A curved surface grouping selection and assembly method based on an improved genetic algorithm

Abstract

The application discloses a curved surface grouping selection and assembly method based on an improved genetic algorithm, and belongs to the field of precision assembly, comprising the following steps: determining a reference part and a matching part to be assembled, and acquiring three-dimensional point cloud data of an assembly interface through sampling; a double-target optimization model of a weighted square difference index is established with the minimum average gap and the maximum gap as targets; the double-target optimization model is solved by using an improved genetic algorithm, and an optimal group mapping relationship pairing index matrix is output when the number of iterations reaches a set threshold; and the optimal matching combination of the reference part and the matching part is generated according to the optimal group mapping relationship pairing index matrix, and the curved surface grouping selection and assembly are completed. The application solves the limitation that the existing two-dimensional size selection and assembly method is difficult to consider three-dimensional topographic errors, realizes the curved surface grouping selection and assembly by constructing a double-target optimization model fusing three-dimensional topographic parameters and combining the multi-target optimization strategy of the genetic algorithm, and improves assembly precision and consistency.

Description

Technical Field

[0001] This invention belongs to the field of computer-aided assembly and simulation, and specifically relates to a surface grouping and selection assembly method based on an improved genetic algorithm. Background Technology

[0002] In aerospace, precision instrumentation, and high-end equipment manufacturing, assembly accuracy is crucial to product performance and service life. The assembly method, chosen as a computer-aided assembly and simulation tool, primarily relies on actual measurement data and utilizes intelligent simulation and optimization algorithms. Through virtual-real interaction and fusion simulation of the assembly objects, it optimizes the fit relationships of parts in virtual space to achieve error cancellation, guiding the assembly and adjustment of actual products. This is of great significance for verifying the feasibility of product assembly processes and improving assembly accuracy and efficiency. However, existing technologies have the following significant shortcomings:

[0003] Traditional two-dimensional dimensional matching methods are based on linear dimensional chains, only considering the impact of dimensional errors on assembly accuracy, while ignoring the complex spatial distribution characteristics of three-dimensional morphological errors at the part assembly interface. The micro-geometric morphology of the part surface (such as peaks, valleys, grooves, etc.) directly affects the contact state and functional performance of the assembly interface. However, existing methods lack a quantitative correlation model between shape errors and assembly functional requirements, making it difficult to guarantee the quality of micro-fitting.

[0004] Faced with the demand for efficient assembly of large batches of parts, existing grouping and matching strategies (such as random matching) are prone to significant fluctuations in assembly clearance. Traditional methods rely solely on dimensional errors for grouping, failing to establish a quantitative mapping between assembly interface shape errors and assembly functional requirements. This makes them unsuitable for 3D matching requirements, resulting in poor consistency in assembly quality for batch products. Specifically, existing part grouping methods based on normal or non-normal distributions rely solely on dimensional errors for grouping, making it difficult to handle the nonlinear characteristics of 3D shape errors and unsuitable for complex dimensional chain models. This leads to large fluctuations in assembly accuracy and low computational efficiency.

[0005] Furthermore, existing selection methods are mostly designed for two-dimensional dimensional chains, lacking systematic characterization and grouping strategies for three-dimensional topographic parameters. For example, traditional grouping methods do not consider three-dimensional topographic parameters such as surface arithmetic mean deviation, root mean square deviation, and surface support index, and cannot accurately characterize the microscopic features of the part surface. As a result, the grouping results cannot effectively guide assembly optimization, making it difficult to achieve a significant improvement in assembly consistency without improving machining accuracy.

[0006] In summary, existing technologies have significant shortcomings in the quantitative characterization, grouping strategies, and multi-objective optimization of 3D topography errors. There is an urgent need for an efficient selection method that can comprehensively consider 3D topography features and adapt to the assembly needs of large batches of parts. Summary of the Invention

[0007] This invention aims to address the limitations of existing two-dimensional size selection methods that cannot account for three-dimensional shape errors. By constructing a dual-objective optimization model that integrates three-dimensional shape parameters and combining it with a multi-objective optimization strategy based on genetic algorithms, it achieves surface grouping selection and assembly, thereby improving assembly accuracy and consistency.

[0008] To achieve the aforementioned objectives, the present invention employs the following technical solution: a surface grouping selection and assembly method based on an improved genetic algorithm, comprising the following steps:

[0009] S1: Determine the reference part and matching part to be assembled, and obtain the three-dimensional point cloud data of the assembly interface through sampling;

[0010] S2: A bi-objective optimization model for the weighted squared difference index is established with the goal of minimizing the average gap and the maximum gap.

