A method for planning a stretch forming path for a sink-type skin

Abstract

The application provides a sunken skin stretch forming path planning method, and belongs to the technical field of stretch forming path planning, and the method comprises the following steps: S1, acquiring the design parameters and forming constraint conditions of the sunken skin; S2, establishing a finite element model of the sunken skin; S3, initial stretch path global planning based on an echo state network-cell mapping hybrid algorithm; S4, finite element simulation verification of the initial stretch path; and S5, stretch path iterative optimization based on a fractional order Kalman filter-dove search hybrid algorithm. The application solves the problems of low stretch forming path planning precision, many forming defects, poor process stability, weak technical reproducibility and the like of the existing sunken skin stretch forming path planning.

Description

Technical Field

[0001] This invention relates to the field of stretch forming path planning technology, and in particular to a method for stretch forming path planning of sunken skin. Background Technology

[0002] As a key load-bearing or appearance component, the quality of the stretch forming of sunken skin directly affects the performance and reliability of the overall equipment.

[0003] Current mainstream path planning technologies for sunken skin stretch forming in the industry suffer from several bottlenecks: First, traditional path planning relies heavily on engineer experience or single algorithms, making it difficult to achieve globally optimal path search and easily leading to dimensional deviations or surface defects in the formed skin. Second, existing technologies often employ algorithms independently, lacking bidirectional interaction and fusion processing, failing to fully leverage the advantages of different algorithms. For example, predictive algorithms and optimization algorithms are disconnected, limiting path optimization accuracy. Third, simulation verification is disconnected from actual forming; noise interference during simulation is not effectively addressed, directly affecting the practicality of optimization results. Fourth, monitoring methods for the actual forming process are limited, making it difficult to capture forming anomalies in real time, easily leading to batch quality problems. Furthermore, the application scenarios of commonly used algorithms in existing technologies are relatively fixed, lacking innovative integration of algorithms, resulting in significant difficulties in technological breakthroughs and challenges in ensuring overall forming stability and consistency. Summary of the Invention

[0004] This invention provides a path planning method for the stretching and forming of sunken skin, addressing the problems of low accuracy, numerous forming defects, poor process stability, and weak technical reproducibility in existing methods. Through innovative bidirectional fusion of algorithms and a comprehensive process design, it overcomes the limitations of traditional methods where algorithms are independent and simulation is disconnected from reality, achieving globally optimal planning and precise optimization of the stretching path. Simultaneously, through full-process monitoring and quality control, it reduces the risk of defects during the forming process, improving the consistency and stability of skin forming quality. Ultimately, it provides a fully disclosed and highly reproducible solution for the stretching and forming of sunken skin, offering reliable technical support for mass production.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for planning the stretching and forming path of a sunken skin type includes:

[0007] S1. Obtain the design parameters and molding constraints of the sunken skin, and generate a list of design parameters and a list of molding constraints;

[0008] S2. Based on the design parameter list and forming constraint list, establish a sunken skin-like finite element model containing geometric information, mesh information, material properties and boundary conditions;

[0009] S3. Based on the forming constraint list and the finite element model of the sunken skin, a hybrid algorithm with bidirectional interaction between the echo state network and the cell mapping algorithm is used to perform global planning of the initial stretching path and generate candidate initial stretching paths. The echo state network is used to predict the forming defect risk, sunken size error and maximum principal stress of the candidate paths. The cell mapping algorithm performs global optimization under the predictive constraints of the echo state network, and the optimization result is fed back to the echo state network to update the model parameters.

[0010] S4. Input the candidate initial stretching path into the sunken skin finite element model for simulation verification and generate a simulation result report;

[0011] S5. Based on the simulation result report, candidate initial stretching paths, and the list of forming constraints, a hybrid algorithm combining fractional Kalman filtering and the Cuckoo Search algorithm is used to iteratively optimize the stretching path and generate the final stretching path. The fractional Kalman filtering is used to extract the pure error features in the simulation results, and the Cuckoo Search algorithm optimizes the parameters with the error features as the target. The optimization results are fed back to the fractional Kalman filtering to update the filtering parameters.

[0012] The method for planning the stretching and forming path of sunken skin in this specification also includes:

[0013] S6. Based on the final stretching path and the list of forming constraints, generate control instructions for the stretching equipment;

[0014] S7. Transmit the control command of the stretching equipment to the stretching equipment, and perform actual stretching and forming of the sunken skin according to the final stretching path. During the forming process, process monitoring data is obtained through multi-dimensional monitoring equipment.

