A method for optimizing press riveting quality based on multi-objective particle swarm optimization and PCA

Abstract

The present invention relates to a riveting quality optimization method based on a multi-objective particle swarm algorithm and PCA. The riveting quality optimization method based on the multi-objective particle swarm algorithm and PCA effectively evaluates the impact of different parameter combinations on a response target by performing nonlinear transformations on defined parameters in the multi-objective particle swarm algorithm and using a Taguchi experiment. Principal component analysis is performed on the signal-to-noise ratio obtained from the Taguchi experiment using PCA. The fitness values of the particles are calculated based on the data obtained from the principal component analysis as a fitness function of the multi-objective particle swarm algorithm. This method can simplify high-dimensional data, extract the main information components, reduce the complexity of the problem, and make the optimization process more efficient. The principal component analysis can extract the nonlinear components that affect the signal-to-noise ratio, thereby helping the multi-objective particle swarm algorithm better handle nonlinear optimization problems.

Description

Technical Field

[0001] The present invention relates to the technical field of press riveting quality optimization, and in particular to a press riveting quality optimization method based on a multi-objective particle swarm algorithm and PCA. Background Art

[0002] Compression riveting is a process that fastens two or more parts together using rivets. In automotive manufacturing, compression riveting can provide high-strength connections, ensuring sealing and corrosion resistance, thus meeting the stringent strength and durability requirements of automobile bodies.

[0003] Factors that affect the quality of press riveting include the selection and quality of riveting materials, the stability and precision of riveting tools and equipment, accurate control of riveting process parameters (such as pressure, time, and temperature), the rationality of riveting design, the skill level and operating techniques of the operator, and the strictness of quality inspection and monitoring. These factors together determine the strength, reliability, and durability of the riveted joint.

[0004] During the automotive production process, to ensure the post-riveting strength of auto parts, it is often necessary to determine the optimal parameter combination for press riveting quality. Existing technologies typically use optimization algorithms to systematically traverse or intelligently search the parameter space, evaluating the objective function values under different parameter combinations to find the optimal objective function. However, existing optimization algorithms often involve multiple parameters when optimizing press riveting quality, and these parameters may have complex nonlinear relationships. If these nonlinear relationships are ignored, the algorithm may fall into a local optimal solution rather than a global optimal solution.

[0005] Therefore, the present invention proposes a riveting quality optimization method based on a multi-objective particle swarm optimization algorithm and PCA. By combining the Taguchi method and grey relational analysis with the multi-objective particle swarm optimization algorithm, the fitness function and search strategy can be effectively adjusted dynamically according to the current state of the group, thereby effectively avoiding falling into the local optimal solution. Summary of the Invention

[0006] In response to the shortcomings of the existing technology, the present invention provides a method for optimizing the quality of press rivets based on a multi-objective particle swarm algorithm and PCA, which has the advantages of being able to achieve precise optimization of press rivets, and solves the problems in the existing technology of being unable to handle the nonlinear relationship between parameters when optimizing press rivets and the large amount of algorithm calculation.

[0007] To achieve the above object, the present invention provides the following technical solution: a method for optimizing riveting quality based on a multi-objective particle swarm optimization algorithm and PCA, comprising the following steps, characterized in that:

[0008] S1. Determine the control parameter set of the riveting machine , press riveting design parameter set and the response set , build a machine control parameter set , press riveting design parameter set To define the parameters of the multi-objective particle swarm optimization model and initialize the model parameters;

[0009] S2, control parameter set for pressure riveting machine , press riveting design parameter set and the response set Perform nonlinear processing to obtain performance indicators after riveting ;

[0010] S3, performance indicators after riveting For quality characteristics, select the machine control parameter set that affects the quality characteristics and press riveting design parameter sets For each parameter, the Taguchi method was used to set different levels for each parameter to construct an orthogonal experimental table to conduct experiments and obtain multiple groups of signal-to-noise ratios;

[0011] S4, perform principal component analysis on multiple groups of signal-to-noise ratio sequences, and construct a fitness function of the multi-objective particle physics algorithm based on the principal component analysis results;

[0012] S5. Calculate each particle according to the fitness function The fitness value of the particle is evaluated using the non-dominated sorting method, the individual optimal position and external archive are updated, and the congestion degree is calculated;

[0013] S6. Iteratively optimize the particles, update the speed and position of the particles, calculate the fitness value of each updated particle, and update the individual best position and external archive;

[0014] S7. After each round of iteration, determine whether the maximum number of iterations T is reached. If so, the termination condition is met and the algorithm stops running. Otherwise, return to S6 and recalculate until the maximum number of iterations is met.