[0011] S3: An improved genetic algorithm is used to solve the bi-objective optimization model. When the number of iterations reaches a set threshold, the optimal group mapping relationship pairing index matrix is ​​output.

[0012] S4: Based on the optimal group mapping relationship, pair the index matrix to generate the best matching combination of the reference part and the matching part, and complete the surface grouping selection assembly.

[0013] Furthermore, the first of the reference components Parameter vector of each part Represented as:

[0014]

[0015] in, For the reference piece The parameter vector of each part denoted as the dimension of the microscopic morphology characterization parameters;

[0016] The first of the matching parts Parameter vector of each part Represented as:

[0017]

[0018] in, For the matching part The parameter vector of each part , This refers to the number of reference or matching parts.

[0019] Furthermore, the dual-objective optimization model includes:

[0020] Minimize average gap for:

[0021]

[0022] in, Indicates the first in the batch of reference parts The first part and the batch matching parts Parts are paired. Let be the weighting coefficients of the parameters, satisfying ;

[0023] Minimize maximum gap for:

[0024] .

[0025] Furthermore, the constraints of the bi-objective optimization model include:

[0026] Uniqueness constraint: Assembly schemes are represented as mapping relationships : Each matching part must be selected only once during the assembly selection process;

[0027] Grouping constraints: Divide the reference part and the mating part into groups. The groups are as follows: The matching parts are grouped as follows: The pairing must meet the following conditions:

[0028]

[0029] in, For the grouping set of reference parts, For the grouped set of matching parts, This represents the objective function of the bi-objective optimization model. The first reference piece Groups, For the first matching part One group;

[0030] Non-negative constraint: Both the average clearance and the maximum clearance are non-negative numbers.

[0031] Furthermore, the improved genetic algorithm includes the following sub-steps:

[0032] A1: Initial data input, including initial population size, maximum number of iterations, crossover probability, mutation probability, and morphological parameter weight vector;

[0033] A2: The initial population is generated by random permutation: First, group mapping is generated to generate a unique mapping sequence for each individual, ensuring that each group of the reference piece is uniquely mapped to a matching piece group. Then, the index of the matching piece is randomly arranged within the group according to the mapping relationship to form a one-to-one pairing relationship.

[0034] A3: For each individual, traverse its pairing index, calculate the weighted squared difference of the corresponding morphological characterization parameters of the reference part and the matching part, and obtain the average gap and the maximum gap as the multi-objective fitness function value;

[0035] A4: Combining tournament selection with elite retention strategy, select the operator;

[0036] A5: Perform single-point crossover on the selected parent generation and mutate the genes of individuals in the population with a set mutation probability.

[0037] A6: After each generation of evolution, retain the individual with the best current fitness until the next generation. Output the current best average gap and maximum gap for each generation until the set number of iterations is reached and then terminate. Output the final Pareto front, the best pairing scheme and the group matching relationship.

[0038] The beneficial effects of this invention are as follows: The invention significantly improves accuracy. Compared to random selection methods, the maximum gap is reduced by approximately 42.82%, the average gap by approximately 7.47%, and the gap standard deviation by approximately 5.94%. Through grouping constraints and genetic algorithm optimization, the gap standard deviation of batch part assembly is reduced by 35.94% compared to random selection, improving the uniformity of assembly quality. Simultaneously, based on five-dimensional parameter characterization and grouping strategies, it effectively quantifies surface micro-features, making it suitable for complex curved surface assembly scenarios. It achieves improved assembly accuracy without increasing machining precision, reducing manufacturing costs through intelligent selection strategies, and is applicable to precision assembly fields such as aerospace and high-end equipment. Attached Figure Description

[0039] Figure 1 The flowchart of the surface grouping selection assembly method based on the improved genetic algorithm provided by the present invention is shown.

[0040] Figure 2 This is a schematic diagram of the PCA dimensionality reduction clustering results for grouping the shape error of the assembly interface of part 1 provided by the present invention.

[0041] Figure 3 This is a schematic diagram of the PCA dimensionality reduction clustering results for grouping the shape error of the assembly interface of part 2 provided by the present invention.

[0042] Figure 4 This is a comparison diagram of the grouping and matching gap distribution provided by the present invention.

[0043] Figure 5 This is a comparison diagram of the random selection and pairing gap distribution provided by the present invention.

