Single-point incremental forming parameter optimization method based on improved grey wolf algorithm
Patent Information
- Application Number
- CN202610744866.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-05-27
- Publication Date
- 2026-09-01
AI Technical Summary
[0028]（1）提高优化效率：本发明采用有限元仿真构建数据集，并以神经网络作为代理模型替代传统反复仿真计算，避免了优化过程中大量有限元重复计算，显著提高了参数优化效率。
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Figure CN122672452A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of sheet metal forming process optimization and intelligent computing technology, and in particular to a single-point progressive forming parameter optimization method based on an improved gray wolf algorithm. Background Technology
[0002] Single-Point Incremental Forming (SPIF), a green and highly flexible sheet metal forming method, has been widely used in the fields of complex curved surface parts and small-batch customized manufacturing. This technology uses a CNC system to control a forming tool to apply load point-by-point along a preset trajectory, causing localized plastic deformation of the sheet metal and accumulating layer by layer to form the final shape. It has the advantage of requiring no special molds or only simple support molds, effectively reducing manufacturing costs and shortening product development cycles.
[0003] However, existing SPIF technology still faces several challenges in practical engineering applications, limiting its further promotion and application. These challenges mainly manifest in the following aspects:
[0004] (1) Insufficient stability of forming quality: During the forming process, the parts are prone to problems such as large geometric deviation and obvious springback, resulting in a large error between the actual forming contour and the target shape.
[0005] (2) Severe material thinning: Local areas are prone to significant thinning under repeated cumulative deformation, and may even experience necking or cracking, affecting the structural integrity and safety of the parts.
[0006] (3) Multiple performance indicators are mutually constrained: There is a clear contradiction between geometric accuracy and thickness reduction. Optimizing one performance indicator often comes at the cost of sacrificing another, making it difficult to achieve synergistic optimization.
[0007] (4) There are limitations to the process improvement methods: although multi-pass forming can reduce springback, it significantly increases processing time; hot-assisted forming has high equipment requirements and limited applicability; although local support or mold assistance can improve quality, it increases manufacturing costs and system complexity.
[0008] (5) Inefficient parameter optimization methods: Existing research mostly adopts single-objective optimization methods, which makes it difficult to take multiple performance indicators into account at the same time; traditional multi-objective optimization algorithms (such as genetic algorithms) have problems such as slow convergence speed and easy to get trapped in local optima when dealing with complex coupled problems.
[0009] (6) Insufficient adaptability of multi-objective optimization algorithms: Although the multi-objective gray wolf optimization algorithm (MOGWO) has certain advantages, it still has problems such as insufficient population diversity, uneven distribution of Pareto front and limited global search capability in high-dimensional, strongly coupled and strictly constrained SPIF parameter optimization problems.
[0010] (7) The accuracy of objective function modeling needs to be improved: Traditional mathematical models are difficult to accurately describe the complex nonlinear relationships in the SPIF process. Although neural network models have been applied, there is still room for improvement in the generalization ability and prediction stability in multi-objective collaborative optimization.
[0011] In summary, existing SPIF process parameter optimization methods still have significant shortcomings in terms of multi-objective collaborative optimization capability, algorithm convergence performance, and optimization result stability, making it difficult to simultaneously achieve a comprehensive improvement in forming accuracy and forming safety. Therefore, it is necessary to propose an efficient, stable parameter optimization method suitable for multi-objective optimization based on existing technologies. Summary of the Invention
[0012] This invention addresses the problems of existing single-point incremental forming process parameter optimization methods, such as difficulty in coordinating multiple objectives, slow algorithm convergence, susceptibility to local optima, and uneven distribution of Pareto fronts. It proposes a single-point incremental forming parameter optimization method based on an improved Grey Wolf algorithm.
[0013] To achieve the above objectives, the present invention provides the following technical solution: a single-point progressive forming parameter optimization method based on an improved gray wolf algorithm, comprising the following steps:
[0014] S1. Establish a finite element model for single-point incremental forming, obtain forming results under different combinations of process parameters through parametric simulation, and construct a dataset based on the forming results;
[0015] S2. Based on the dataset, establish a proxy model with process parameters as input and forming performance indicators as output;
[0016] S3. Using the aforementioned proxy model as the objective function, construct a multi-objective optimization model with the goal of minimizing multiple forming performance indicators;
[0017] S4. The multi-objective optimization model is solved using an improved multi-objective gray wolf optimization algorithm to obtain the Pareto optimal solution set; wherein, the improvement includes: initializing the gray wolf population with a chaotic mapping strategy, controlling the algorithm search behavior with a nonlinear convergence factor, and introducing a population association learning mechanism to update the position of individual gray wolves;
[0018] S5. Select the optimal combination of process parameters from the Pareto optimal solution set based on the multi-attribute decision method.