[0015] S8. After the algorithm stops running, the non-dominated solution in the external archive is output as the optimal riveting quality parameter combination.

[0016] Furthermore, the control parameter set of the pair of riveting machines in S2 is , press riveting design parameter set and the response set For nonlinear processing, logarithmic function and power function are used for nonlinear transformation. The specific formula is as follows:

[0017] ;

[0018] in: It is the performance index after riveting. is a constant term, and is the regression coefficient representing the interaction between the design parameters and the machine control parameters, and Representing the The first press riveting design parameter and the The value of each machine control parameter, is the constant term of the logarithmic transformation, which is used to adjust the reference point of the logarithmic transformation. is the power term associated with the power function, indicating The nonlinear effect of and They represent the number of press riveting design parameters and machine control parameters respectively.

[0019] Furthermore, the degree to which the quality characteristic approaches the target value and the fluctuation caused by noise interference are considered in S3, and the response set The signal-to-noise ratios of the three response targets within the WT are calculated using the following formulas:

[0020] ;

[0021] in, is the signal-to-noise ratio, , is the expected value of the quality characteristic, is the standard deviation of the quality characteristic, which can be obtained according to the above formula:

[0022] The response target is Signal-to-noise ratio data: ;

[0023] The response target is Signal-to-noise ratio data: ;

[0024] The response target is Signal-to-noise ratio data: ;

[0025] where n is the number of trials responding to the target.

[0026] Furthermore, performing principal component analysis on the signal-to-noise ratio sequence in S4 includes the following sub-steps:

[0027] S4.1. Organize the signal-to-noise ratio data of the response target j into a data matrix X, where each row represents a sample and each column represents the signal-to-noise ratio of a corresponding target;

[0028] ;

[0029] S4.2. Standardize the data matrix X to obtain the standardized matrix , the calculation process is as follows:

[0030] ;

[0031] in, is the mean of the i response targets, is the standard deviation of the i-th response target;

[0032] S4.3. Calculate the covariance matrix; use the standardized data matrix To calculate the covariance matrix C, the calculation process is as follows:

[0033] ;

[0034] Where C is the covariance matrix, n represents the number of observations, Representation matrix The transposed matrix of

[0035] S4.4. Covariance Matrix Perform eigenvalue decomposition to obtain eigenvalues , =( 、 、 ), and the eigenvector , , the eigenvectors constitute the principal component directions;

[0036] S4.5. Select the principal component and normalize the matrix The data is projected into the subspace composed of the selected principal components;

[0037] ;

[0038] Projection Matrix It is composed of selected eigenvectors;

[0039] S4.6. Calculate the principal component scores. The calculation process of the principal component score matrix T is as follows:

[0040] ;

[0041] in is the standardized matrix, W is the eigenvector matrix;

[0042] S4.7, according to the data obtained by principal component analysis, the fitness function of the multi-objective particle swarm algorithm is established. First, the fitness function of each particle is calculated. Projection score in each principal component direction , by taking the particle position vector and the eigenvector of the jth principal component This is achieved by performing a dot product. The calculation process is as follows:

[0043] ;

[0044] in, It is a particle The kth component of is the eigenvector The kth component of , m is the dimension of the particle and also the number of variables in principal component analysis;

[0045] S4.8. Calculate the fitness function components and calculate the fitness value of the particle for each principal component direction. The calculation process is as follows:

[0046] ;

[0047] in, and are the mean and standard deviation of the projection scores of the original data in the direction of the jth principal component, and wj is the weight determined according to the eigenvalue;

[0048] S4.9. The final fitness function is established based on the fitness function components as follows:

[0049] ;

[0050] in , , Corresponding to the principal component directions .

