CN117634232A - Large flexible sheet clamp number optimization method based on improved particle swarm algorithm - Google Patents
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Abstract
The invention provides a method for optimizing the number of large flexible sheet clamps based on an improved particle swarm algorithm, which comprises the following steps: step1, constructing a three-dimensional model of a large flexible sheet, and deriving a data interaction file of the constructed model; step2, dividing the finite element grids, and deriving form source code files; step3, extracting characteristic data, and reading form source code files to extract related data, wherein the related data comprise node coordinates of finite element grid division, a rigidity matrix of a model, a force matrix of the model and the like; step4, optimizing by utilizing an improved particle swarm algorithm to obtain the optimal fixture number and the fixture distribution at the moment under the condition of meeting the assembly requirement; and 5, checking and visualizing the optimized result. On the premise of meeting engineering requirements, the invention makes the cost brought by the number of the clamps and the movement of the clamps as small as possible, and provides an optimization scheme for the number of the clamps used in the assembly process of the large flexible thin plate.
Description
Technical Field
The invention relates to the field of quality management and intelligent assembly system design optimization, in particular to a large flexible sheet clamp number optimization method based on an improved particle swarm algorithm.
Background
In the field of production and assembly, parts such as an airplane body and a ship hull are formed by splicing and assembling large flexible thin plates, and the thin plates are mainly characterized in that: the internal dimensions are very large (the width and length of the plate are very large), while the thickness of the plate is very small, i.e. the plate has the characteristics of large scale and low rigidity, so that the parts are easy to locally deform under the action of gravity. In the current production assembly, large flexible sheets are generally positioned by using an N-2-1 principle, and then are spliced in pairs in a connecting mode of riveting, welding and the like, so that a larger sheet is assembled. The layout scheme of the N positioning fixtures used in the assembly positioning process can directly influence the flexible deformation degree of the large flexible sheet, and further can directly influence the assembly quality of the large flexible sheet. Meanwhile, each fixture is added or each fixture is moved once, extra cost is generated, so that the number and movement of the fixtures are reduced as much as possible under the condition of meeting the assembly and splicing requirements, and the improvement of profits and added value of products is very important.
The positioning fixture used in the assembly process of the large-scale sheet at present mainly adopts a fixed column-type jig frame structure, and the fixture is uniformly distributed in the projection plane of the sheet in an equidistant mode. Since the large sheets used for aircraft fuselages and ship hulls mostly have a relatively complex profile, simply increasing the number of "N" and evenly distributing them while reducing the assembly gap between the two sheets to some extent allows them to meet the maximum allowable gap before welding or riveting, but creates more additional costs, reduces average profits, is "uneconomical" and "unreasonable" for the manufacture of single piece products, and can be improved. Aiming at the problems, the invention provides a large flexible sheet clamp number optimization method based on an improved particle swarm algorithm.
Disclosure of Invention
The invention aims to provide a method for optimizing the number of large flexible sheet clamps based on an improved particle swarm algorithm, aiming at the defects of the prior large flexible sheet clamps in the assembly process and unnecessary cost caused by a large number of clamps.
In order to achieve the above purpose, the invention provides a method for optimizing the number of large flexible sheet clamps based on an improved particle swarm algorithm, which comprises the following steps:
s1, constructing a large flexible sheet three-dimensional model, and deriving a data interaction file of the constructed model;
s2, dividing the finite element grids, and deriving form source code files;
s3, extracting characteristic data, setting parameters such as material properties, load distribution, constraint and the like, and extracting finite element grid node coordinates, a rigidity matrix of the sheet model and a force matrix of the sheet model; setting constraint point serial numbers in x and y directions according to an N-2-1 positioning method;
s4, optimizing an improved particle swarm algorithm, and searching to obtain the optimal fixture number and the fixture layout at the moment under the condition of meeting the assembly requirement by utilizing the improved particle swarm algorithm;
and S5, verifying the optimizing effect and visualizing the optimizing result, and respectively restraining in finite element analysis by utilizing the obtained optimal fixture number meeting the assembly requirement condition and the fixture layout (namely the z-direction fixture restraint sequence number and the x-direction and y-direction restraint point sequence numbers set according to the N-2-1 positioning method) at the moment to obtain a deformation cloud picture of the sheet, thereby completing verification and visualization.
