Pressing rivet quality optimization method based on multi-objective particle swarm algorithm and PCA (Principal Component Analysis)

Abstract

The invention relates to a pressing rivet quality optimization method based on a multi-objective particle swarm algorithm and PCA. According to the pressing rivet quality optimization method based on the multi-objective particle swarm algorithm and the PCA, the influence of different parameter combinations on a response target is effectively evaluated through nonlinear transformation of defined parameters in the multi-objective particle swarm algorithm and a Taguchi experiment; principal component analysis is performed on a signal-to-noise ratio obtained by a Taguchi test through PCA, and data obtained by the principal component analysis is used as a fitness function of a multi-target particle swarm algorithm to calculate a fitness value of particles, so that high-dimensional data can be simplified, main information components can be extracted, the problem complexity is reduced, the optimization process is more efficient, and the optimization efficiency is improved. The principal component analysis can extract the nonlinear component influencing the signal-to-noise ratio, thereby helping the multi-target particle swarm optimization to better process the nonlinear optimization problem.

Description

Technical Field

[0001] The 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] The riveting process is a process method that fastens two or more parts together through rivets. In automobile manufacturing, the riveting process can provide high-strength connections, ensure the sealing and corrosion resistance of the connection, thus meeting the strict requirements of automobile bodies for strength and durability; Factors that affect the quality of riveting mainly include the selection and quality of riveting materials, the stability and precision of riveting tools and equipment, the accurate control of riveting process parameters (such as pressure, time and temperature), the rationality of riveting design, the skill level and operating techniques of operators, and the strictness of quality inspection and monitoring. These factors together determine the strength, reliability and durability of the riveted points; In the process of automobile production, in order to ensure the strength of automobile parts after riveting, it is usually necessary to determine the best riveting quality parameter combination. In the prior art, the optimization algorithm is usually used to systematically traverse or intelligently search the parameter space, evaluate the objective function value under different parameter combinations, and find the optimal objective function. However, when optimizing the riveting quality, the existing optimization algorithm usually involves multiple parameters, and there may be complex nonlinear relationships between these parameters. If these nonlinear relationships are ignored, the algorithm may fall into a local optimal solution instead of a global optimal solution.

[0003] Therefore, the present invention proposes a riveting quality optimization method based on a multi-objective particle swarm algorithm and PCA. The Taguchi method and grey correlation analysis combined with the multi-objective particle swarm algorithm can effectively dynamically adjust the fitness function and the search strategy according to the current state of the group, thereby effectively avoiding falling into the local optimal solution. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a method for optimizing the quality of press riveting based on a multi-objective particle swarm algorithm and PCA, which has the advantages of being able to achieve precise optimization of press riveting, and solves the problems in the prior art that the nonlinear relationship between parameters cannot be handled when optimizing press riveting and the algorithm has a large amount of calculation.

[0005] To achieve the above object, the present invention provides the following technical solution: a method for optimizing the quality of riveting based on a multi-objective particle swarm algorithm and PCA, comprising the following steps, characterized in that: S1. Determine the control parameter set of the riveting machine , Riveting design parameter set and the response set , build a machine control parameter set , Riveting design parameter set To define the parameters of the multi-objective particle swarm algorithm model and initialize the model parameters; S2, control parameter set for pressure riveting machine , Riveting design parameter set and the response set Perform nonlinear processing to obtain the performance indicators after riveting ; S3, performance index 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; S4, performing principal component analysis on multiple groups of signal-to-noise ratio sequences, and constructing a fitness function of a multi-objective particle algorithm according to the results of the principal component analysis; 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 crowding 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.

[0006] Furthermore, the control parameter set of the pair of press riveting machines in S3 is , 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 Respectively represent The first press riveting design parameters and the The value of the 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.

[0007] Furthermore, in S3, the degree to which the quality characteristic approaches the target value and the fluctuation caused by noise interference are considered, and the response set The signal-to-noise ratios of the three response targets 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 responding to the target.