[0051] Furthermore, the step S5 further includes the following sub-steps:

[0052] S5.1. Calculate the fitness value of the particle according to the fitness function F(xi) and obtain three fitness values: 、 、 ;

[0053] S5.2. Create an empty list to store each frontier surface, and for each particle xi, create another empty list to store the particles that dominate it and the particles that are dominated by it;

[0054] S5.3. For each pair of particles as well as For comparison, according to the formula:

[0055] ;

[0056] In the above formula, if at least one inequality holds, then Dominate , if not, they are non-dominated;

[0057] S5.4. Place all particles that are not dominated by other particles into a first frontier, check the dominating particle of each particle in the frontier, and place each dominated particle into a new frontier;

[0058] S5.5. Repeat the above process, placing the particles in the temporary list into the next frontier, and updating the temporary list with the particles dominated by these particles, until no more particles are placed into the frontier;

[0059] S5.6. For each particle in each frontier, initialize its crowding to 0. For each fitness function F(xi), find the maximum and minimum values of all particles in the frontier.

[0060] S5.7. For all particles except the first and last particles in each frontier, calculate the distance difference between the particle and its adjacent particles on each fitness function, and add up the distance differences to obtain the congestion degree of the particle.

[0061] Furthermore, the weight wj in S4.7 is calculated by the following steps:

[0062] S4.8.1. Calculate the sum of the principal component analysis eigenvalues using the following formula:

[0063] ;

[0064] S4.8.2. Normalize the eigenvalues to obtain the weights wj, calculated using the following formula:

[0065] ;

[0066] in, Eigenvalue corresponding to a single particle.

[0067] Compared with the existing technology, the technical solution of this application has the following beneficial effects:

[0068] 1. This riveting quality optimization method based on a multi-objective particle swarm optimization algorithm and PCA improves the exploration efficiency of the search space through nonlinear transformation, making it easier for the algorithm to find the global optimal solution. The Taguchi test effectively evaluates the impact of different parameter combinations on the response target through orthogonal design, reducing the number of experiments and improving optimization efficiency.

[0069] 2. This is a riveting quality optimization method based on a multi-objective particle swarm algorithm and PCA. Traditional fitness functions usually directly evaluate the quality of the solution based on the value of the objective function, but in high-dimensional data space, this may become complicated and difficult to apply directly. The fitness function in the present invention reduces the dimensionality of high-dimensional data to several main components through principal component analysis, thereby simplifying the problem and reducing the computational complexity. The fitness function improves the exploration efficiency of the search space through the application of nonlinear transformation and PCA, making it easier for the algorithm to escape from the local optimum and find the global optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Schematic diagram of the algorithm flow of the present invention; DETAILED DESCRIPTION

[0071] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0072] See also Figure 1 In this embodiment, a method for optimizing the riveting quality based on a multi-objective particle swarm optimization algorithm and PCA includes the following steps, which are characterized by:

[0073] S1. Determine the control parameter set of the riveting machine , press riveting design parameter set and the response set , build a machine control parameter set , press riveting design parameter set To define the parameters of the multi-objective particle swarm algorithm model and initialize the model parameters; including initializing the particle swarm size , maximum number of iterations , learning factor and , inertia weight and the external archive size ;Press riveting design parameter set Including, pressing loading force, pressing speed, pressing holding time and the distance between the hole center line and the edge, etc., the riveting design parameters include busbar design parameters: hole diameter, material and thickness, etc., the response set Including push-out force after riveting, twist-out force and maximum installation torque, etc.

[0074] Randomly generated in parameter space The particle position is recorded as , randomly assign a velocity vector to each particle , initialize the optimal position of individual particles is the current position, recorded as , initialize the global best historical position Empty.

[0075] S2, control parameter set for pressure riveting machine , press riveting design parameter set and the response set Perform nonlinear processing to obtain performance indicators after riveting ; Use logarithmic function and power function for nonlinear transformation. The specific formula is as follows:

[0076] ;

[0077] in: It is the performance index after riveting. is a constant term, and is the regression coefficient representing the interaction between the design parameters and the machine control parameters, and Representing the The first press riveting design parameter and the The value of each machine control parameter, is the constant term of the logarithmic transformation, which is used to adjust the reference point of the logarithmic transformation. is the power term associated with the power function, indicating The nonlinear effect of and They represent the number of press riveting design parameters and machine control parameters respectively.