Further, in S2, the finite element mesh is divided on the model by the finite element mesh dividing software, the data interaction file of the model at this time is derived, and the number of nodes of the finite element mesh of the two sheets and the coordinates corresponding to each node are extracted from the data interaction file.
Further, in S3, finite element analysis software is utilized to analyze, and the material properties, density, young' S modulus and Poisson ratio of the two plates are set; model simplification is carried out according to the actual situation when two thin plates are assembled and spliced: setting no interaction between the two thin plates and only loading gravity; after the parameters are set, the rigidity matrix and the force matrix of the two thin plates are derived and respectively recorded as K 1 、K 2 And f 1 、f 2 。
Further, in S4, the minimum number of jigs N on the two sheets is set by using an algorithm for improving the particle swarm 1 And N 2 Randomly generating a series of z-direction clamp constraint sequence numbers, and changing the number of clamps by using out-of-limit particles generated during position updating in a particle swarm algorithm: firstly, screening particles meeting the number requirement through number limitation, and screening a z-direction clamp constraint sequence number meeting the assembly requirement from the particles to finally obtain the optimal number of clamps and the clamp distribution at the moment under the condition of meeting the assembly and splicing requirements;
by equation in particle swarm algorithm
Establishing a relation among a rigidity matrix, a displacement matrix and a moment matrix;
wherein:and->Respectively K i And f i (i=1, 2) the stiffness matrix and the force matrix of the two sheets after correction by the N-2-1 positioning method are calculated as follows:
step1, inputting the fixture position serial number x of two thin plates i Number of nodes of sheet n i And constraint point location Constratx in x and y directions by N-2-1 positioning method i And construct i (i＝1,2)；
Step2 loading the rigidity matrix K of two sheets i And moment array f i ；
Step3, setting a Z-direction constraint Constraz of an N-2-1 positioning method i ＝x i +NF i ；
Step4, setting constraints in three directions of x, y and z and obtaining total constraints:
Constr i ＝[Constr ix ,Constr ix ,Constr ix ]；
step5 set index sequence index= {1,2, …,6n i }；
Step6, performing iterative loop
Forj＝1,2,…,length(Constr i )
Removal of Constr in q=index i Sequence of positions in line j
K i (Constr i (j),q)＝0
End；
Step7 correction force matrix f i (Constr i )＝0，
The optimization objective is to minimize the total cost, so the objective function is defined as:
in order to meet the requirements of actual engineering, the maximum clearance H (x) and the profile epsilon at the assembly intersection point of two plates are constrained in the calculation process, wherein the constraint equation of the profile deformation tolerance epsilon is as follows:
when the individual does not meet the constraint, a penalty coefficient M is added to the calculation result of the objective function (M is a value far greater than the objective function);
the constraint equation that the maximum gap H (x) needs to satisfy is:
H(x)≤H max
the H (x) calculating method comprises the following steps:
the specific implementation steps of the algorithm are as follows:
setting parameters and loading constraints: setting total number of nodes n of two thin plates 1 And n 2 Number of initial jigs for two sheets m 1 And m 2 Junction sequence a at joint of two plates 1 And a 2 Node sequence NF of two plates without clamp 1 And NF (NF) 2 Setting the population number P, the iteration number D and the dimension D of a decision variable 1 And D 2 Individual and social learning factor l 1 And l 1 And a contraction factor calculated based on the learning factor:
the variation range omega E [ omega ] of the inertia weight min ,ω max ]The range of change in particle update rate:
V i ∈[V imin ,V imax ](i＝1,2)；
variation range of particle position numbers:
setting the minimum fixture number N of two plates 1min And N 2min Gap maximum H meeting assembly requirements max Gap maximum H meeting assembly requirements max Setting a cost factor C 1 And C 2 Clamp moving speed V x ,V y ,V z The method comprises the steps of carrying out a first treatment on the surface of the Loading constraint point sequence numbers Constratx in x and y directions on two sheets i And construct i (i=1, 2), loading the position coordinates of each node of the two boards, part1_loc and part2_loc;
particle swarm algorithm population individual initialization: in the I-dimensional space, initializing a particle position number:
initializing the update rate of the particles: v (V) i ＝V imin +r(V imax -V imin ),Is equal to V o Random number sequences of the same dimension; initializing optimal positions pbest of population individuals, and utilizing:
calculating an fitness value corresponding to the optimal position of the individual, calculating the deformation H (x) assembled at the moment by using the formula (4), judging whether the formula (3) is satisfied, and according to the formula (3):
updating the pbest_fit; initializing a global optimal position gbest of the population, and updating an adaptability value gbest_fit corresponding to the global optimal position.