[0019] Optionally, the proxy model in S2 is a multilayer perceptron neural network model, whose inputs are tool radius, initial sheet thickness, tool path strategy, step distance and forming angle, and outputs are maximum thinning rate and maximum geometric deviation.
[0020] Optionally, the chaotic mapping strategy in S4 is specifically Spm chaotic mapping, which generates an initial gray wolf population through a chaotic sequence, so that the initial solution is evenly distributed in the search space.
[0021] Optionally, the nonlinear convergence factor in S4 is updated using a cosine function, so that the convergence factor decreases slowly in the early stage of iteration to maintain global search capability, and decreases rapidly in the later stage of iteration to enhance local exploitation capability.
[0022] Optionally, the group association learning mechanism is as follows: when updating the position of individual gray wolves, it is not only guided by the current best individual, but also randomly selects other non-dominant individuals from the current Pareto front for information interaction; wherein, the learning weight is dynamically adjusted with the number of iterations, strengthening the influence of associated individuals in the early stage of iteration, and gradually shifting to being dominated by the best individual in the later stage of iteration.
[0023] Optionally, the multi-attribute decision-making method in S5 is the entropy-weighted TOPSIS method, which determines the objective weight by calculating the information entropy of each optimization objective, and sorts the solutions based on their relative proximity to the positive and negative ideal solutions, so as to select the optimal combination of process parameters.
[0024] Optionally, the plurality of forming performance indicators include at least the maximum thinning rate and the maximum geometric deviation, and the multi-objective optimization model takes minimizing the maximum thinning rate and the maximum geometric deviation as the common optimization objective.
[0025] Optionally, in S4, the population size, maximum number of iterations, and Pareto file capacity of the improved multi-objective gray wolf optimization algorithm are all preset to the same value, preferably an integer between 50 and 200.
[0026] Optionally, in the finite element model of S1, the forming tool and fixture are modeled as rigid bodies, and the sheet metal is modeled as an elastoplastic body; the process parameters include tool radius, initial sheet metal thickness, tool path strategy, step distance, and forming angle; the forming results include sheet metal thickness distribution and forming contour data.
[0027] Compared with the prior art, the present invention has at least one of the following beneficial technical effects:
[0028] (1) Improve optimization efficiency: The present invention uses finite element simulation to construct a dataset and uses neural network as a proxy model to replace the traditional repeated simulation calculation, which avoids a large number of repeated finite element calculations during the optimization process and significantly improves the parameter optimization efficiency.
[0029] (2) Achieving multi-objective collaborative optimization: This invention uses the maximum thinning rate and the maximum geometric deviation as dual objectives for optimization. By introducing the Pareto optimal solution set, it can simultaneously take into account forming accuracy and structural safety, and avoid performance imbalance caused by single index optimization.
[0030] (3) Enhance global search capability: By introducing a chaotic mapping initialization strategy into the gray wolf optimization algorithm, the initial population is more evenly distributed in the solution space, expanding the search range and improving the algorithm's ability to escape local optima.
[0031] (4) Improve convergence speed and optimization accuracy: By adopting a nonlinear convergence factor, the algorithm maintains a strong global search capability in the early stage of iteration and enhances the local development capability in the later stage, thereby accelerating the convergence speed while ensuring search accuracy.
[0032] (5) Avoid the algorithm getting trapped in local optima: Introduce a group association learning mechanism so that gray wolf individuals are not only guided by the alpha wolf during the search process, but can also interact with other individuals in the Pareto solution set, thereby enhancing population diversity and effectively avoiding the algorithm getting trapped in local optima.
[0033] (6) Improve the stability and uniformity of the optimization results: By improving the multi-objective gray wolf optimization algorithm, the distribution of the obtained Pareto optimal solution set is more uniform, which is conducive to selecting appropriate process parameters under different engineering requirements. Attached Figure Description
[0034] Figure 1(a) and Figure 1(b) are the distribution diagrams of the chaotic mapping initialization population used in this invention;
[0035] Figure 2 This is a comparison chart of the convergence factor changes before and after the improvement of this invention;
[0036] Figure 3 The flowchart below shows the improved multi-objective gray wolf optimization algorithm of this invention.