[0015] S8. Based on the formed sunken skin workpiece, process monitoring data, design parameter list, and forming constraint list, perform forming quality inspection. If all inspection indicators meet the forming constraints, output the qualified skin finished product and the final stretching path as the standard forming path; otherwise, return to S5 for re-optimization.

[0016] In this specification, the model training process of the echo state network in S3 includes: randomly generating multiple sets of initial path samples based on the sunken skin finite element model, each set of samples containing clamp displacement, tensile velocity, and segmented tensile sequence parameters; obtaining the forming defect state, sunken size error, and maximum principal stress corresponding to each set of samples through explicit dynamic simulation, and constructing training datasets and validation datasets; solving the output weight matrix of the echo state network using the ridge regression method, training the model using the training dataset, calculating the prediction error using the validation dataset, until the prediction error meets the preset accuracy requirements, and completing the model training.

[0017] In this specification, the state space construction and feasible cell selection process of the S3 cell mapping algorithm includes: constructing a state space with clamp displacement, stretching speed, and segmented stretching sequence as three dimensions, where the segmented stretching sequence is a full permutation of edge region, non-sunken body region, sunken periphery region, and sunken core region; discretizing the three-dimensional state space into uniform cells with a preset step size, each cell corresponding to a unique set of path parameter combinations; based on the molding defect risk probability and maximum principal stress prediction value output by the echo state network, combined with the maximum tensile force limit in the molding constraints, determining the feasibility of each cell, and selecting feasible cells with defect risk probability lower than a preset threshold and tensile force not exceeding the maximum tonnage.

[0018] In this specification, the bidirectional interaction process between the echo state network and the cell mapping algorithm in S3 includes: the echo state network outputs the forming defect risk probability, the predicted value of the sinking size error, and the predicted value of the maximum principal stress corresponding to each set of candidate path parameters to the cell mapping algorithm, which serves as the core basis for cell feasibility determination and the calculation parameters of the fitness function; the cell mapping algorithm selects several paths with optimal fitness through global optimization, substitutes these optimal paths back to the trained echo state network, calculates the prediction error corresponding to the path, and adjusts the output weight matrix of the echo state network based on the prediction error, thereby realizing the iterative update of the echo state network and forming a closed-loop interaction of "prediction-optimization-update".

[0019] In this specification, the error extraction process of fractional Kalman filtering in S5 includes: defining a state vector containing displacement adjustment, velocity adjustment, and order adjustment factor, wherein the order adjustment factor is used to fine-tune the priority of the segmented stretching order; establishing fractional state equations and observation equations based on fractional calculus theory, wherein the state equations describe the time evolution of the state vector, and the observation equations correlate the state vector with the simulation observation data; and filtering out grid discretization noise and numerical solution noise in the simulation results through an iterative process of state prediction, error covariance prediction, Kalman gain calculation, state update, and error covariance update, thereby extracting pure estimates of displacement adjustment, velocity adjustment, and order adjustment factor.

[0020] In this specification, the optimization process of the cuckoo search algorithm in S5 includes: using the pure error estimate extracted by fractional-order Kalman filtering as a benchmark, generating an initial population by adding a random perturbation of a preset magnitude, with each individual in the population corresponding to a set of path adjustment parameters, and the parameter values ​​conforming to the forming constraint conditions; constructing a fitness function with the goal of minimizing the error estimate, the fitness function comprehensively considering the weight ratio of displacement adjustment, velocity adjustment, and order adjustment factor; updating the population individuals through the Lévy flight strategy, eliminating inferior solutions with poor fitness using a preset discovery probability, and after iterating a preset number of times, selecting the individual with the best fitness as the optimal path adjustment parameter.

[0021] In this specification, the bidirectional interaction process between the fractional-order Kalman filter and the cuckoo search algorithm in S5 includes: the pure error estimate output by the fractional-order Kalman filter is directly used as the basis for calculating the fitness function of the cuckoo search algorithm, clarifying the target direction and magnitude of path adjustment; the optimal adjustment parameters selected by the cuckoo search algorithm are fed back to the fractional-order Kalman filter to correct the state estimation results of the fractional-order Kalman filter, and the process noise variance is updated based on the fitness value corresponding to the optimal adjustment parameters, reducing noise interference in subsequent filtering processes and improving error extraction accuracy.