Iteration is performed: two-layer nested loops with outer layer k= {1,2, …, P } and inner layer d= {1,2, …, d } were used, according to:
updating the inertia weight;
according to the following: is->Random number sequences of the same dimensions) for a speed update.
Judging and processing the speed out-of-limit particles in iteration: judging whether the speed value in each updating process exceeds the allowable range, and if so, pulling back the boundary value, namely:
updating position sequence numbers in iteration: adding speed to the current position number and rounding up by using a position update formula, i.e
And retaining the particles with out-of-limit positions in the iteration.
Extraction of the number of active jigs in the iteration: extracting the number of effective clamps after updating the position sequence number, wherein the number updating formula is as follows: n (N) i ＝card(X i )-card(X i >X imax )-card(X i <X imin ),(i＝1,2)。
Screening the number N value of clamps in iteration: and screening the number of clamps for all population individuals in the round of circulation, wherein the screening mode is as follows:
screening of individual maximum gap H values in the iteration: judging whether the maximum clearance value of each individual of all populations in the round of circulation is smaller than the allowable maximum clearance value, wherein the screening mode is as follows:
calculating individual history optimal and global optimal in iteration: traversing all populations, calculating each time the fitness of the optimal position of the individual satisfying Tag2=1And compare with the position of the pbest_fit if->Updating the pbest and pbest_fit; finding out the minimum position pb in all individual historic optimal fitness, comparing the global optimal fitness value pbest_fit with min (pbest), if pbest_fit (pb)<pbest_fit, then update gbest=pbest (pb) and gbest_fit=pbest_fit (pb); and finally obtaining the optimal number of clamps and the distribution of the clamps at the moment under the condition of meeting the assembly and splicing requirements.
Wherein, the meaning of each parameter is as follows:
further, in S5, the relevant finite element analysis software is used, after the relevant material attribute and load attribute are set, the obtained fixture distribution corresponding to the optimal fixture number meeting the assembly and splicing requirements is used as a z-direction fixture constraint sequence number, and the z-direction of the corresponding positions in the two sheets is constrained; and after constraint loading is completed, a cloud image of the deformation of the two sheets is exported to realize visualization of the optimization result, and verification of the optimization effect is carried out.
Compared with the prior art, the invention has the advantages that:
1. according to the method for optimizing the number of the large flexible thin plate clamps based on the improved particle swarm optimization, the optimal number of clamps and the clamp layout at the moment under the condition of meeting the maximum allowable value of the assembly and the initial number of clamps can be finally obtained.
2. The invention can better meet the splicing requirement of engineering assembly, simultaneously reduce the unnecessary cost caused by increasing the number of clamps and moving as much as possible, and improve the economical type of the intelligent assembly system. Meanwhile, the methodology provided by the invention has certain universality for the problem of optimizing the number of the large flexible thin plate clamps.
3. The invention introduces a particle swarm algorithm for optimization and carries out some related improvements on the particle swarm algorithm: the inertia weight omega in the traditional particle swarm algorithm is improved, so that the inertia weight omega can be changed along with the change of the fitness; updating formula for improving speed in traditional particle swarm algorithm and introducing shrinkage factorThe change in the update rate of the particles is controlled. Through the improvements, the particle convergence of the algorithm in the solving process is enhanced, which is more beneficial to the algorithm to search the global optimal solution by combining the problems, and the time efficiency of solving is improved.
