CN117634232A - An optimization method for the number of large flexible thin plate fixtures based on improved particle swarm algorithm - Google Patents

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

An optimization method for the number of large flexible thin plate fixtures based on improved particle swarm algorithm

Technical field

The invention relates to the field of quality management and intelligent assembly system design optimization, and in particular to a method for optimizing the number of large flexible thin plate fixtures based on an improved particle swarm algorithm.

Background technique

In the field of production and assembly, parts such as aircraft fuselages and ship hulls are assembled from large flexible thin plates. The main characteristics of such thin plates are: their internal dimensions are large (the width and length of the plate are both large), and the plate parts The thickness is very small, that is, it has the characteristics of "large scale" and "low stiffness", so such parts are prone to local deformation under the action of gravity. In current production and assembly, large flexible sheets are generally positioned using the "N-2-1" principle, and then spliced in pairs through riveting, welding and other connection methods, and then assembled into a larger sheet. The layout scheme of the "N" positioning fixtures used in the assembly and positioning process will directly affect the degree of flexible deformation of the large flexible thin plate, which will in turn directly affect the assembly quality of the large flexible thin plate. At the same time, each additional fixture or each additional movement of a fixture will incur additional costs. Therefore, it is very important to reduce the number and movement of fixtures as much as possible while meeting the assembly and splicing requirements to increase profits and the added value of the product.

At present, the positioning fixtures used in the assembly process of large thin plates mainly adopt fixed column-type tire frame structures, and the fixtures are evenly distributed in the projection plane of the thin plate at equal intervals. Since most of the large thin plates used in aircraft fuselages and ship hulls have relatively complex profiles, simply increasing the number of "N" and distributing them evenly will reduce the assembly gap between the two plates to a certain extent, making the It can meet the maximum allowable gap before welding or riveting, but it generates more additional costs and reduces the average profit. It is "uneconomical" and "unreasonable" for the manufacture of a single product, and it can be carried out improved. In response to such problems, the present invention proposes a method for optimizing the number of large flexible thin plate clamps based on an improved particle swarm algorithm.

Contents of the invention

The purpose of this invention is to propose a method for optimizing the number of large flexible thin plate clamps based on an improved particle swarm algorithm in view of the insufficient layout of the fixtures and the unnecessary costs caused by the large number in the existing large flexible thin plate assembly process. .

In order to achieve the above objectives, the present invention proposes a method for optimizing the number of large flexible thin plate clamps based on an improved particle swarm algorithm, which includes the following steps:

S1: Construct a large-scale flexible thin plate three-dimensional model and export the data interaction file of the constructed model;

S2: Divide the finite element mesh and export the form source code file;

S3: Extract feature data, set parameters such as material properties, load distribution and constraints, and extract the finite element grid node coordinates, the stiffness matrix of the thin plate model, and the force matrix of the thin plate model; according to the N-2-1 positioning method, Set the constraint point numbers in the x and y directions;

S4: Improved particle swarm algorithm optimization, use the improved particle swarm algorithm to search to obtain the optimal number of fixtures that meet the assembly requirements and the fixture layout at this time;

S5: Optimization effect verification and optimization result visualization, using the optimal number of fixtures that meet the assembly requirements and the fixture layout at this time (i.e., the z-direction fixture constraint number and the x set according to the N-2-1 positioning method at this time and the constraint point number in the y direction), perform constraints respectively in the finite element analysis, and obtain the deformation cloud diagram of the thin plate to complete verification and visualization.

Further, in S2, the model is divided into finite element meshes through finite element meshing software, the data interaction file of the model is exported, and the number of finite element mesh nodes of the two thin plates and the number of each of them are extracted. The coordinates corresponding to the node.

