A large flexible sheet clamp number optimization method based on improved particle swarm algorithm

Abstract

The application provides a large flexible sheet clamp number optimization method based on an improved particle swarm algorithm, which comprises the following steps: step 1, a three-dimensional model of a large flexible sheet is constructed, and a data interaction file of the constructed model is exported; step 2, finite element mesh division is carried out, and a form source code file is exported; step 3, feature data is extracted, and relevant data including node coordinates of finite element mesh division, a stiffness matrix of the model and a force matrix of the model are read from the form source code file; step 4, optimization is carried out by using the improved particle swarm algorithm, so that the optimal clamp number and clamp distribution under the condition of meeting assembly requirements are obtained; and step 5, the optimization result is tested and visualized. Under the premise of meeting engineering requirements, the cost caused by the clamp number and clamp movement is as small as possible, and an optimization scheme for the clamp number used in the large flexible sheet assembly process is provided.

Description

Technical Field

[0001] This 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 optimization algorithm. Background Technology

[0002] In the manufacturing and assembly field, components such as aircraft fuselages and ship hulls are assembled from large flexible thin plates. The main characteristics of these plates are their large internal dimensions (both width and length are large) and small thickness, exhibiting characteristics of "large scale" and "low stiffness." Therefore, these parts are prone to localized deformation under gravity. Currently, large flexible thin plates are generally positioned using the "N-2-1" principle, and then joined in pairs using riveting, welding, or other connection methods to assemble a larger plate. The layout of the "N" positioning fixtures used in the assembly and positioning process directly affects the degree of flexible deformation of the large flexible thin plate, and thus directly affects the assembly quality. Furthermore, each additional fixture or movement incurs additional costs. Therefore, minimizing the number of fixtures and movements while meeting assembly requirements is crucial for improving profits and product added value.

[0003] Currently, the positioning fixtures used in the assembly of large thin plates mainly adopt a fixed column-type jig structure, 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 complex shapes, simply increasing the number of fixtures ("N") and distributing them evenly, while reducing the assembly gap between the two plates to some extent to meet the maximum allowable gap before welding or riveting, generates additional costs and reduces average profit. This is "uneconomical" and "unreasonable" for the manufacturing of individual products, and improvements are possible. To address this problem, this invention proposes a method for optimizing the number of fixtures for large flexible thin plates based on an improved particle swarm optimization algorithm. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing fixture layouts and the unnecessary costs caused by the large number of fixtures in the assembly of large flexible thin plates, and to propose a method for optimizing the number of fixtures for large flexible thin plates based on an improved particle swarm optimization algorithm.

[0005] To achieve the above objectives, this invention proposes a method for optimizing the number of fixtures for large flexible thin plates based on an improved particle swarm optimization algorithm, comprising the following steps:

[0006] S1: Construct a large flexible thin plate 3D model and export the data interaction file of the constructed model;

[0007] S2: Generate the finite element mesh and export the form source code file;

[0008] S3: Extract feature data, set parameters such as material properties, load distribution and constraints, extract finite element mesh node coordinates, stiffness matrix of thin plate model, and force matrix of thin plate model; set constraint point numbers in x and y directions according to N-2-1 positioning method;

[0009] S4: Improved particle swarm optimization algorithm: The improved particle swarm optimization algorithm is used to search for the optimal number of fixtures and the fixture layout under the condition of meeting the assembly requirements.

[0010] 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 constraint number of the fixture in the z direction and the constraint point numbers in the x and y directions set according to the N-2-1 positioning method), constraints are applied in the finite element analysis to obtain the deformation cloud diagram of the thin plate, thus completing the verification and visualization.

[0011] Furthermore, in S2, the model is divided into finite element meshes using finite element meshing software, and the data interaction file of the model at this time is exported. The number of finite element mesh nodes of the two thin plates and the coordinates corresponding to each node are then extracted from the data.

[0012] Furthermore, in S3, finite element analysis software is used to analyze the material properties of the two plates, including density, Young's modulus, and Poisson's ratio. The model is simplified based on the actual situation when the two thin plates are assembled and spliced: it is assumed that there is no interaction between the two thin plates and only gravity is applied. After these parameters are set, the stiffness matrix and force matrix of the two thin plates are exported and denoted as K1, K2 and f1, f2, respectively.

[0013] Furthermore, in S4, using an improved particle swarm optimization algorithm, the minimum number of fixtures N1 and N2 on the two thin plates is set, and a series of z-axis fixture constraint sequence numbers are randomly generated. The number of fixtures is changed by using the superboundary particles that appear during position updates in the particle swarm optimization algorithm: first, particles that meet the number requirements are filtered out by the number limit, and then z-axis fixture constraint sequence numbers that meet the assembly requirements are filtered out from them. Finally, the optimal number of fixtures and the fixture distribution at this time are obtained under the condition of meeting the assembly splicing requirements.