[0037] Figures 4(a) and 4(b) are comparison diagrams of the convergence process of the IMOGWO of the present invention and the original MOGWO;
[0038] Figure 5 This is a distribution map of the Pareto front obtained by the present invention. Detailed Implementation
[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0040] This embodiment provides a single-point incremental forming parameter optimization method based on the improved multi-objective gray wolf optimization algorithm (IMOGWO), including the following steps:
[0041] Step 1: Chaotic Map Initialization
[0042] Figures 1(a) and 1(b) illustrate the initialization results of the chaotic mapping used in this embodiment. This embodiment employs the Spm chaotic mapping to initialize the gray wolf population, mapping the optimization variables to the upper and lower bounds of given parameters. Initial solutions are generated through chaotic sequences, making the population distribution more uniform in the search space. Compared to traditional random initialization, this method introduces nonlinear chaotic perturbations to improve the randomness and ergodicity of the solutions, thereby enhancing the algorithm's ability to cover the global search space and avoiding premature convergence caused by the concentrated distribution of the initial population.
[0043] During SPIF parameter optimization, continuous parameter variables are initialized using the Spm chaotic mapping:
[0044] ;
[0045] in, This represents the initialization parameters for the i-th gray wolf in IMOGWO. and These represent the lower and upper bounds of the parameters to be optimized, respectively. Spm chaotic mapping initialization factor. It can be represented as:
[0046] ;
[0047] in, It is a random number uniformly distributed within the interval (0,1), used as the initial seed for chaotic iteration. This is the modulo operator, used to ensure that the generated value remains within a predetermined range. and The coefficients used to control the dynamic characteristics of the mapping range from 0 to 1. In this paper, we take... =0.4, =0.3, to obtain a relatively uniform and random initial population distribution.
[0048] It should be understood that, in addition to the Spm chaotic mapping, other chaotic mappings such as the Logistic mapping, Tent mapping, or Circle mapping can also be used for population initialization.
[0049] Step 2: Improve the convergence factor update
[0050] like Figure 2The figure shows a comparison of the convergence factor changes before and after the improvement. This embodiment replaces the traditional linearly decreasing convergence factor with a nonlinear update method based on the cosine function, causing the convergence factor to decrease slowly in the early stages of iteration and rapidly decrease in the later stages. This improvement allows the algorithm to maintain strong global search capabilities in the initial stage and enhance local search capabilities in the later stages, thereby improving convergence speed while maintaining search accuracy. The specific steps are as follows:
[0051] In the MOGWO algorithm, the process of finding the optimal solution can be compared to the search and capture of prey by a pack of gray wolves. During the algorithm's iteration, the behavior of individual wolves is guided by the alpha wolf, and its update method is as follows: ;
[0052] in, Let represent the potential parameter solution for the i-th gray wolf after the (k+1)-th iteration; , and They represent in , and The updated solution obtained under the influence of the three alpha wolves is calculated as follows:
[0053] ;
[0054] in, This represents the potential optimal parameter solution indicated by the alpha wolf at the k-th iteration; and A random number uniformly distributed within the interval (0,1); Let be the convergence factor in the k-th iteration. During the search for the optimal solution, this convergence factor decreases linearly with the number of iterations, influencing... To regulate the behavior of the gray wolves. When At that time, the gray wolf performs a global search; when At that time, the gray wolves cooperated to surround and capture the prey and gradually converged to the optimal solution.
[0055] To improve the global search capability of the IMOGWO algorithm, the traditional linear decreasing strategy is replaced with an iterative approach based on the cosine function to construct the convergence factor. As shown in the following formula: ;
[0056] in, Indicates the maximum number of iterations. Before and after improvement. Comparisons that change with the number of iterations Figure 2 As shown in the image. It can be seen that the improved... The decrease is slow in the initial stage, but rapidly decreases with subsequent iterations. Therefore, based on the improved convergence factor... IMOGWO maintains a strong global search capability in the early stages, thereby effectively improving the algorithm's global optimization performance.
[0057] Step 3: Update Mechanism Based on Association Learning
[0058] like Figure 3 The diagram shows a flowchart of the improved multi-objective gray wolf optimization algorithm. In the traditional MOGWO algorithm, each iteration update is only affected by the alpha wolf; if the alpha wolf gets stuck in a local optimum, the algorithm as a whole may fail. To enhance the algorithm's global search capability, this embodiment introduces an association learning mechanism in IMOGWO. Gray wolves (excluding alpha wolves) on the Pareto front are updated according to the following formula:
[0059] ;
[0060] in, This represents a bounded random perturbation, the magnitude of which is adaptively constrained based on the distance of the current solution to the upper and lower boundaries; and is a random number uniformly distributed within the interval (0,1); This represents the parameters of a gray wolf (excluding the alpha wolf) randomly selected from the current Pareto front. This update process, based on association learning, is influenced not only by the alpha wolf but also by other gray wolves in the Pareto front, reflecting the association learning behavior among gray wolves.