[0022] In this manual, during the simulation verification process of S4, the simulation step size is set to a fixed value, and the simulation termination condition is that the clamp reaches the maximum stroke in the forming constraint condition or the skin forming deformation is less than the preset threshold. The specific analysis indicators included in the simulation result report are: sinking depth error, maximum principal stress, overall stress difference, surface wrinkling state and cracking state. The judgment criteria for each indicator are set according to the quality requirements in the forming constraint condition.

[0023] In this manual, the multi-dimensional monitoring equipment in the S7 includes a displacement sensor, a tension sensor, an infrared thermometer, and an industrial camera. The displacement sensor is used to monitor the actual displacement of the clamp in real time and compare it with the displacement parameters in the final stretching path. When the deviation exceeds the preset range, the equipment is automatically adjusted. The tension sensor is used to monitor the actual tensile force to ensure that it does not exceed the maximum tonnage in the forming constraints. The infrared thermometer is used to monitor the surface temperature of the skin to avoid excessive temperature affecting the material properties. The industrial camera is used to capture images of the skin surface in real time, identify defects such as wrinkles and cracks, and trigger an emergency stop.

[0024] In summary, the present invention has at least the following beneficial effects:

[0025] Significant synergistic effect of algorithm fusion: Through the bidirectional interaction of two types of hybrid algorithms, the application limitations of a single algorithm are overcome, the rationality and adaptability of stretching path planning are improved, and the generation of forming defects is reduced from the source.

[0026] Improved molding quality stability: The closed-loop design of the entire process enables full-chain control from parameter acquisition to quality inspection, reducing reliance on engineers' experience and ensuring the consistency of skin molding quality across different batches.

[0027] High technical reproducibility: The finite element modeling and equipment debugging process is standardized, making it easy for those skilled in the art to reproduce and promote it.

[0028] Production safety and efficiency optimization: Multi-dimensional process monitoring and emergency stop mechanisms reduce safety risks during the molding process, and optimized paths reduce the number of iterative trials and errors, indirectly improving production efficiency. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the path planning method for the stretching and forming of sunken skin involved in this invention.

[0030] Figure 2 This is a flowchart illustrating the path planning method for the stretching and forming of sunken skin involved in this invention.

[0031] Figure 3 This is a schematic diagram illustrating the bidirectional interaction between the echo state network and the cell mapping algorithm involved in this invention.

[0032] Figure 4 This is a schematic diagram illustrating the bidirectional interaction between the fractional-order Kalman filter and the cuckoo search algorithm involved in this invention. Detailed Implementation

[0033] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0034] like Figure 1 and Figure 2 As shown, embodiments of the present invention provide a path planning method for the stretching and forming of sunken skin. This solution addresses the core requirements of stretching and forming of sunken skin by constructing a complete technical system encompassing parameter acquisition, modeling, path planning, simulation verification, iterative optimization, instruction generation, forming monitoring, and quality inspection. The core innovation lies in integrating four types of algorithms to form a bidirectional interactive collaborative mechanism: echo state networks and cell mapping algorithms are used to complete the global planning of the initial stretching path, achieving a prediction-optimization-iterative closed loop; fractional-order Kalman filtering and cuckoo search algorithms are used to complete iterative path optimization, achieving error purification-precise optimization-parameter update closed loop. The entire process is based on design parameters and forming constraints, relying on a finite element model to build a bridge between virtual simulation and actual forming. Through equipment instruction conversion and multi-dimensional process monitoring, the accurate implementation of the planned path is ensured, and finally, the feasibility of the solution is verified through comprehensive quality inspection.

[0035] S1: Obtain the design parameters and molding constraints for the sunken skin.

[0036] Design parameters and molding constraints are the foundation for all subsequent modeling, planning, simulation, and molding work, and the accuracy of their acquisition directly determines the implementation effect of the entire scheme. Therefore, this step requires accurate collection of relevant data through multiple channels to ensure that each parameter has a clear source and empirical basis.

[0037] The design parameters are divided into two categories: geometric parameters and material parameters. Geometric parameters cover both the skin body and the recessed area: the skin body's length ranges from 500 mm to 3000 mm, its width from 300 mm to 1500 mm, and its thickness from 1 mm to 10 mm; the recessed area has only two possible locations: the front and back of the skin. The recessed shape includes all four types: circular, rectangular, trapezoidal, and irregular. The recessed depth ranges from 2 mm to 50 mm, and the corner radius of the recessed edge ranges from 1 mm to 5 mm. Material parameters include elastic modulus, yield strength, Poisson's ratio, and hardening index. The elastic modulus ranges from 200 GPa to 220 GPa, the yield strength from 235 MPa to 700 MPa, the Poisson's ratio from 0.26 to 0.30, and the hardening index from 0.1 to 0.3.