Further, in S3, finite element analysis software was used to analyze and set the material properties, density, Young's modulus and Poisson's ratio of the two plates; the model was simplified based on the actual situation when the two thin plates were assembled and spliced: It is assumed that there is no interaction between the two thin plates and only gravity is loaded; after setting these parameters, the stiffness matrix and force matrix of the two thin plates are derived and recorded as K ₁ , K ₂ and f ₁ , f ₂ respectively.

Further, in S4, the improved particle swarm algorithm is used to set the minimum number of clamps N ₁ and N ₂ on the two thin plates, and a series of z-direction clamp constraint sequence numbers are randomly generated, using the position update in the particle swarm algorithm. Change the number of fixtures with super-boundary particles: first filter out the particles that meet the number requirements through number restrictions, then filter out the z-direction fixture constraint numbers that meet the assembly requirements, and finally get the optimal number of fixtures that meet the assembly splicing requirements and at this time The fixture distribution;

Through the equation in particle swarm optimization

Establish the relationship between the stiffness matrix, displacement matrix and force matrix;

In the formula: and/> are respectively the stiffness matrix and force matrix of the two thin plates K _i and f _i (i=1,2) corrected by the N-2-1 positioning method. The calculation steps are as follows:

Step1: Enter the fixture position number x _i of the two thin plates, the number of nodes of the thin plate n _i and the constraint points Constrx _i and Constry _i (i=1,2) in the x and y directions of the N-2-1 positioning method;

Step2: Load the stiffness matrix K _i and force matrix f _i of the two thin plates;

Step3: Set the z-direction constraint Constrz _i = _xi +NF _i of the N-2-1 positioning method;

Step4: Set constraints in the three directions of x, y, and z and get the total constraints:

Constr _i = [Constr _ix ,Constr _ix ,Constr _ix ];

Step5: Set the index sequence index={1,2,…,6n _i };

Step6: Carry out iterative loop

Forj＝1,2,…,length(Constr _i )

Remove the position sequence in the jth row of Constr _i from q=index

K _i (Constr _i (j),q)=0

End;

Step7: Correction force matrix f _i (Constr _i )=0,

The optimization goal is to minimize the total cost, so the objective function is defined as:

In order to meet the needs of actual engineering, the maximum gap H (x) and the contour ε at the assembly intersection of the two plates are constrained during the calculation process. The section deformation tolerance value ε constraint equation is as follows:

When an individual does not meet this constraint, a penalty coefficient M needs to be added to the calculation result of the objective function (M is a value much larger than the objective function);

The constraint equation that the maximum gap H(x) needs to satisfy is:

H(x)≤H _max

The calculation method of H(x) is:

The specific implementation steps of the algorithm are as follows:

Set parameters and loading constraints: set the total number of nodes n ₁ and n ₂ of the two thin plates, the initial fixture numbers m ₁ and m ₂ of the two thin plates, the node sequences a ₁ and a ₂ at the splicing of the two plates, the two plates The node sequences NF ₁ and NF ₂ where the fixture cannot be placed, the number of populations P, the number of iterations d, the dimensions of the decision variables D ₁ and D ₂ , the individual and social learning factors l ₁ and l ₁ , and the values calculated based on the learning factors Shrinkage factor:

The changing range of inertia weight ω∈[ω _min ,ω _max ], the changing range of particle update speed:

V _i ∈[V _imin ,V _imax ](i=1,2);

The variation range of particle position number:

Set the minimum number of fixtures for the two boards N _1min and N _2min , the maximum gap H _max that meets the assembly requirements, the maximum gap H _max that meets the assembly requirements, set the cost factors C ₁ and C ₂ , and the movement speed of the fixtures V _x , V _y ,V _z ; Load the constraint point numbers Constrx _i and Constry _i (i=1,2) in the x and y directions of the two thin plates, and load the position coordinates part1_loc and part2_loc of each node of the two plates;

Particle swarm algorithm population individual initialization: In the I-dimensional space, initialize the particle position number:

Initialize the update speed of particles: V _i =V _imin +r(V _imax -V _imin ), is a random number sequence with the same dimension as V _o ; initialize the optimal position pbest of the population individual, using:

Calculate the fitness value corresponding to the individual's optimal position, use equation (4) to calculate the deformation H(x) of the assembly at this time, and determine whether it satisfies equation (3), and based on:

Update pbest_fit; initialize the global optimal position of the population gbest, and update the fitness value gbest_fit corresponding to the global optimal position.