[0014] In particle swarm optimization, through equations

[0015]

[0016] Establish the relationship between the stiffness matrix, displacement matrix, and force matrix;

[0017] In the formula: and K i and f i (i=1,2) The stiffness and force matrices of the two thin plates after correction using the N-2-1 positioning method are calculated as follows:

[0018] Step 1: Enter the fixture position number x for the two thin plates. i The number of nodes n of the thin plate i The N-2-1 positioning method for constrained points in the x and y directions. i and Constry i (i = 1, 2);

[0019] Step 2: Load the stiffness matrix K of the two thin plates i Sum of force matrix f i ;

[0020] Step 3: Set the z-direction constraint Constrz for the N-2-1 positioning method. i =x i +NF i ;

[0021] Step 4: Set constraints in the x, y, and z directions and obtain the total constraints:

[0022]

[0023] Constr i =[Constr ix ,Constr ix ,Constr ix ];

[0024] Step 5: Set the index sequence index = {1, 2, ..., 6n} i};

[0025] Step 6: Perform iterative loops

[0026] Forj = 1, 2, ..., length(Constr) i )

[0027] q = index excluding Constr i The position sequence in row j

[0028] K i (Constr i (j),q)=0

[0029] End;

[0030] Step 7: Correct the force matrix f i (Constr i) = 0,

[0031] The optimization objective is to minimize the total cost; therefore, the objective function is defined as:

[0032]

[0033] To meet the needs of practical engineering, the maximum gap H(x) and profile tolerance ε at the intersection of the two plates are constrained during the calculation process. The constraint equation for the section deformation tolerance ε is as follows:

[0034]

[0035] When an individual does not meet this constraint, a penalty coefficient M (M is a value much larger than the objective function) needs to be added to the calculation result of the objective function.

[0036] The constraint equation that the maximum clearance H(x) needs to satisfy is:

[0037] H(x)≤H max

[0038] The method for calculating H(x) is as follows:

[0039]

[0040] The specific implementation steps of the algorithm are as follows:

[0041] Setting parameters and loading constraints: Set the total number of nodes n1 and n2 of the two thin plates, the initial number of fixtures m1 and m2 of the two thin plates, the node sequences a1 and a2 at the splicing point of the two plates, the node sequences NF1 and NF2 on the two plates where fixtures cannot be placed, set the population size P, the number of iterations d, the dimensions D1 and D2 of the decision variables, the individual and social learning factors l1 and l2, and the shrinkage factor calculated based on the learning factors:

[0042]

[0043] The range of inertial weight variation ω∈[ω min ,ω max The range of variation in particle renewal rate:

[0044] V i ∈[V imin V imax (i = 1, 2);

[0045] The range of particle position numbers:

[0046]

[0047] Set the minimum number of fixtures N for two plates. 1min and N2min The maximum clearance H that meets assembly requirements max The maximum clearance H that meets assembly requirements max Set cost factors C1 and C2, and fixture moving speed V. x V y V z ; The constraint point numbers (Constrx) in the x and y directions of the two thin plates are loaded. i and Constry i (i = 1, 2), load the position coordinates of each node of the two boards, part1_loc and part2_loc;

[0048] Particle Swarm Optimization (PSO) Population Individual Initialization: In I-dimensional space, initialize the particle position indices:

[0049]

[0050] Initialize particle update rate: V i =V imin +r(V imax -V imin ), To be with V o A sequence of random numbers of the same dimension; initialize the optimal position pbest of the population individuals, and use:

[0051]

[0052] 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, determine whether it satisfies equation (3), and according to:

[0053]

[0054] Update pbest_fit; initialize the global best position gbest of the population, and update the fitness value gbest_fit corresponding to the global best position.

[0055] Iteration: A two-level nested loop is used, with an outer loop k = {1,2,…,P} and an inner loop d = {1,2,…,d}, based on:

[0056]

[0057] Update the inertia weights;

[0058] according to: To and The speed is updated using a random number sequence of the same dimension.

[0059] Judgment and handling of particles with speed exceeding the boundary during iteration: Determine whether the speed value in each update process exceeds the allowable range. If it exceeds, pull it back to the boundary value, that is:

[0060] Update of position sequence number during iteration: Use the position update formula to add the speed to the current position number and round it, that is

[0061] Retain the particles with positions exceeding the boundary during iteration.