Drawings
FIG. 1 is a schematic block diagram of the present invention;
FIG. 2 is a schematic flow chart of a particle swarm algorithm according to the present invention;
FIG. 3 is a diagram of an optimization process in the present invention;
FIG. 4 is a schematic diagram of the pre-optimized (equispaced) and post-optimized fixture point placement of the present invention;
fig. 5 is a schematic diagram showing deformation of the plate before (uniformly distributed) and after optimizing the number of the clamps in the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be further described below.
As shown in figure 1, the method for optimizing the number of the large flexible sheet clamps based on the improved particle swarm algorithm is characterized by constructing a three-dimensional model of the large flexible sheet, dividing finite element grids, extracting relevant characteristic data, optimizing the improved particle swarm algorithm, visualizing an optimizing result and checking the optimizing result.
Specific embodiments of the invention are shown below:
the first step: and constructing a three-dimensional model of the large flexible sheet. Taking two thin plates on a large ship body as research objects, and constructing a three-dimensional model according to the actual sizes and shapes of the two thin plates: the first sheet of the two selected sheets is a curved sheet, and the four sides of the curved sheet are respectively provided with the following lengths: 5600mm,4600mm,550 mm,3200mm, four sides having a thickness to length ratio and a thickness to width ratio of about 0.0011,0.0011 and 0.0013,0.0019, respectively; the second piece was a rectangular flat plate having a length of 5500mm and a width of 600mm, and a thickness to length ratio and a thickness to width ratio of about 0.0011 and 0.0013, respectively. And finally, after the model construction is completed, a data interaction file in the two-sheet model igs format is exported.
And a second step of: dividing a finite element mesh. Finite element mesh division is carried out on the model through Hypermesh software, and as the two plates are regular, two meshes of quadrangle and triangle are obtained after division. After grid division is completed, a model data interaction file in inp format is derived, and the number of finite element grid nodes of two thin plates and coordinates corresponding to each node can be extracted from the model data interaction file, wherein in the sample: the total number of nodes of board 1 is 2346 and the total number of nodes of board 2 is 392.
And thirdly, extracting relevant characteristic data. Reading a form source code inp file, wherein the third step is to use Abaqus software for analysis, and the material properties of the two plates are set to be the same: set density ρ=7.85×10 -3 g/mm 3 Poisson's ratio v=0.3, young's modulus e=210000n/mm 2 . According to the actual situation when the two sheets are assembled and spliced, reasonably simplifying the model, setting that the two sheets have no interaction, and setting g= -9800mm/s assuming that the external loads born by the two sheets are only gravity 2 And applies a gravitational load to the whole. And finally, relevant characteristic data such as rigidity matrixes, moment matrixes and the like of the two thin plates after relevant parameter setting is conducted.
Fourth, the improved particle swarm optimization is performed, as shown in fig. 2, by using the optimal fixture number obtained by searching the improved particle swarm algorithm and the corresponding z-direction fixture constraint sequence number. Number of initial jigs on two sheets m in the sample 1 ＝22,m 2 =8, junction sequence a at the splice of two plates 1 = {56,55, …,1} and a 2 = {1,2, …,56}, node sequence NF with no clamp placed on two boards 1 =189 and NF 2 =122, setting population number p=300, iteration number d=20, dimension D of decision variable 1 =22 and D 2 =8, individual and social learning factor l 1 ＝l 1 =2.05, and thus calculate the shrinkage factorω min ＝0.4,ω max ＝0.9,V 1max ＝78.2,V 1min ＝-78.2,V 2max ＝469,V 2min In the setting condition of the sample, the fitness value of the sample does not exceed 1000, so that the punishment coefficient M is set to 1000, and the minimum clamp number N of two plates is set 1min =16 and N 2min =4, the maximum value H of the clearance meeting the assembly requirement max =2, set cost factor C 1 ＝1,C 2 =0.05, gripper movement speed V x ＝V y ＝V z =1, calculating S using the position coordinates of each node of the two plates, part1_loc and part2_loc jx ,S jy S jz The objective function is defined as +.>In the I-dimensional space, initializing particle position number +.