[0078] Performing nonlinear transformation on data before Taguchi test can significantly enhance the model's fit to the complex relationship between parameters and performance indicators, increase sensitivity to parameter changes, effectively reduce the impact of interference factors, optimize experimental design and improve decision-making efficiency, and provide more accurate and reliable guidance for product design and optimization.

[0079] S3, performance indicators after riveting For quality characteristics, select the machine control parameter set that affects the quality characteristics and press riveting design parameter sets For each parameter, the Taguchi method was used to set different levels for each parameter to construct an orthogonal experimental table to conduct experiments and obtain multiple groups of signal-to-noise ratios;

[0080] Considering the degree to which the quality characteristics are close to the target value and the fluctuation caused by noise, the response set The signal-to-noise ratios of the three response targets within the WT are calculated using the following formulas:

[0081] ;

[0082] in, is the signal-to-noise ratio, , is the expected value of the quality characteristic, is the standard deviation of the quality characteristic, which can be obtained according to the above formula:

[0083] The response target is Signal-to-noise ratio data: ;

[0084] The response target is Signal-to-noise ratio data: ;

[0085] The response target is Signal-to-noise ratio data: ;

[0086] where n is the number of trials responding to the target.

[0087] S4, performing principal component analysis on multiple groups of signal-to-noise ratio sequences, and constructing the fitness function of the multi-objective particle physics algorithm based on the principal component analysis results;

[0088] Preferably, performing principal component analysis on the signal-to-noise ratio sequence in S4 includes the following sub-steps:

[0089] S4.1. Organize the signal-to-noise ratio data of the response target j into a data matrix X, where each row represents a sample and each column represents the signal-to-noise ratio of a corresponding target;

[0090] ;

[0091] S4.2. Standardize the data matrix X to obtain the standardized matrix , the calculation process is as follows:

[0092] ;

[0093] in, is the mean of the i response targets, is the standard deviation of the i-th response target;

[0094] S4.3. Calculate the covariance matrix; use the standardized data matrix To calculate the covariance matrix C, the calculation process is as follows:

[0095] ;

[0096] Where C is the covariance matrix, n represents the number of observations, Representation matrix The transposed matrix of

[0097] S4.4. Covariance Matrix Perform eigenvalue decomposition to obtain eigenvalues , =( 、 、 ), and the eigenvector , , the eigenvectors constitute the principal component directions;

[0098] S4.5. Select the principal component and normalize the matrix The data is projected into the subspace composed of the selected principal components;

[0099] ;

[0100] Projection Matrix It is composed of selected eigenvectors;

[0101] S4.6. Calculate the principal component scores. The calculation process of the principal component score matrix T is as follows:

[0102] ;

[0103] in is the standardized matrix, W is the eigenvector matrix;

[0104] S4.7, according to the data obtained by principal component analysis, the fitness function of the multi-objective particle swarm algorithm is established. First, the fitness function of each particle is calculated. Projection score in each principal component direction , by taking the particle position vector and the eigenvector of the jth principal component This is achieved by performing a dot product. The calculation process is as follows:

[0105] ;

[0106] in, It is a particle The kth component of is the eigenvector The kth component of , m is the dimension of the particle and also the number of variables in principal component analysis;

[0107] S4.8. Calculate the fitness function components and calculate the fitness value of the particle for each principal component direction. The calculation process is as follows:

[0108] ;

[0109] in, and are the mean and standard deviation of the projection scores of the original data in the direction of the jth principal component, and wj is the weight determined according to the eigenvalue;

[0110] The weight wj in S5.7 is calculated by the following steps:

[0111] S4.8.1. Calculate the sum of the principal component analysis eigenvalues using the following formula:

[0112] ;

[0113] S4.8.2. Normalize the eigenvalues to obtain the weights wj, calculated using the following formula:

[0114] ;

[0115] in, Eigenvalue corresponding to a single particle.

[0116] S4.9. The final fitness function is established based on the fitness function components as follows:

[0117] ;

[0118] in , , Corresponding to the principal component directions .