[0044] Figure 6 The curve showing the change in average gap during the iteration process of the genetic algorithm provided in this invention.

[0045] Figure 7The curve showing the maximum gap change during the iteration process of the genetic algorithm provided in this invention.

[0046] Figure 8 This is a comparison chart of the average gap under different mutation probabilities provided by the present invention.

[0047] Figure 9 This is a comparison chart of the maximum gap under different mutation probabilities provided by the present invention.

[0048] Figure 10 A schematic diagram of the Pareto front solution set for grouping selection provided by the present invention. Detailed Implementation

[0049] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0050] like Figure 1 As shown, a surface grouping selection assembly method based on an improved genetic algorithm includes the following steps:

[0051] S1: Determine the reference part and matching part to be assembled, and obtain the three-dimensional point cloud data of the assembly interface through sampling;

[0052] Calculate 5 morphological parameters: surface arithmetic mean deviation ( ), root mean square deviation ( ), three-dimensional surface support index ( ), core area liquid retention index ( ), Valley bottom liquid retention index ( );

[0053] The first reference component Parameter vector of each part Represented as:

[0054]

[0055] in, For the reference piece The parameter vector of each part denoted as the dimension of the microscopic morphology characterization parameters;

[0056] The first matching part Parameter vector of each part Represented as:

[0057]

[0058] in, For the matching part The parameter vector of each part , This refers to the number of reference or matching parts.

[0059] S2: A bi-objective optimization model for the weighted squared difference index is established with the goal of minimizing the average gap and the maximum gap.

[0060] The dual-objective optimization model includes:

[0061] Minimize average gap for:

[0062]

[0063] in, Indicates the first in the batch of reference parts The first part and the batch matching parts Parts are paired. Let be the weighting coefficients of the parameters, satisfying This parameter is used to reflect the degree of influence of different parameters on assembly quality;

[0064] Minimize maximum gap for:

[0065]

[0066] The constraints of the dual-objective optimization model include:

[0067] Uniqueness constraint: Assembly schemes are represented as mapping relationships : Each matching part must be selected only once during the assembly selection process;

[0068] Grouping constraints: Divide the reference part and the mating part into groups. The groups are as follows: The matching parts are grouped as follows: The pairing must satisfy the following formula, that is, each Uniquely mapped to And all All are mapped:

[0069]

[0070] in, For the grouping set of reference parts, For the grouped set of matching parts, This represents the objective function of the bi-objective optimization model. The first reference piece Groups, For the first matching part One group;

[0071] Non-negative constraint: Both the average clearance and the maximum clearance are non-negative numbers, i.e. and .

[0072] S3: An improved genetic algorithm is used to solve the bi-objective optimization model. When the number of iterations reaches a set threshold, the optimal group mapping relationship pairing index matrix is ​​output.

[0073] The improved genetic algorithm includes the following steps:

[0074] A1: Initial data input, including initial population size Maximum number of iterations Crossover probability Probability of mutation and topography parameter weight vector ;

[0075] In this embodiment, take , , , , .

[0076] A2: The initial population is generated by random permutation: First, group mapping is generated to generate a unique mapping sequence for each individual, ensuring that each group of the reference piece is uniquely mapped to a matching piece group. Then, the index of the matching piece is randomly arranged within the group according to the mapping relationship to form a one-to-one pairing relationship.

[0077] In this embodiment, group mapping is first generated. Based on the number of clusters of part 1 (5 groups), a unique mapping sequence for part 2 is generated for each individual, ensuring that each group of part 1 uniquely maps to a group of part 2. Then, according to the mapping relationship, the indices of part 2 are randomly arranged within the group to form a one-to-one pairing relationship. The initial population contains 100 individuals, represented as... Chromosomes of each individual It contains complete group mapping and pairing index information, covering different regions of the feasible solution space. For the selection and matching of parts 1 and 2, it includes the grouping and arrangement of 5 part characterization parameters, i.e., 5 gene fragments. .

[0078] A3: For each individual, traverse its pairing index, calculate the weighted squared difference of the corresponding morphological characterization parameters of the reference part and the matching part, and obtain the average gap and the maximum gap as the multi-objective fitness function value;

[0079] A4: Combining tournament selection with elite retention strategy, select the operator;

[0080] In this embodiment, three candidate individuals are randomly selected from the population in each round. The optimal individual is selected based on the Pareto dominance relationship. The dominance rule is that if the average gap and maximum gap of individual A are not inferior to those of individual B, then the Pareto dominance relationship is satisfied. and If A dominates B, then the elite individuals (currently the best) are directly retained to the next generation, while the remaining individuals are selected through a tournament, ensuring that the algorithm converges quickly.