Iterate: Use two levels of nested loops with outer k={1,2,…,P} and inner d={1,2,…,d}, according to:

Update inertia weight;

according to: For and/> Random number sequence with the same dimensions) for speed update.

Judgment and processing of speed out-of-bounds particles during iteration: judge whether the speed value in each update process exceeds the allowed range, and if it exceeds, pull back the boundary value, that is:

Update of position number during iteration: Use the position update formula to add speed to the current position number and round it up, that is

Particles whose positions are out of bounds during the iteration are retained.

Extraction of the number of effective fixtures in the iteration: Extract the number of effective fixtures after the position serial number is updated. The number update formula is: N _i =card(X _i )-card(X _i >X _imax )-card(X _i <X _imin ), (i=1,2).

Screening of the N value of the number of clamps in the iteration: Screening of the number of clamps for all population individuals in this round of cycles, the screening method is:

Screening of the maximum gap H value of individuals in the iteration: Determine whether the maximum gap value of each individual of all populations in the cycle is less than the maximum allowed gap value. The screening method is:

Calculation of individual historical optimal and global optimal in iteration: traverse all populations, and calculate the fitness of the individual optimal position that satisfies Tag2=1 each time And compare with pbest_fit at this position, if/> Then update pbest and pbest_fit; find the minimum value position pb among all individual historical optimal fitness values, compare the global optimal fitness value pbest_fit with min(pbest), if pbest_fit(pb)<pbest_fit, update gbest=pbest( pb) and gbest_fit=pbest_fit(pb); finally, the optimal number of fixtures and the distribution of fixtures at this time are obtained to meet the assembly and splicing requirements.

In the formula, the meaning of each parameter is:

Further, in S5, relevant finite element analysis software is used. After setting the relevant material properties and load properties, the obtained fixture distribution corresponding to the optimal number of fixtures that meets the assembly splicing requirements is used as the z-direction The fixture constraint serial number is used to constrain the z-direction of the corresponding position in the two thin plates; after the constraint loading is completed, the deformation cloud diagram of the two thin plates is exported to visualize the optimization results and verify the optimization effect.

Compared with the existing technology, the advantages of the present invention are:

1. A method for optimizing the number of large flexible thin plate clamps based on the improved particle swarm algorithm described in the present invention can finally obtain the optimal number of clamps and the clamps at this time that satisfy the maximum allowable value of the assembly gap and the initial number of clamps. layout.

2. The present invention can better meet the splicing requirements of engineering assembly, while minimizing unnecessary costs caused by increasing the number and movement of fixtures, and improving the economy of the intelligent assembly system. At the same time, the methodology proposed by the present invention has certain universal applicability to the problem of optimizing the number of large-scale flexible thin plate clamps.

3. The present invention introduces the particle swarm algorithm for optimization and makes some related improvements: improving the inertia weight ω in the traditional particle swarm algorithm so that it can change with the change of fitness; improving the inertial weight ω in the traditional particle swarm algorithm. Update formula of speed, introducing shrinkage factor Control changes in particle update speed. After these improvements, the particle convergence of the algorithm has been enhanced during the solution process, which is more conducive to this algorithm searching for the global optimal solution in combination with such problems, and improves the time efficiency of solution.

Description of drawings

Figure 1 is a schematic block diagram of the principle of the present invention;

Figure 2 is a schematic flow chart of the particle swarm algorithm of the present invention;

Figure 3 is a diagram of the optimization process in the present invention;

Figure 4 is a schematic diagram of the fixture point layout before optimization (uniform distribution) and after optimization of the present invention;

Figure 5 is a schematic diagram of plate deformation before (evenly distributed) and after optimization of the number of clamps according to the present invention.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be further described below.