[0119] S5. Calculate each particle according to the fitness function The fitness value of the particle is evaluated using the non-dominated sorting method, the individual optimal position and external archive are updated, and the congestion is calculated; for each particle The current fitness value and the individual's best historical position If the current fitness value dominates the individual's best historical position , then the updated individual best historical position is If not, keep ;

[0120] S5 also includes the following sub-steps:

[0121] S5.1. Calculate the fitness value of the particle according to the fitness function F(xi) and obtain three fitness values: 、 、 ;

[0122] S5.2. Create an empty list to store each frontier surface, and for each particle xi, create another empty list to store the particles that dominate it and the particles that are dominated by it;

[0123] S5.3. For each pair of particles as well as For comparison, according to the formula:

[0124] ;

[0125] In the above formula, if at least one inequality holds, then Dominate , if not, they are non-dominated;

[0126] S5.4. Place all particles that are not dominated by other particles into a first frontier, check the dominating particle of each particle in the frontier, and place each dominated particle into a new frontier;

[0127] S5.5. Repeat the above process, placing the particles in the temporary list into the next frontier, and updating the temporary list with the particles dominated by these particles, until no more particles are placed into the frontier;

[0128] S5.6. For each particle in each frontier, initialize its crowding to 0. For each fitness function F(xi), find the maximum and minimum values of all particles in the frontier.

[0129] S5.7. For all particles except the first and last particles in each frontier, calculate the distance difference between the particle and its adjacent particles on each fitness function, and add up the distance differences to obtain the congestion degree of the particle.

[0130] S6. Iteratively optimize the particles, update the particle speed and position, calculate the fitness value of each particle after the update, and update the individual best position and external archive; select the non-dominated solution set from the current particle swarm and external archive, and select the optimal solution from the non-dominated solution set as the global best position based on the comprehensive evaluation index , update the particle speed and position, maintain the external archive, compare the updated particle fitness with the solution in the external archive, if the particle dominates some solutions in the archive, replace these solutions with the particle, if the new particle is dominated by a solution in the external archive, it will not be added to the external archive, if the archive size exceeds the preset value M, it will be pruned according to the congestion;

[0131] S7. After each round of iteration, determine whether the maximum number of iterations T is reached. If so, the termination condition is met and the algorithm stops running. Otherwise, return to S6 and recalculate until the maximum number of iterations is met.

[0132] S8. After the algorithm stops running, the non-dominated solution in the external archive is output as the optimal riveting quality parameter combination.

[0133] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0134] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for optimizing riveting quality based on a multi-objective particle swarm optimization algorithm and PCA, comprising the following steps, characterized in that: S1. Determine the control parameter set of the riveting machine , press riveting design parameter set and the response set , build a machine control parameter set , press riveting design parameter set To define the parameters of the multi-objective particle swarm optimization model and initialize the model parameters; S2, control parameter set for pressure riveting machine , press riveting design parameter set and the response set Perform nonlinear processing to obtain performance indicators after riveting ; The control parameter set of the pair riveting machine in S2 , press riveting design parameter set and the response set For nonlinear processing, logarithmic function and power function are used for nonlinear transformation. The specific formula is as follows: ； in: It is the performance index after riveting. is a constant term, and is the regression coefficient representing the interaction between the design parameters and the machine control parameters, and Representing the The first press riveting design parameter and the The value of each machine control parameter, is the constant term of the logarithmic transformation, which is used to adjust the reference point of the logarithmic transformation. is the power term associated with the power function, indicating The nonlinear effect of and Represent the number of press riveting design parameters and machine control parameters respectively; S3, performance indicators after riveting For quality characteristics, select the machine control parameter set that affects the quality characteristics and press riveting design parameter sets For each parameter, the Taguchi method was used to set different levels for each parameter to construct an orthogonal experimental table to conduct experiments and obtain multiple groups of signal-to-noise ratios; In S3, the degree to which the quality characteristic approaches the target value and the fluctuation caused by noise interference are considered. The signal-to-noise ratios of the three response targets within the WT are calculated using the following formulas: ； in, is the signal-to-noise ratio, , is the expected value of the quality characteristic, is the standard deviation of the quality characteristic, which can be obtained according to the above formula: The response target is Signal-to-noise ratio data: ; The response target is Signal-to-noise ratio data: ; The response target is Signal-to-noise ratio data: ; Where n is the number of trials to respond to the target; S4, perform principal component analysis on multiple groups of signal-to-noise ratio sequences, and construct a fitness function of the multi-objective particle physics algorithm based on the principal component analysis results; The principal component analysis of the signal-to-noise ratio sequence in S4 includes the following sub-steps: S4.