[0061] Convergence factor and Calculateable: ;
[0062] As the number of iterations k increases, Gradually decrease, while The number of alpha wolves gradually increases. Therefore, in the early stages of iteration, the update process of the gray wolves is more influenced by random individuals in the Pareto front, thereby enhancing the interaction between the populations and preventing the algorithm from getting trapped in local optima. In the later stages of iteration, the update process gradually shifts to be dominated by alpha wolves, thereby ensuring the convergence accuracy of the algorithm.
[0063] Step 4: Construct the SPIF multi-objective optimization model
[0064] Minimize the maximum thinning rate during the forming process. and maximum geometric deviation Constraints include tool radius. Toolpath strategy Initial plate thickness , forming angle and stride All of the above parameters must be limited within a given range. Based on the established MLP model for predicting SPIF thinning rate and geometric deviation, the mathematical optimization model of IMOGWO can be expressed as:
[0065] ;
[0066] in, Let represent the set of real numbers. In IMOGWO, the gray wolf population size, maximum number of iterations, and Pareto archive capacity are all set to 100. A significant advantage of this method is its low dependence on hyperparameters; only the population size and number of iterations need to be set, thus effectively avoiding the performance fluctuation problem common in multi-parameter intelligent optimization algorithms.
[0067] As shown in Figures 4(a) and 4(b), a comparison of the convergence processes of IMOGWO and MOGWO reveals that IMOGWO converges on the 45th iteration, while MOGWO requires approximately 80 iterations, indicating that IMOGWO has a faster convergence speed. After convergence, the maximum thinning rate corresponding to IMOGWO is approximately 19.3%, and the maximum geometric deviation is approximately 2.065 mm, demonstrating that this method effectively suppresses sheet thinning while maintaining high forming performance.
[0068] Step 5: Pareto Front and Optimal Solution Selection
[0069] like Figure 5 As shown, the Pareto front obtained by the IMOGWO algorithm contains 47 sets of optimal parameter solutions, and their objective function values are shown in Table 1:
[0070] Table 1: Partial Objective Values of the Pareto Optimal Solution
[0071]
[0072] Because the two optimization objectives of maximum thinning rate and maximum geometric deviation are clearly conflicting and constrained, the solutions on the Pareto optimal front are non-dominated solutions, and their merits cannot be directly compared. Therefore, this embodiment introduces the entropy-weighted TOPSIS multi-attribute decision-making method to rank and optimize the 47 sets of Pareto optimal solutions.
[0073] The Entropy-Weighted TopSIS method determines the weights of each indicator by calculating its information entropy, thereby improving the objectivity and accuracy of the evaluation results. The specific calculation process is as follows:
[0074] First, construct the standardized decision matrix Q:
[0075] ;
[0076] in, This represents the number of Pareto optimal solutions. This indicates the number of cost-based evaluation indicators (optimization objectives). This represents the value of the i-th solution on the j-th index. In this embodiment, m=2.
[0077] Information entropy of the j-th indicator It can be represented as: ;
[0078] in, Let represent the normalized value of the j-th indicator under the i-th scheme, which is calculated as the proportion of this indicator value to the sum of all indicator values under that scheme:
[0079] ;
[0080] Entropy weight of the j-th index It can be calculated as:
[0081] ;
[0082] Combining the above formulas, the weighted normalized decision matrix can be obtained. :
[0083] ;
[0084] Since both the thinning rate and geometric deviation need to be minimized in SPIF processing, a perfect ideal solution is required. With negative ideal solution They are defined as follows:
[0085] ;
[0086] in , ;
[0087] Further calculate the Euclidean distance between the i-th solution and both the positive and negative ideal solutions. and The final relative similarity is :
[0088] ;
[0089] in Sort the values from largest to smallest and select The largest possible solution is considered the optimal combination of process parameters.
[0090] Step Six: Comparison and Verification
[0091] To verify the effectiveness of the proposed method, IMOGWO was compared with MOGWO, NSGA-II, and MOGWO (DEML-MOGWO) based on dynamic ensemble machine learning. All algorithms used the same population size (100) and maximum number of iterations (100). The performance of each multi-objective optimization algorithm was quantitatively evaluated using the hypervolume (HV) and spacing metrics.