[0081] A5: Perform single-point crossover on the selected parent generation and mutate the genes of individuals in the population with a set mutation probability.

[0082] In this embodiment, a random intersection point (such as between group 3 and group 4) is selected, and the group mapping sequence after the parent intersection point is swapped. Then, duplicate mappings are repaired, that is, duplicate groups are replaced with unmapped groups. For example:

[0083] Parent 1 mapping: [1, 2, 3, 4, 5];

[0084] Parent 2 mapping: [5, 4, 3, 2, 1];

[0085] After crossover, the offspring mapping may be generated as [1, 2, 3, 2, 1] (which needs to be corrected to [1, 2, 3, 4, 5]), with a crossover probability of 80%, ensuring population diversity.

[0086] Then, a group mapping position is randomly selected (e.g., group 3), and its mapping target is changed to the unused cluster number of part 2, ensuring bijective constraints. Then, the pairing indices within the new mapping group are regenerated. For example, if the original mapping is [1, 2, 3, 4, 5], after mutation it may become [1, 2, 4, 4, 5] (which needs to be corrected to [1, 2, 4, 3, 5]), and the pairing relationships within the group are updated. The mutation operation enhances population diversity by introducing new features.

[0087] A6: After each generation of evolution, retain the individual with the best current fitness until the next generation. Output the current best average gap and maximum gap for each generation until the set number of iterations is reached and then terminate. Output the final Pareto front, the best pairing scheme and the group matching relationship.

[0088] In this embodiment, elite preservation and population renewal are achieved by merging elites with mutated offspring and truncating the previous generation. Each effective offspring is then combined with elite individuals to maintain a constant population size of 100. This mechanism ensures that superior solutions are not eliminated while allowing new individuals to participate in evolution.

[0089] S4: Based on the optimal group mapping relationship, pair the index matrix to generate the best matching combination of the reference part and the matching part, and complete the surface grouping selection assembly.

[0090] In one embodiment of the present invention, the PCA dimensionality reduction clustering results of the assembly interface shape error grouping of parts 1 and 2 are provided below. Figure 2 , 3Please refer to Tables 1 and 2 for the grouped data of assembly interface shape errors for parts 1 and 2:

[0091] Table 1 Grouping data of assembly interface shape error for part 1

[0092]

[0093] Table 2 Grouping data of assembly interface shape error for part 2

[0094]

[0095] Using the algorithm proposed in this invention, the problem of grouping and matching two types of parts is solved. The optimal group matching relationship output by the algorithm is shown in Table 3. That is, in the matching process, the first group of part 1 is matched with the fourth group of part 2; the second group of part 1 is matched with the first group of part 2; the third group of part 1 is matched with the fifth group of part 2; the fourth group of part 1 is matched with the second group of part 2; and the fifth group of part 1 is matched with the third group of part 2.

[0096] Table 3. Optimal group matching relationships for group selection.

[0097]

[0098] The optimal pairing schemes for 50 groups of parts were finally output using a grouping and random selection method. The pairing results for these 50 groups of parts were statistically analyzed based on their gap values. For the gap distribution of the grouping and random selection pairings, please refer to [link to relevant documentation]. Figure 4 and Figure 5 .

[0099] See Figure 4 and Figure 5 The pairing gap distribution range of the 50 groups of parts obtained by the group selection method is [0, 3.75]; the pairing gap distribution range of the 50 groups of parts obtained by the random selection method is [0, 5.85]. Therefore, the method proposed in this invention can significantly reduce the pairing gap between all parts, and avoids the phenomenon that some pairing combinations have very small gap values ​​while others have large gap values, as seen in the random selection method.

[0100] Referring to Table 4, although the minimum gap among the 50 pairs of parts obtained by the group selection method is slightly larger than that of the random selection method, the maximum gap, average gap, and gap standard deviation are significantly smaller than those of the random selection method. The maximum gap is reduced by about 42.82%, the average gap by about 27.47%, and the gap standard deviation by about 35.94%.

[0101] Table 4. Statistical results of assembly clearance between grouped and randomized matching.

[0102]

[0103] When the algorithm has completed 100 iterations, please refer to the iterative curve of the average gap. Figure 6 Please refer to the maximum gap iteration curve. Figure 7 .