[0062] Extraction of the number of effective fixtures during iteration: Extract the number of effective fixtures after the update of the position sequence number. The number update formula is: N i =card(X i ) - card(X i >X imax ) - card(X i <X imin ), (i = 1, 2).

[0063] Screening of the N value of the number of fixtures during iteration: Screen the number of fixtures for all population individuals in this round of loop. The screening method is:

[0064] Screening of the maximum gap H value of individuals during iteration: Judge whether the maximum gap value of each individual in all populations in this round of loop is less than the allowable maximum gap value. The screening method is:

[0065]

[0066] Calculation of individual historical optimum and global optimum during iteration: Traverse all populations and calculate the fitness of the optimum position of individuals satisfying Tag2 = 1 each time and compare it with pbest_fit at this position. If then update pbest and pbest_fit; find the position pb of the minimum value among all individual historical optimum fitnesses, compare the global optimum fitness value pbest_fit with min(pbest). If pbest_fit(pb) < pbest_fit, then update gbest = pbest(pb) and gbest_fit = pbest_fit(pb); finally, obtain the optimum number of fixtures and the fixture distribution at this time under the conditions satisfying the assembly and splicing requirements.

[0067] In the formula, the meanings of each parameter are:

[0068]

[0069]

[0070] Furthermore, in S5, relevant finite element analysis software is used. After setting the relevant material properties and load properties, the fixture distribution corresponding to the optimal number of fixtures that meets the assembly and splicing requirements is used as the z-axis fixture constraint number, and the z-axis of the corresponding positions in the two thin plates is constrained. After the constraint loading is completed, the cloud map of the deformation of the two thin plates is exported to visualize the optimization results and verify the optimization effect.

[0071] Compared with the prior art, the advantages of the present invention are:

[0072] 1. The present invention provides a method for optimizing the number of fixtures for large flexible thin plates based on an improved particle swarm optimization algorithm, which can ultimately obtain the optimal number of fixtures and the fixture layout under the given conditions of maximum allowable assembly clearance and initial number of fixtures.

[0073] 2. This invention can effectively meet the splicing requirements of engineering assembly while minimizing unnecessary costs associated with increasing the number of fixtures and movement, thus improving the economic efficiency of the intelligent assembly system. Furthermore, the methodology proposed in this invention has a certain degree of universality in addressing the optimization of the number of fixtures for such large flexible thin plates.

[0074] 3. This invention introduces the particle swarm optimization algorithm for optimization and makes some related improvements: It improves the inertia weight ω in the traditional particle swarm optimization algorithm so that it changes with the fitness; it improves the velocity update formula in the traditional particle swarm optimization algorithm by introducing a shrinkage factor. The particle update rate is controlled. These improvements enhance the particle convergence of the algorithm during the solution process, making it more suitable for searching for the global optimum in this type of problem and improving the time efficiency of the solution. Attached Figure Description

[0075] Figure 1 This is a schematic block diagram illustrating the principle of the present invention;

[0076] Figure 2 This is a schematic diagram of the particle swarm algorithm of the present invention;

[0077] Figure 3 This is a diagram illustrating the optimization process in this invention;

[0078] Figure 4 The diagram shows the fixture point layout before (uniformly distributed) and after optimization according to the present invention.

[0079] Figure 5 The diagram shows the deformation of the plate before (uniformly distributed) and after the optimization of the number of fixtures in this invention. Detailed Implementation

[0080] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be further described below.

[0081] As attached Figure 1 As shown, a method for optimizing the number of fixtures for large flexible thin plates based on an improved particle swarm optimization algorithm is characterized by constructing a three-dimensional model of the large flexible thin plate, dividing it into finite element meshes, extracting relevant feature data, using the improved particle swarm optimization algorithm for optimization, and visualizing and verifying the optimization results.

[0082] The specific implementation scheme of the present invention is shown below:

[0083] Step 1: Constructing a 3D model of a large flexible thin plate. Taking two thin plates from a large ship's hull as the research object, a 3D model is constructed based on the actual size and shape of these two plates: The first plate is a curved plate with side lengths of 5600mm, 4600mm, 5500mm, and 3200mm, and the thickness-to-length and thickness-to-width ratios are approximately 0.0011, 0.0011, 0.0013, and 0.0019, respectively; the second plate is a rectangular flat plate with a length of 5500mm and a width of 600mm, and the thickness-to-length and thickness-to-width ratios are approximately 0.0011 and 0.0013, respectively. After completing the model construction, the final data exchange file of the two thin plate models in igs format is exported.

