear wall layout of a post-iteration project, where X is the number of iterations and Y is the material usage; the results of the design comparison of the optimized engineering example wall and the original scheme are given in table 1.
TABLE 1 comparison of the design of the actual engineering with the main mechanical performance indexes of the design iteratively generated by the optimization algorithm
As can be seen from FIG. 5, the optimization of the method of the invention reduces the dosage of the concrete material along with the increase of the iteration times, and the optimization is converged according to the limiting conditions, which shows that the method of the invention is real and effective.
From table 1, it can be seen that the original solution has performed many rounds of manual optimization adjustments in order to control structure torsion, base shear, etc. However, the optimization of the structural performance needs the cooperative consideration of the shear walls of all parts, the optimization efficiency is low through manual adjustment, and the optimal solution distance is large.
The displacement angle is only increased by 13% and 6.3% in two directions respectively, but the shearing force of the substrate is reduced by 24% and 16% in two directions respectively, and particularly the surplus degree of the original scheme in the X direction is remarkably reduced, so that the performances of the structure in the X, Y two directions are as close as possible, the optimization of the shear wall is realized under the condition that the structural performance is not remarkably reduced, and the effect is good. The optimization algorithm can improve the material utilization efficiency of the shear wall, improve the plane arrangement of the shear wall of the frame-shear structure, reduce the material consumption of the structure and the wall arrangement rate of floors, and improve the mechanical property of the structure.
Compared with the actual engineering, the shear wall has the advantages that the accuracy of size selection is higher, the material consumption is better, automatic optimization and adjustment can be realized, the optimization and adjustment of the shear wall can be quickly realized after the building scheme is adjusted, and the working efficiency is improved.
The above description is only a preferred embodiment of the present invention, and does not limit the present invention in any way. It will be understood by those skilled in the art that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. A frame-shear structure wall layout optimization method based on an improved particle swarm algorithm is characterized by comprising the following steps:
step 1: designing a variable vector: constructing a frame-shear structure model, then determining a wall distribution base point of the shear wall, and carrying out parameterization construction on the position coordinates of the base point, the direction of the shear wall and the lengths of wall limbs in all directions;
step 2: designing a first-level code of the position coordinates of each base point and a second-level code of the lengths of the wall limbs in each direction based on a two-level coding method;
and step 3: designing a constraint condition of the length of the wall limb, and then constructing an upper limit value vector according to the sequence of the secondary coding in the step2 based on the two-stage coding method in the step2, so that the upper limit value of the length of the wall limb is in one-to-one correspondence with the secondary coding in the step 2;
and 4, step 4: improving a particle swarm optimization algorithm;
and 5: and (4) inputting the secondary codes in the step (2) into the particle swarm algorithm improved in the step (4), and obtaining the wall limb length vector which can meet the constraint condition in the step (3) and enable the fitness function value in the step (4) to be continuously optimized through iteration.
2. The improved particle swarm algorithm-based frame-shear structure wall layout optimization method according to claim 1, wherein the step2 specifically comprises:
step 21: based on a two-stage floating point number coding method, a first-stage code W, a second-stage code X arranged corresponding to a base point in the first-stage code W and a directional vector P corresponding to the second-stage code X one to one are constructed in sequencedDirection number vector Pn；
The primary code W comprises coordinate vectors which are arranged according to a set sequence and can be used for setting base points of the shear wall; the second-level code X is composed of shear wall information vectors S arranged in rowsiComposition is carried out; siThe lengths of the wall limbs corresponding to all directions;
step 22: based on the orientation vector PdRemoving invalid codes which cannot be laid on the wall in the secondary codes X;
step 23: vector P based on number of directionsnDecoding the optimized secondary coding X into a plurality of partitioned shear wall information vectors Si。
3. The improved particle swarm optimization-based frame-shear structure wall layout optimization method according to claim 1, wherein the constraint conditions in the step3 are as follows:
XL＝(xj1,lim,xj2,lim,…,xjd,lim,…,xjD,lim)T；
in the formula, xjd,limIs a length limit value; j is an individual number; d is a dimension value; lim represents a limit.
4. The improved particle swarm optimization-based frame-shear structure wall layout optimization method according to claim 1, wherein the improvement of the particle swarm optimization in the step4 comprises design of inertia weight factors, design of learning factors, selection of fitness functions and design of variation strategies.
5. The improved particle swarm optimization-based frame-shear structure wall layout optimization method according to claim 4, wherein the inertia weight factor ω and the learning factor c are1、c2The models of (a) are respectively:
in the formula, TmaxIs the set maximum iteration number; t is the iteration number;
ω (T) is an inertial weight factor that varies dynamically with the number of iterations T;
ωstartfor a set initial value of the inertial weight factor, ωendSetting the final value of the inertia weight factor after iteration is finished;
k1、k2respectively are regulating factors;
c1、c2is a learning factor that dynamically changes with the number of iterations T;
c1,startis c1An initial value of the iteration; c. C1,endIs c1A final value of the iteration;
c2,startis c2An initial value of the iteration; c. C2,endIs c2The final value of the iteration.
6. The improved particle swarm optimization-based frame-shear structure wall layout optimization method according to claim 5, wherein the fitness function model is as follows:
wherein F is the number of the floor, and F is the total number of the floors;
i is a length grouping number of the shear wall component;
n is the total number of all the shear wall arrangements;
Lithe length value of the ith shear wall is obtained;
tfthe thickness value of the shear wall of the f floor is shown, and H is the height value of the floor;
j is the number of the beam member, and M is the total number of all the beam members of the single-storey floor;
Blis the width of the beam section, BwIs a height value of the beam section, Lb,jIs the length value of the jth beam member;
k is the number of the column members, and P is the total number of all the column members of the single-storey floor;
Clis the value of the width of the column section, CwIs a height value of the column section, Lc,kIs the length value of the kth column member;
s is the number of the column or wall member having the wall bottom tensile stress, and S is the total number of the column or wall member having the wall bottom tensile stress;
γsfor conversion ratio of reinforcing bars to concrete, VsThe amount of steel bars needed to be allocated for considering the tensile stress of the wall bottom.
7. The improved particle swarm optimization-based frame-shear structure wall layout optimization method according to claim 6, wherein the function model of the mutation strategy is as follows:
in the formula, PmIs the threshold of variation; d is the dimension; dmIs a diversity threshold;
k is a control parameter, 0<K<1 for controlling PmThe degree of smoothness of the curve;
Pm,startis the initial value of the variation; pm,endIs the final value of the variation.
8. The improved particle swarm algorithm-based frame-shear structure wall layout optimization method according to any one of claims 1 to 7, wherein the improved particle swarm algorithm in the step4 specifically comprises the following steps:
step 1: initializing parameters in a particle swarm algorithm: omegastart、c1,start、c2,startMaximum number of iterations TmaxSetting the historical optimal value of each particle as pbest and the group optimal value as gbest;
step 2: in contemporary evolution, the fitness function value of each particle is calculated
Step 3: updating pbest and gbest of the particle;
step 4: updating the speed and position of the particles;
step 5: checking and calculating population diversity: calculating the population diversity of the current generation, if the population diversity is greater than the diversity threshold, skipping Step6, and executing Step 7; if the population diversity is smaller than the diversity threshold, executing Step 6;
step 6: randomly generating variation probability, if the variation probability is greater than a variation threshold, executing variation operation to change the length of the wall limb according to the set probability;
step 7: and (3) iterative calculation: judging whether the maximum iteration number is reached, if not, returning to Step4, and continuing to execute steps 4-Step 6; otherwise, the iteration is terminated, and gbest is output.
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