>Initializing update speed V of particles i ＝V imin +r(V imax -V imin ),/>Is equal to V i Random number sequences of the same dimension; initializing the optimal position pbest of the population individuals, and calculating the fitness value corresponding to the optimal position of the individuals by utilizing an objective function in a formula Calculating the deformation H (x) assembled at this time by using the formula (4), and judging whether H (x) is less than or equal to H max And according toUpdating the pbest_fit; initializing a global optimal position gbest of the population, and updating an adaptability value gbest_fit corresponding to the global optimal position. Iteration is performed: two-layer nested loops with outer layer k= {1,2, …, P } and inner layer d= {1,2, …, d } are used, according toUpdating inertial weights according to ∈>Is in combination withRandom number sequence with the same dimension), judging whether the speed value in each updating process exceeds the allowable range, and if so, pulling back the edgeLimit value, update position->Particles with out-of-limit positions are not treated; extraction of the number of active jigs in the iteration: extracting the number of effective clamps after updating the position sequence number, wherein the number updating formula is as follows: n (N) i ＝card(X i )-card(X i >X imax )-card(X i <X imin ) (i=1, 2); screening the number N value of clamps in iteration: and screening the number of clamps for all population individuals in the round of circulation, wherein the screening mode is as follows:screening of individual maximum gap H values in the iteration: judging whether the maximum clearance value of each individual of all populations in the round of circulation is smaller than the allowable maximum clearance value, wherein the screening mode is as follows: /> And calculating particles meeting Tag2=1 in the population, updating individual history optimal and global optimal, and completing optimizing. Finally, the optimized result is obtained:
the minimum total cost is 46.0693.
The total number of jigs at this time was 25, the number of jigs on the board 1 was 17, and as shown in FIG. 4 (a), the position was [2199 2114 1098 1616 868 669 1933 1030 1676 326 984 1004 1505 1503 1297 1869 500 ]].
The number of clamps on the plate 2 is 8; as shown in FIG. 4 (b), the position is [ [175 216 170 344 389 128 312 281]。
As shown in fig. 3, the change of the global optimum found in the course of 20 iterations is reflected.
And fifthly, visualizing an optimization result, namely, after setting related material properties and load properties by using finite element analysis software abaqus, constraining the z direction of the corresponding position in the two sheets by using the obtained group of z-direction fixture constraint serial numbers which enable the average deformation quantity of the assembly positions of the two sheets to be minimum, and leading out cloud images of the deformation of the two sheets to realize visualization. As shown in fig. 4 (a) and fig. 4 (b) which are schematic views of the point positions of the clamps before and after the number of the clamps is optimized, fig. 5 is a schematic view of the deformation of the plate before and after the number of the clamps is optimized, the number of the clamps is obviously reduced by 5 after the optimization, and meanwhile, the deformation amounts of the two thin plates are all smaller than the maximum deformation amount allowed by the assembly.
The foregoing is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any person skilled in the art will make any equivalent substitution or modification to the technical solution and technical content disclosed in the invention without departing from the scope of the technical solution of the invention, and the technical solution of the invention is not departing from the scope of the invention.
Claims (5)
1. The method for optimizing the number of the large flexible sheet clamps based on the improved particle swarm algorithm is characterized by comprising the following steps of:
s1, constructing a large flexible sheet three-dimensional model, and deriving a data interaction file of the constructed model;
s2, dividing the finite element grids, and deriving form source code files;
s3, extracting characteristic data, setting parameters such as material properties, load distribution, constraint and the like, and extracting finite element grid node coordinates, a rigidity matrix of the sheet model and a force matrix of the sheet model; setting constraint point serial numbers in x and y directions according to an N-2-1 positioning method;
s4, optimizing an improved particle swarm algorithm, and searching to obtain the optimal fixture number and the fixture layout at the moment under the condition of meeting the assembly requirement by utilizing the improved particle swarm algorithm;
and S5, verifying the optimizing effect and visualizing the optimizing result, and respectively restraining in finite element analysis by utilizing the obtained optimal fixture number meeting the assembly requirement condition and the fixture layout (namely the z-direction fixture restraint sequence number and the x-direction and y-direction restraint point sequence numbers set according to the N-2-1 positioning method) at the moment to obtain a deformation cloud picture of the sheet, thereby completing verification and visualization.