As shown in Figure 1, a method for optimizing the number of large flexible thin plate fixtures based on the improved particle swarm algorithm is characterized by constructing a three-dimensional model of a large flexible thin plate, dividing the finite element grid, extracting relevant feature data, and improving the search method of the particle swarm algorithm. Optimization and visualization of optimization results and inspection of optimization results.

Specific embodiments of the present invention are as follows:

Step one: Build a 3D model of the large flexible sheet. Taking two thin plates on a large ship hull as the research object, a three-dimensional model was constructed based on the actual size and shape of the two thin plates: of the two selected thin plates, the first one is a curved plate, and the lengths of its four sides are respectively : 5600mm, 4600mm, 5500mm, 3200mm, the ratio of the thickness to the length of the four sides and the ratio of the thickness to the width are about 0.0011, 0.0011 and 0.0013, 0.0019 respectively; the second piece is a rectangular flat plate with a length of 5500mm, a width of 600mm, and a thickness of The ratio to length and the ratio of thickness to width are approximately 0.0011 and 0.0013 respectively. After completing the model construction, the data interaction files in the igs format of the two thin plate models were finally exported.

Step 2: Divide the finite element mesh. The model was divided into finite element meshes through HyperMesh software. Since both plates were relatively regular, only quadrilateral and triangular meshes were obtained after division. After the meshing is completed, export the model data interaction file in inp format, from which the number of finite element mesh nodes of the two thin plates and the coordinates corresponding to each node can be extracted. In this example: the total number of nodes of plate 1 is 2346, the total number of nodes on board 2 is 392.

The third step is to extract relevant feature data. Read the form source code inp file, use Abaqus software for analysis in the third step, and set the material properties of the two plates to be the same: set the 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 two thin plates are assembled and spliced, the model is reasonably simplified. It is assumed that there is no interaction between the two thin plates, and it is assumed that the external load on the two plates is only gravity. Set g=-9800mm/s ² and Apply gravity load to the whole. Finally, the relevant characteristic data such as the stiffness matrix and force matrix of the two thin plates after the relevant parameter settings are completed are exported.

The fourth step is to optimize using the improved particle swarm algorithm. As shown in Figure 2, the optimal number of fixtures obtained through the improved particle swarm algorithm search and the corresponding z-direction fixture constraint number are obtained. In the example, the initial number of clamps on the two thin plates is m ₁ =22, m ₂ =8, and the node sequences at the splicing of the two plates are a ₁ ={56,55,…,1} and a ₂ ={1,2 ,...,56}, the node sequences NF ₁ = 189 and NF ₂ = 122 on the two boards where the fixture cannot be placed, the number of populations P = 300, the number of iterations d = 20, the dimensions of the decision variable D ₁ = 22 and D ₂ =8, individual and social learning factors l ₁ =l ₁ =2.05, and the shrinkage factor is calculated from this ω _min ＝0.4, ω _max ＝0.9, V _1max ＝78.2, V _1min ＝-78.2, V _2max ＝469, V _2min ＝-469. Under the conditions set in this example, the fitness value will not exceed 1000. Therefore, the penalty coefficient M is set to 1000, the minimum number of fixtures for two boards is set to N _1min = 16 and N _2min = 4, the maximum gap H _max = 2 that meets the assembly requirements, and the cost factors C ₁ = 1, C ₂ = 0.05, Clamp moving speed V _x =V _y =V _z =1, use the position coordinates part1_loc and part2_loc of each node of the two boards to calculate S _jx , S _jy S _jz , and define the objective function as/> In the I-dimensional space, initialize the particle position number/> Initialize particle update speed V _i =V _imin +r(V _imax -V _imin ),/> is a random number sequence with the same dimension as V _i ; initialize the optimal position pbest of the individual population, and use the objective function in (*) to calculate the fitness value corresponding to the optimal position of the individual Use equation (4) to calculate the deformation H(x) of the assembly at this time, and determine whether it satisfies H(x) ≤ H _max , and based on Update pbest_fit; initialize the global optimal position of the population gbest, and update the fitness value gbest_fit corresponding to the global optimal position. Iterate: Use two levels of nested loops with outer k={1,2,…,P} and inner d={1,2,…,d}. According to Update the inertia weight according to/> for and Random number sequence with the same dimensions) performs speed update, and determines whether the speed value in each update process exceeds the allowable range. If it exceeds, pull back the boundary value and update the position/> Particles whose positions exceed the bounds are not processed; extraction of the number of effective fixtures in the iteration: extract the number of effective fixtures after the position number is updated. The number update formula is: N _i =card(X _i )-card(X _i >X _imax )- card(X _{i <} Screening of the maximum gap H value of individuals in the iteration: Determine whether the maximum gap value of each individual of all populations in the cycle is less than the maximum allowed gap value. The screening method is: /> Calculate the particles in the population that satisfy Tag2=1, update the individual historical optimal and global optimal, and the optimization is completed. Finally, the optimization result is obtained:

The minimum total cost is 46.0693.

At this time, the total number of clamps is 25, and the number of clamps on board 1 is 17, as shown in Figure 4(a), and its position is [2199 21141098 1616 868 669 1933 1030 1676 326 984 1004 1505 1503 1297 1869 500].

The number of clamps on board 2 is 8; as shown in Figure 4(b), its position is [175 216 170 344 389 128 312281].

As shown in Figure 3, it reflects the changes in the global optimal value searched during the 20 iterations.

The fifth step is to visualize the optimization results. Through the finite element analysis software abaqus, after setting the relevant material properties and load properties, use the obtained set of z-direction fixture constraint numbers that minimize the average deformation of the two thin plates at the assembly to compare the two thin plates. The z-direction of the corresponding position in the two thin plates is constrained, and the cloud diagram of the deformation of the two thin plates is derived to achieve visualization. Figure 4(a) is a schematic diagram of the fixture point layout before the number is optimized. Figure 4(b) is a schematic diagram of the fixture point layout after the number is optimized. Figure 5 is a schematic diagram of the plate deformation before and after the number of fixtures is optimized. It is obvious that the fixtures are optimized. The number was reduced by 5, and at the same time, the deformation amount of the two thin plates was less than the maximum allowable deformation amount of the assembly.

The above are only preferred embodiments of the present invention and do not limit the present invention in any way. Any person skilled in the technical field who makes any form of equivalent substitution or modification to the technical solutions and technical contents disclosed in the present invention shall not deviate from the technical solutions of the present invention. The contents still fall within the protection scope of the present invention.

Claims (5)