1. Organize the signal-to-noise ratio data of the response target j into a data matrix X, where each row represents a sample and each column represents the signal-to-noise ratio of a corresponding target; ； S4.

2. Standardize the data matrix X to obtain the standardized matrix , the calculation process is as follows: ； in, is the mean of the i response targets, is the standard deviation of the ith response target; S4.

3. Calculate the covariance matrix; use the standardized data matrix To calculate the covariance matrix C, the calculation process is as follows: ； Where C is the covariance matrix, n represents the number of observations, Representation matrix The transposed matrix of S4.

4. Covariance Matrix Perform eigenvalue decomposition to obtain eigenvalues , =( 、 、 ), and the eigenvector , , the eigenvectors constitute the principal component directions; S4.

5. Select the principal component and normalize the matrix The data is projected into the subspace composed of the selected principal components; ； Projection Matrix It is composed of selected eigenvectors; S4.

6. Calculate the principal component scores. The calculation process of the principal component score matrix T is as follows: in is the standardized matrix, W is the eigenvector matrix; S4.7, according to the data obtained by principal component analysis, the fitness function of the multi-objective particle swarm algorithm is established. First, the fitness function of each particle is calculated. Projection score in each principal component direction , by taking the particle position vector and the eigenvector of the jth principal component This is achieved by performing a dot product. The calculation process is as follows: ； in, It is a particle The kth component of is the eigenvector The kth component of , m is the dimension of the particle and also the number of variables in principal component analysis; S4.

8. Calculate the fitness function components and calculate the fitness value of the particle for each principal component direction. The calculation process is as follows: ； in, and are the mean and standard deviation of the projection scores of the original data in the direction of the jth principal component, and wj is the weight determined according to the eigenvalue; S4.

9. The final fitness function is established based on the fitness function components as follows: ； in , , Corresponding to the principal component directions ; S5. Calculate each particle according to the fitness function The fitness value of the particle is evaluated using the non-dominated sorting method, the individual optimal position and external archive are updated, and the congestion degree is calculated; S6. Iteratively optimize the particles, update the speed and position of the particles, calculate the fitness value of each updated particle, and update the individual best position and external archive; S7. After each round of iteration, determine whether the maximum number of iterations T is reached. If so, the termination condition is met and the algorithm stops running. Otherwise, return to S6 and recalculate until the maximum number of iterations is met. S8. After the algorithm stops running, the non-dominated solution in the external archive is output as the optimal riveting quality parameter combination.

2. The method for optimizing riveting quality based on a multi-objective particle swarm optimization algorithm and PCA according to claim 1, characterized in that: The S5 further includes the following sub-steps: S5.

1. Calculate the fitness value of the particle according to the fitness function F(xi) and obtain three fitness values: 、 、 ; S5.

2. Create an external archive to store each frontier surface. For each particle xi, create another empty list to store the particles that dominate it and the particles that are dominated by it. S5.

3. For each pair of particles as well as For comparison, according to the formula: ； In the above formula, if at least one inequality holds, then Dominate , if not, they are non-dominated; S5.

4. Place all particles that are not dominated by other particles into a first frontier, check the dominating particle of each particle in the frontier, and place each dominated particle into a new frontier; S5.

5. Repeat the above process, placing the particles in the temporary list into the next frontier, and updating the temporary list with the particles dominated by these particles, until no more particles are placed into the frontier; S5.

6. For each particle in each frontier, initialize its crowding to 0. For each fitness function F(xi), find the maximum and minimum values of all particles in the frontier. S5.

7. For all particles except the first and last particles in each frontier, calculate the distance difference between the particle and its adjacent particles on each fitness function, and add up the distance differences to obtain the congestion degree of the particle.

3. The method for optimizing riveting quality based on a multi-objective particle swarm optimization algorithm and PCA according to claim 1, characterized in that: The weight wj in S4.8 is calculated by the following steps: S4.8.

1. Calculate the sum of the principal component analysis eigenvalues using the following formula: ； S4.8.

2. Normalize the eigenvalues to obtain the weights wj, calculated using the following formula: ； in, Eigenvalue corresponding to a single particle.

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