2. The method for optimizing the number of large flexible thin plate fixtures based on the improved particle swarm optimization according to claim 1, wherein in S2, finite element mesh is divided on the model by finite element mesh dividing software, a data interaction file of the model at the moment is derived, and the number of nodes of the finite element mesh of the two thin plates and coordinates corresponding to each node are extracted from the data interaction file.
3. The method for optimizing the number of large flexible thin plate fixtures based on the improved particle swarm optimization according to claim 1, wherein in S3, the material properties, density, young' S modulus and poisson ratio of the two plates are set by analyzing with finite element analysis software; model simplification is carried out according to the actual situation when two thin plates are assembled and spliced: setting no interaction between the two thin plates and only loading gravity; after the parameters are set, the rigidity matrix and the force matrix of the two thin plates are derived and respectively recorded as K 1 、K 2 And f 1 、f 2 。
4. The method for optimizing the number of clamps for a large flexible sheet based on the modified particle swarm algorithm according to claim 1, wherein in S4, the minimum number of clamps N on two sheets is set by using the modified particle swarm algorithm 1 And N 2 Randomly generating a series of z-direction clamp constraint sequence numbers by using a particle swarm algorithmThe number of clamps is changed by out-of-limit particles occurring during medium position updating: firstly, screening particles meeting the number requirement through number limitation, and screening a z-direction clamp constraint sequence number meeting the assembly requirement from the particles to finally obtain the optimal number of clamps and the clamp distribution at the moment under the condition of meeting the assembly and splicing requirements;
by equation in particle swarm algorithm
Establishing a relation among a rigidity matrix, a displacement matrix and a moment matrix;
wherein:and->Respectively K i And f i (i=1, 2) the stiffness matrix and the force matrix of the two sheets after correction by the N-2-1 positioning method are calculated as follows:
step1, inputting the fixture position serial number x of two thin plates i Number of nodes of sheet n i And constraint point location Constratx in x and y directions by N-2-1 positioning method i And construct i (i＝1,2)；
Step2 loading the rigidity matrix K of two sheets i And moment array f i ；
Step3, setting a Z-direction constraint Constraz of an N-2-1 positioning method i ＝x i +NF i ；
Step4, setting constraints in three directions of x, y and z and obtaining total constraints:
Constr i ＝[Constr ix ,Constr ix ,Constr ix ]；
step5 set index sequence index= {1,2, …,6n i }；
Step6, performing iterative loop
Forj＝1,2,…,length(Constr i )
Removal of Constr in q=index i Sequence of positions in line j
K i (Constr i (j),q)＝0
End；
Step7 correction force matrix f i (Constr i )＝0，
The optimization objective is to minimize the total cost, so the objective function is defined as:
in order to meet the requirements of actual engineering, the maximum clearance H (x) and the profile epsilon at the assembly intersection point of two plates are constrained in the calculation process, wherein the constraint equation of the profile deformation tolerance epsilon is as follows:
when the individual does not meet the constraint, a penalty coefficient M is added to the calculation result of the objective function (M is a value far greater than the objective function);
the constraint equation that the maximum gap H (x) needs to satisfy is:
H(x)≤H max
the H (x) calculating method comprises the following steps:
wherein, the meaning of each parameter is as follows:
5. the method for optimizing the number of large flexible thin plate clamps based on the improved particle swarm optimization according to claim 1, wherein in S5, the method is performed by using related finite element analysis software, and after the related material property and load property are set, the obtained clamp distribution corresponding to the optimal number of clamps meeting the assembly and splicing requirements is used as a z-direction clamp constraint sequence number, and the z-direction of the corresponding positions in the two thin plates is constrained; and after constraint loading is completed, a cloud image of the deformation of the two sheets is exported to realize visualization of the optimization result, and verification of the optimization effect is carried out.
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