[0008] Further, the principal component analysis of the signal-to-noise ratio sequence in S4 includes the following sub-steps: S4.1, the signal-to-noise ratio data of the response target j are organized 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 and obtain the eigenvalue , =( , , ), and the eigenvector , , the eigenvectors constitute the principal component directions; S4.5. Select the principal component and standardize the matrix The data is projected into the subspace formed by the selected principal components; Projection Matrix It is composed of selected feature vectors; 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, based on the data obtained from 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, respectively, 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 .

[0009] Furthermore, the step S5 also includes the following sub-steps: S5.1. Calculate the fitness value of the particle according to the fitness function F(xi) to obtain three fitness values: , , ; 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; 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, then they are non-dominated; S5.4, placing all particles that are not dominated by other particles into a first frontier surface, checking the dominating particles of each particle in the frontier surface, and placing each dominated particle into a new frontier surface; S5.5, repeat the above process, put the particles in the temporary list into the next frontier surface, and update the temporary list with the particles dominated by these particles, until there are no more particles that can be put into the frontier surface; S5.6. For each particle in each frontier, initialize its crowding degree to 0, and 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, the distance difference between the particle and the adjacent particles is calculated on each fitness function, and the distance differences are added to obtain the crowding degree of the particle.

[0010] Further, the weight wj in S4.7 is calculated by the following steps: S4.7.1. Calculate the sum of the principal component analysis eigenvalues ​​using the following formula: S4.7.2. Normalize the eigenvalues ​​to obtain the weights wj, calculated by the following formula: in, Eigenvalues ​​corresponding to a single particle.

[0011] Compared with the prior art, the technical solution of this application has the following beneficial effects: 1. This riveting quality optimization method based on multi-objective particle swarm 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 experiment effectively evaluates the impact of different parameter combinations on the response target through orthogonal design, reduces the number of experiments, and improves the optimization efficiency.

[0012] 2. This is a riveting quality optimization method based on a multi-objective particle swarm algorithm and PCA. The traditional fitness function usually directly evaluates 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 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 jump out of the local optimum and find the global optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a schematic diagram of the algorithm flow of the present invention; DETAILED DESCRIPTION

[0014] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0015] See also Figure 1 In this embodiment, a method for optimizing the riveting quality based on a multi-objective particle swarm algorithm and PCA includes the following steps, which are characterized in that: S1. Determine the control parameter set of the riveting machine , Riveting design parameter set and the response set , build a machine control parameter set , 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 limit installation torque, etc.; Randomly generate in parameter space The particle position is denoted by , randomly assigning a velocity vector to each particle , initialize the best position of individual particles is the current position, recorded as , initialize the global best historical position Is empty.

[0016] S2, control parameter set for pressure riveting machine , Riveting design parameter set and the response set Perform nonlinear processing to obtain the performance indicators after riveting ; Use logarithmic function and power function 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 Respectively represent The first press riveting design parameters and the The value of the 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.

[0017] Performing nonlinear transformation on data before Taguchi test can significantly enhance the model's fit to the complex relationship between parameters and performance indicators, improve the sensitivity of 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.

[0018] S3, performance index 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; Considering the degree to which the quality characteristics are close to the target value and the fluctuations caused by noise, the response set The signal-to-noise ratios of the three response targets 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 responding to the target.

[0019] S4, performing principal component analysis on multiple groups of signal-to-noise ratio sequences, and constructing a fitness function of a multi-objective particle algorithm according to the results of the principal component analysis; Preferably, performing principal component analysis on the signal-to-noise ratio sequence in S4 comprises the following sub-steps: S4.1, the signal-to-noise ratio data of the response target j are organized 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 and obtain the eigenvalue , =( , , ), and the eigenvector , , the eigenvectors constitute the principal component directions; S4.5. Select the principal component and standardize the matrix The data is projected into the subspace formed by the selected principal components; Projection Matrix It is composed of selected feature vectors; 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, based on the data obtained from 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, respectively, and wj is the weight determined according to the eigenvalue; The weight wj in S5.7 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 by the following formula: in, Eigenvalues ​​corresponding to a single particle.

[0020] S4.9. The final fitness function is established based on the fitness function components as follows: in , , Corresponding to the principal component directions .