1. A method for optimizing the number of large flexible thin plate fixtures based on an improved particle swarm algorithm, which is characterized by including the following steps: S1: Construct a large-scale flexible thin plate three-dimensional model and export the data interaction file of the constructed model; S2: Divide the finite element mesh and export the form source code file; S3: Extract feature data, set parameters such as material properties, load distribution and constraints, and extract the finite element grid node coordinates, the stiffness matrix of the thin plate model, and the force matrix of the thin plate model; according to the N-2-1 positioning method, Set the constraint point numbers in the x and y directions; S4: Improved particle swarm algorithm optimization, use the improved particle swarm algorithm to search to obtain the optimal number of fixtures that meet the assembly requirements and the fixture layout at this time; S5: Optimization effect verification and optimization result visualization, using the optimal number of fixtures that meet the assembly requirements and the fixture layout at this time (i.e., the z-direction fixture constraint number and the x set according to the N-2-1 positioning method at this time and the constraint point number in the y direction), perform constraints respectively in the finite element analysis, and obtain the deformation cloud diagram of the thin plate to complete verification and visualization. 2. The method for optimizing the number of large flexible thin plate clamps based on the improved particle swarm algorithm according to claim 1, characterized in that, in S2, the model is divided into finite element meshes through finite element meshing software, and the finite element mesh is derived. The data interaction file of the current model was extracted from it, and the number of finite element mesh nodes of the two thin plates and the coordinates corresponding to each node were extracted. 3. The method for optimizing the number of large flexible thin plate clamps based on the improved particle swarm algorithm according to claim 1, characterized in that in S3, finite element analysis software is used to analyze the material properties, density, and density of the two plates. Modulus and Poisson's ratio are set; the model is simplified according to the actual situation when two thin plates are assembled and spliced: there is no interaction between the two thin plates, and only gravity is loaded; after setting these parameters, export two The stiffness matrix and force matrix of the thin plate are denoted as K ₁ , K ₂ and f ₁ , f ₂ respectively. 4. The method for optimizing the number of large flexible thin plate clamps based on the improved particle swarm algorithm according to claim 1, characterized in that, in S4, the improved particle swarm algorithm is used to set the minimum number of clamps on the two thin plates N ₁ and N ₂ , randomly generate a series of z-direction fixture constraint sequence numbers, and use the superbound particles that appear when the position is updated in the particle swarm algorithm to change the number of fixtures: first, filter out the particles that meet the number requirements through the number limit, and then filter out the particles that meet the assembly requirements. The required z-direction clamp constraint sequence number is finally obtained to obtain the optimal number of clamps and the distribution of clamps at this time that meet the assembly and splicing requirements; Through the equation in particle swarm optimization Establish the relationship between the stiffness matrix, displacement matrix and force matrix; In the formula: and/> are respectively the stiffness matrix and force matrix of the two thin plates K _i and f _i (i=1,2) corrected by the N-2-1 positioning method. The calculation steps are as follows: Step1: Enter the fixture position number x _i of the two thin plates, the number of nodes of the thin plate n _i and the constraint points Constrx _i and Constry _i (i=1,2) in the x and y directions of the N-2-1 positioning method; Step2: Load the stiffness matrix K _i and force matrix f _i of the two thin plates; Step3: Set the z-direction constraint Constrz _i = _xi +NF _i of the N-2-1 positioning method; Step4: Set constraints in the three directions of x, y, and z and get the total constraints: Constr _i = [Constr _ix ,Constr _ix ,Constr _ix ]; Step5: Set the index sequence index={1,2,…,6n _i }; Step6: Carry out iterative loop Forj＝1,2,…,length(Constr _i ) Remove the position sequence in the jth row of Constr _i from q=index K _i (Constr _i (j),q)=0 End; Step7: Correction force matrix f _i (Constr _i )=0, The optimization goal is to minimize the total cost, so the objective function is defined as: In order to meet the needs of actual engineering, the maximum gap H (x) and the contour ε at the assembly intersection of the two plates are constrained during the calculation process. The section deformation tolerance value ε constraint equation is as follows: When an individual does not meet this constraint, a penalty coefficient M needs to be added to the calculation result of the objective function (M is a value much larger than the objective function); The constraint equation that the maximum gap H(x) needs to satisfy is: H(x)≤H _max The calculation method of H(x) is: In the formula, the meaning of each parameter is: 5. The method for optimizing the number of large flexible thin plate clamps based on the improved particle swarm algorithm according to claim 1, characterized in that in S5, relevant finite element analysis software is used, and relevant material properties and load properties are set. Finally, the obtained fixture distribution corresponding to the optimal number of fixtures that meets the assembly and splicing requirements is used as the z-direction fixture constraint number, and the z-direction at the corresponding position in the two thin plates is constrained; after the constraint loading is completed, the two pieces are derived The cloud diagram of the thin plate deformation realizes the visualization of the optimization results and verifies the optimization effect.