[0092] Table 2: Performance Comparison of Multi-Objective Optimization Algorithms
[0093]
[0094] Table 2 above presents the mean and standard deviation of HV and Spacing based on the Pareto front obtained from 30 independent runs. The results show that the mean HV for IMOGWO is (7.50 ± 0.01) × 10⁻⁶. −3 Higher than NSGA-II (7.20×10 −3 DEML-MOGWO (7.23×10) −3 ) and the original MOGWO (7.02×10 −3 Meanwhile, the mean spacing value of IMOGWO was (0.19±0.01)×10. −3 It is significantly lower than MOGWO (0.50×10). −3 ) and NSGA-II (0.55×10 −3 This indicates that its Pareto solution distribution is more uniform. Furthermore, the spacing of IMOGWO is similar to that of DEML-MOGWO (0.18 × 10⁻⁶). −3 The results are basically equivalent, indicating that both algorithms have similar capabilities in maintaining the uniformity of the solution set. IMOGWO outperforms the comparison algorithms in both convergence performance and Pareto front distribution uniformity, demonstrating higher optimization quality.
[0095] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for optimizing single-point incremental forming parameters based on an improved gray wolf algorithm, characterized in that, Includes the following steps: S1. Establish a finite element model for single-point incremental forming, obtain forming results under different combinations of process parameters through parametric simulation, and construct a dataset based on the forming results; S2. Based on the dataset, establish a proxy model with process parameters as input and forming performance indicators as output; S3. Using the aforementioned proxy model as the objective function, construct a multi-objective optimization model with the goal of minimizing multiple forming performance indicators; S4. The multi-objective optimization model is solved using an improved multi-objective gray wolf optimization algorithm to obtain the Pareto optimal solution set; wherein, the improvement includes: initializing the gray wolf population with a chaotic mapping strategy, controlling the algorithm search behavior with a nonlinear convergence factor, and introducing a population association learning mechanism to update the position of individual gray wolves; S5. Select the optimal combination of process parameters from the Pareto optimal solution set based on the multi-attribute decision method.
2. The single-point incremental forming parameter optimization method based on the improved gray wolf algorithm according to claim 1, characterized in that, The proxy model in S2 is a multilayer perceptron neural network model. Its inputs are tool radius, initial sheet thickness, tool path strategy, step distance and forming angle, and its outputs are maximum thinning rate and maximum geometric deviation.
3. The single-point incremental forming parameter optimization method based on the improved gray wolf algorithm according to claim 1, characterized in that, The chaotic mapping strategy in S4 is specifically the Spm chaotic mapping, which generates an initial gray wolf population through a chaotic sequence, so that the initial solution is evenly distributed in the search space.
4. The single-point incremental forming parameter optimization method based on the improved gray wolf algorithm according to claim 1, characterized in that, The nonlinear convergence factor in S4 is updated using a cosine function, which causes the convergence factor to decrease slowly in the early stage of iteration to maintain global search capability, and to decrease rapidly in the later stage of iteration to enhance local exploration capability.
5. The single-point incremental forming parameter optimization method based on the improved gray wolf algorithm according to claim 1, characterized in that, The group association learning mechanism is as follows: when updating the position of gray wolf individuals, it is not only guided by the current best individual, but also randomly selects other non-dominant individuals from the current Pareto front for information interaction; wherein, the learning weight is dynamically adjusted with the number of iterations, strengthening the influence of associated individuals in the early stage of iteration, and gradually shifting to being dominated by the best individual in the later stage of iteration.
6. The single-point incremental forming parameter optimization method based on the improved gray wolf algorithm according to claim 1, characterized in that, The multi-attribute decision-making method in S5 is the entropy-weighted TOPSIS method, which determines the objective weight by calculating the information entropy of each optimization objective and sorts them based on the relative closeness of each solution to the positive ideal solution and the negative ideal solution, so as to select the optimal combination of process parameters.
7. The single-point incremental forming parameter optimization method based on the improved gray wolf algorithm according to claim 1, characterized in that, The plurality of forming performance indicators include at least the maximum thinning rate and the maximum geometric deviation, and the multi-objective optimization model takes minimizing the maximum thinning rate and the maximum geometric deviation as the common optimization objective.
8. The single-point incremental forming parameter optimization method based on the improved gray wolf algorithm according to claim 1, characterized in that, In S4, the population size, maximum number of iterations, and Pareto file capacity of the improved multi-objective gray wolf optimization algorithm are all preset to the same value, preferably an integer between 50 and 200.
9. A single-point incremental forming parameter optimization method based on an improved gray wolf algorithm according to claim 1, characterized in that, In the finite element model of S1, the forming tool and fixture are modeled as rigid bodies, and the sheet metal is modeled as an elastoplastic body; the process parameters include tool radius, initial sheet metal thickness, tool path strategy, step distance, and forming angle; the forming results include sheet metal thickness distribution and forming contour data.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the single-point progressive forming parameter optimization method based on the improved multi-objective gray wolf optimization algorithm as described in any one of claims 1-9.