[0084] Step 2: Finite element mesh generation. The model is meshed using HyperMesh software. Since both plates are relatively regular, only quadrilateral and triangular meshes are obtained after meshing. After meshing, the model data exchange file in .inp format is exported. From this file, the number of finite element mesh nodes for both plates and the coordinates of each node can be extracted. In this example, plate 1 has a total of 2346 nodes, and plate 2 has a total of 392 nodes.

[0085] The third step is to extract relevant feature data. This involves reading the form's source code (inp file) and analyzing it using Abaqus software, assuming the two plates have the same material properties: density ρ = 7.85 × 10⁻⁶. -3 g / mm 3 Poisson's ratio V = 0.3, Young's modulus E = 210000 N / mm 2 Based on the actual situation of assembling and splicing two thin plates, a simplified model is reasonably constructed. It is assumed that there is no interaction between the two plates, and that the only external load on both plates is gravity. The formula is set as g = -9800 mm / s². 2 Gravity load is then applied to the entire structure. Finally, the stiffness matrix and force matrix of the two thin plates, along with other relevant characteristic data, are exported after the relevant parameters have been set.

[0086] The fourth step involves optimizing the particle swarm optimization algorithm, such as... Figure 2 The optimal number of fixtures and the corresponding z-axis fixture constraint numbers are obtained using an improved particle swarm optimization algorithm. In the example, the initial number of fixtures on the two thin plates is m1 = 22, m2 = 8. The node sequences at the joint of the two plates are a1 = {56, 55, ..., 1} and a2 = {1, 2, ..., 56}. The node sequences on the two plates where fixtures cannot be placed are NF1 = 189 and NF2 = 122. The population size is set to P = 300, the number of iterations is d = 20, the dimensions of the decision variables are D1 = 22 and D2 = 8, and the individual and social learning factors are l1 = l1 = 2.05. The shrinkage factor is then calculated based on these factors. 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, its fitness value will not exceed 1000. Therefore, the penalty coefficient M is set to 1000, and the minimum number of fixtures N for two boards is set. 1min =16 and N 2min =4, the maximum clearance H that meets the assembly requirements. max =2, set cost factors C1=1, C2=0.05, and fixture moving speed V x =V y =V z =1, calculate S using the position coordinates of each node on the two boards, part1_loc and part2_loc. jx ,S jy S jz Define the objective function as In I-dimensional space, initialize the particle position indices. Initialize the particle update rate V i =V imin +r(V imax -V imin ), To be with V i A random number sequence of the same dimension is used; the optimal position pbest of each individual in the population is initialized, and the fitness value corresponding to the optimal position of the individual is calculated using the objective function in equation (*). Calculate the deformation H(x) produced during assembly using equation (4), and determine whether H(x) ≤ H max and according to Update `pbest_fit`; initialize the global best position `gbest` and update the fitness value `gbest_fit` corresponding to the global best position. Perform iterations: using a two-layer nested loop with an outer loop `k = {1,2,…,P}` and an inner loop `d = {1,2,…,d}`, based on... Update inertia weights according to To and The speed is updated using a random number sequence of the same dimension. It is checked whether the speed value exceeds the allowed range during each update; if it does, the boundary value is pulled back, and the position is updated. Particles whose positions are out of bounds are not processed; Extraction of the number of effective grippers during iteration: Extract the number of effective grippers after the position index is updated, and the number update formula is: N i =card(X) i )-card(X i >X imax )-card(X i <X imin ), (i=1,2); Selection of the number of fixtures N in the iteration: The number of fixtures is selected for all individuals in the population in this round of the loop. The selection method is as follows: Filtering the maximum gap H value of individuals in the iteration: Determine whether the maximum gap value of each individual in all populations in this round of the loop is less than the maximum allowable gap value. The filtering method is as follows: For particles in the population that satisfy Tag2=1, calculations are performed to update their individual historical optimalities and global optimalities, thus completing the optimization process. The final optimization result is obtained:

[0087] The minimum total cost is 46.0693.

[0088] At this point, the total number of fixtures is 25, and the number of fixtures on plate 1 is 17. Figure 4 As shown in (a), its position is [2199 21141098 1616 868 669 1933 1030 1676 326 984 1004 1505 1503 1297 1869 500].

[0089] The number of clamps on plate 2 is 8; for example Figure 4 As shown in (b), its position is [175 216 170 344 389 128 312281].

[0090] like Figure 3 This reflects the changes in the globally optimal value searched during the 20 iterations.