[0021] 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 crowding degree is calculated; for each particle The current fitness value and the best historical position of the individual If the current fitness value dominates the individual's best historical position, , then the updated individual best historical position is If not, keep ; S5 also includes the following sub-steps: S5.1. Calculate the fitness value of the particle according to the fitness function F(xi) to obtain three fitness values: , , ; 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; 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, then they are non-dominated; S5.4, placing all particles that are not dominated by other particles into a first frontier surface, checking the dominating particles of each particle in the frontier surface, and placing each dominated particle into a new frontier surface; S5.5, repeat the above process, put the particles in the temporary list into the next frontier surface, and update the temporary list with the particles dominated by these particles, until there are no more particles that can be put into the frontier surface; S5.6. For each particle in each frontier, initialize its crowding degree to 0, and 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, the distance difference between the particle and the adjacent particles is calculated on each fitness function, and the distance differences are added to obtain the crowding degree of the particle.

[0022] S6, iteratively optimize the particles, update the speed and position of the particles, calculate the fitness value of each particle after the update, and update the individual best position and external archive; select a 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 according to the comprehensive evaluation index , update particle speed and position, maintain 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 crowding degree; 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.

[0023] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0024] Although 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 the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for optimizing riveting quality based on multi-objective particle swarm optimization and PCA, comprising the following steps, characterized in that: S1. Determine the control parameter set of the riveting machine , Riveting design parameter set and the response set , build a machine control parameter set , Riveting design parameter set To define the parameters of the multi-objective particle swarm algorithm model and initialize the model parameters; S2, control parameter set for pressure riveting machine , Riveting design parameter set and the response set Perform nonlinear processing to obtain the performance indicators after riveting ; S3, performance index 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; S4, performing principal component analysis on multiple groups of signal-to-noise ratio sequences, and constructing a fitness function of a multi-objective particle algorithm according to the results of the principal component analysis; 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 crowding 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 multi-objective particle swarm optimization and PCA as claimed in claim 1, characterized in that: The control parameter set of the pair of press riveting machines in S3 , 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 Respectively represent The first press riveting design parameters and the The value of the 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.

3. The method for optimizing riveting quality based on multi-objective particle swarm optimization and PCA as claimed in claim 1, characterized in that: In S3, the degree to which the quality characteristic approaches the target value and the fluctuation caused by noise are considered, and the response set The signal-to-noise ratios of the three response targets 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 responding to the target.

4. The method for optimizing riveting quality based on multi-objective particle swarm optimization and PCA as claimed in claim 3, characterized in that: The step of performing principal component analysis on the signal-to-noise ratio sequence in S4 includes the following sub-steps: S4.1, the signal-to-noise ratio data of the response target j are organized 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 and obtain the eigenvalue , =( , , ), and the eigenvector , , the eigenvectors constitute the principal component directions; S4.

5. Select the principal component and standardize the matrix The data is projected into the subspace formed by the selected principal components; Projection Matrix It is composed of selected feature vectors; 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, based on the data obtained from 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, respectively, 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 .

5. The method for optimizing riveting quality based on multi-objective particle swarm optimization and PCA as claimed in claim 4, characterized in that: The S5 also includes the following sub-steps: S5.

1. Calculate the fitness value of the particle according to the fitness function F(xi) to 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, then they are non-dominated; S5.4, placing all particles that are not dominated by other particles into a first frontier surface, checking the dominating particles of each particle in the frontier surface, and placing each dominated particle into a new frontier surface; S5.5, repeat the above process, put the particles in the temporary list into the next frontier surface, and update the temporary list with the particles dominated by these particles, until there are no more particles that can be put into the frontier surface; S5.

6. For each particle in each frontier, initialize its crowding degree to 0, and 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, the distance difference between the particle and the adjacent particles is calculated on each fitness function, and the distance differences are added to obtain the crowding degree of the particle.

6. The method for optimizing riveting quality based on multi-objective particle swarm optimization and PCA as claimed in claim 4, characterized in that: The weight wj in S4.7 is calculated by the following steps: S4.7.

1. Calculate the sum of the principal component analysis eigenvalues ​​using the following formula: S4.7.

2. Normalize the eigenvalues ​​to obtain the weights wj, calculated by the following formula: in, Eigenvalues ​​corresponding to a single particle.

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