[0104] After solving the matching problem for the two types of parts, the average gap iteration curves were obtained using crossover probabilities of 0.1, 0.05, 0.01, 0.005, and 0.001, respectively. Figure 8 It can be seen that when the number of iterations is set to 100, the average gap value obtained by using a mutation probability of 0.05 is the smallest, followed by the average gap value obtained by using a mutation probability of 0.1, and the average gap value obtained by using a mutation probability of 0.01 is the largest. Please refer to the maximum gap iteration curve. Figure 9 It can be seen that when the number of iterations is set to 100, the maximum gap value obtained by using a mutation probability of 0.1 is the smallest, the maximum gap value obtained by using a mutation probability of 0.05 is the second largest, and the average gap value obtained by using a mutation probability of 0.001 is the largest. For the Pareto front solution set with grouped selection provided by this invention, please refer to... Figure 10 Please refer to Table 5 for a comparison of assembly gap indices under different mutation probabilities. When the algorithm mutation probability is set to 0.1, the standard deviation of the gap for the 50 paired combinations is the smallest, indicating the most stable assembly quality.

[0105] Table 5 Comparison of assembly clearance indices under different probabilities of variation.

[0106]

[0107] This embodiment verifies the effectiveness and engineering applicability of the method of the present invention in dealing with three-dimensional topography errors through specific parameter settings, algorithm flow, and experimental comparison.

[0108] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the invention.

Claims

1. A surface grouping selection assembly method based on an improved genetic algorithm, characterized in that, Includes the following steps: S1: Determine the reference part and matching part to be assembled, and obtain the three-dimensional point cloud data of the assembly interface through sampling; S2: A bi-objective optimization model for the weighted squared difference index is established with the goal of minimizing the average gap and the maximum gap. The dual-objective optimization model includes: Minimize average gap for: in, The number of reference parts or matching parts. Indicates the first in the batch of reference parts The first part and the batch matching parts Parts are paired. Let be the weighting coefficients of the parameters, satisfying , The dimension of the micromorphological characterization parameters, The parameter vector representing the reference component. A parameter vector representing the matched parts; Minimize maximum gap for: The constraints of the bi-objective optimization model include: Uniqueness constraint: Assembly schemes are represented as mapping relationships : Each matching part must be selected only once during the assembly selection process; Grouping constraints: Divide the reference part and the mating part into groups. The groups are as follows: The matching parts are grouped as follows: The pairing must meet the following conditions: in, For the grouping set of reference parts, For the grouped set of matching parts, This represents the objective function of the bi-objective optimization model. The first reference piece Groups, For the first matching part One group; Non-negative constraint: Both the average clearance and the maximum clearance are non-negative numbers; S3: An improved genetic algorithm is used to solve the bi-objective optimization model. When the number of iterations reaches a set threshold, the optimal group mapping relationship pairing index matrix is ​​output. The improved genetic algorithm includes the following steps: A1: Initial data input, including initial population size, maximum number of iterations, crossover probability, mutation probability, and morphological parameter weight vector; A2: The initial population is generated by random permutation: First, group mapping is generated to generate a unique mapping sequence for each individual, ensuring that each group of the reference piece is uniquely mapped to a matching piece group. Then, the index of the matching piece is randomly arranged within the group according to the mapping relationship to form a one-to-one pairing relationship. A3: For each individual, traverse its pairing index, calculate the weighted squared difference of the corresponding morphological characterization parameters of the reference part and the matching part, and obtain the average gap and the maximum gap as the multi-objective fitness function value; A4: Combining tournament selection with elite retention strategy, select the operator; A5: Perform single-point crossover on the selected parent generation and mutate the genes of individuals in the population with a set mutation probability. A6: After each generation of evolution, retain the individual with the best current fitness until the next generation. Output the current best average gap and maximum gap for each generation until the set number of iterations is reached and then terminated. Output the final Pareto front, the best pairing scheme and group matching relationship. S4: Based on the optimal group mapping relationship, pair the index matrix to generate the best matching combination of the reference part and the matching part, and complete the surface grouping selection assembly.

2. The surface grouping selection and assembly method based on an improved genetic algorithm according to claim 1, characterized in that, The first of the reference components Parameter vector of each part Represented as: in, For the reference piece The parameter vector of each part denoted as the dimension of the microscopic morphology characterization parameters; The first of the matching parts Parameter vector of each part Represented as: in, For the matching part The parameter vector of each part , This refers to the number of reference or matching parts.

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