[0091] The fifth step is to optimize the visualization of the results. Using the finite element analysis software Abaqus, after setting the relevant material and load properties, the set of z-axis clamp constraint numbers that minimize the average deformation at the assembly of the two thin plates is used to constrain the z-axis at corresponding positions in the two thin plates. The resulting cloud map of the deformation of the two thin plates is then exported for visualization. For example... Figure 4 (a) is a schematic diagram of the fixture point layout before the number optimization. Figure 4 (b) is a schematic diagram of the fixture location layout after optimization. Figure 5 The diagram shows the deformation of the plates before and after the number of fixtures was optimized. It is clear that the number of fixtures was reduced by 5 after optimization, and the deformation of both plates was less than the maximum allowable deformation for assembly.

[0092] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. A method for optimizing the number of fixtures for large flexible thin plates based on an improved particle swarm optimization algorithm, characterized in that, Includes the following steps: S1: Construct a large flexible thin plate 3D model and export the data interaction file of the constructed model; S2: Generate the finite element mesh and export the form source code file; S3: Extract feature data, set material properties, load distribution and constraints, extract finite element mesh node coordinates, stiffness matrix of thin plate model, force matrix of thin plate model; set constraint point numbers in x and y directions according to N-2-1 positioning method; S4: Improved particle swarm optimization algorithm: The improved particle swarm optimization algorithm is used to search for the optimal number of fixtures and the fixture layout under the condition of meeting the assembly requirements. 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, that is, the constraint number of the fixture in the z direction and the constraint point numbers in the x and y directions set according to the N-2-1 positioning method, constraints are applied in the finite element analysis to obtain the deformation cloud diagram of the thin plate, thus completing the verification and visualization. In S4, an improved particle swarm optimization algorithm is used to set the minimum number of clamps on the two thin plates. and Randomly generate a series The number of fixtures is changed by using the superboundary particles that appear during position update in the particle swarm algorithm to change the fixture constraint sequence: First, the particles that meet the number requirements are selected by limiting the number of fixtures, and then the z-axis fixture constraint sequence that meets the assembly requirements is selected from them. Finally, the optimal number of fixtures and the fixture distribution at this time are obtained under the condition of meeting the assembly splicing requirements. In particle swarm optimization, through equations ； Establish the relationship between the stiffness matrix, displacement matrix, and force matrix; In the formula: and They are respectively and The calculation steps for the stiffness and force matrices of the two thin plates after correction using the N-2-1 positioning method are as follows: Step 1: Enter the fixture position numbers for the two thin plates. Number of nodes in thin plates The N-2-1 positioning method for constrained points in the x and y directions and ; Step 2: Load the stiffness matrix of the two thin plates Sum of forces ; Step 3: Set the z-axis constraint for the N-2-1 positioning method ; Step 4: Set constraints in the x, y, and z directions and obtain the total constraints: ； ； Step 5: Set the index sequence ; Step 6: Perform iterative loops For j=1,2,…,length( ); q= Remove The position sequence in row j End; Step 7: Correct the force matrix , The optimization objective is to minimize the total cost; therefore, the objective function is defined as: ； To meet the needs of actual engineering, the maximum gap at the junction of the two plates was calculated during the process. The profile tolerance ε is constrained, and the constraint equation for the profile deformation tolerance ε is as follows: ； When an individual does not meet this constraint, a penalty coefficient must be added to the calculated result of the objective function. ; Maximum gap The constraint equations that need to be satisfied are: ； in The calculation method is as follows: ； In the formula, the meanings of each parameter are as follows: 。 2. The method for optimizing the number of large flexible thin-plate fixtures based on the improved particle swarm optimization algorithm according to claim 1, characterized in that, In S2, the model is divided into finite element meshes using finite element meshing software, and the data interaction file of the model at this time is exported. The number of finite element mesh nodes of the two thin plates and the coordinates corresponding to each node are then extracted from the data.

3. The method for optimizing the number of large flexible thin-plate fixtures based on the improved particle swarm optimization algorithm according to claim 1, characterized in that, In S3, finite element analysis software is used to analyze the material properties of the two plates, including density, Young's modulus, and Poisson's ratio. The model is simplified based on the actual situation when the two thin plates are assembled and spliced: it is assumed that there is no interaction between the two thin plates and only gravity is applied. After setting these parameters, export the stiffness matrix and force matrix of the two thin plates, and denote them as follows: , and , .

4. The method for optimizing the number of large flexible thin-plate fixtures based on the improved particle swarm optimization algorithm according to claim 1, characterized in that, In S5, relevant finite element analysis software is used. After setting the relevant material properties and load properties, the fixture distribution corresponding to the optimal number of fixtures that meet the assembly and splicing requirements is used as the z-axis fixture constraint number, and the z-axis of the corresponding positions in the two thin plates is constrained. After the constraint loading is completed, the cloud map of the deformation of the two thin plates is exported to visualize the optimization results and verify the optimization effect.

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