[0038] Forming constraints include two categories: equipment parameters and quality constraints. Equipment parameters are determined by the inherent performance of the stretching equipment. The maximum tonnage of the stretching equipment is 500 kN to 5000 kN, the maximum stroke of the clamp is 100 mm to 500 mm, and the clamping range is 200 mm to 1200 mm. Quality constraints are the core standards for product acceptance. The maximum allowable deformation is 0.1 mm to 0.5 mm, the surface roughness must reach Ra no greater than 1.6 micrometers, and the formed skin must completely avoid three types of defects: wrinkling, cracking, and excessive springback.

[0039] Geometric parameters are obtained based on the 3D design drawings of the recessed skin, limited to the two common industrial formats STEP and IGES. Dimensional data are directly extracted using the measurement functions of professional CAD software (such as CATIA). Material parameters are obtained experimentally using a universal testing machine for tensile testing, strictly following the GB / T 228.1-2010 standard (or the latest standard). The specific procedure is as follows: prepare standard tensile specimens, set the loading rate to 2 mm / min, record the stress-strain curve, and calculate key parameters such as the elastic modulus and yield strength from the curve. Equipment parameters are directly obtained from the technical specifications of the tensile testing equipment, provided by the equipment manufacturer to ensure the authority and accuracy of the parameters. Quality constraint indicators are determined based on the product technical requirements document, which is formulated by the design department in conjunction with the product's usage scenario and assembly requirements, clearly defining the acceptable range for each quality indicator.

[0040] This step ultimately generates a design parameter list and a forming constraint list. The design parameter list details the specific values ​​of geometric and material parameters and the basis for their values, while the forming constraint list clarifies the operational limitations of the equipment and the quality requirements of the product. These two lists will serve as the foundational data for subsequent S2 finite element modeling, providing a basis for the model's geometric construction and material assignment; they will also serve as constraints for S3 path planning, limiting the range of path parameter values; and they will be the criteria for S4 simulation verification, used to evaluate the rationality of the simulation results.

[0041] S2: Establish a finite element model of a sunken skin-like structure.

[0042] The finite element model serves as a bridge connecting design parameters and actual molding; its construction quality directly impacts the accuracy of path planning and the reliability of simulation results. This step will utilize professional finite element software to complete the entire model construction process based on the design parameters and molding constraints obtained in S1, ensuring a high degree of consistency between the model and the actual skin and molding scenario.

[0043] The core input data for this step are the design parameter list and the forming constraint list output by S1. The design parameter list provides the geometric dimensions and material properties required for model construction, while the forming constraint list clarifies the basis for setting the boundary conditions related to the equipment.

[0044] The first step is geometric modeling. Launch Abaqus software, create a new 3D modeling module, and construct the initial model of the skin body using sketching and extrusion based on the geometric parameters of the skin body in the design parameter list. Then, precisely model the sunken areas. Based on the sunken location, shape, depth, and corner radius recorded in the list, draw the sunken outline at the corresponding position on the body model, and form the sunken structure through extrusion cutting. During the modeling process, all dimensions are strictly set according to the values ​​in the list, especially the corner radius of the sunken areas, which must be accurate to one decimal place to ensure complete consistency with the design requirements.

[0045] The second step is mesh generation. The key to mesh generation is balancing computational accuracy and efficiency, requiring the selection of appropriate element types based on the skin thickness and geometric complexity. When the skin thickness is less than or equal to three millimeters, the shell element S4R is used. This element has good thin-film and bending characteristics, making it suitable for simulating thin-shell structures. When the skin thickness is greater than three millimeters, the solid element C3D8R is used. This element is an eight-node hexahedral element, capable of accurately simulating the stress and strain distribution of thick plate structures. To further improve computational accuracy, a fine mesh (0.5 mm to 2 mm) is used in the sunken area and the surrounding 50 mm area; a coarse mesh (2 mm to 5 mm) is used in other areas of the skin body. After meshing, the distortion rate of all elements is checked using Abaqus' mesh quality check tool. If any element has a distortion rate greater than 5%, it needs to be corrected by adjusting the mesh size and optimizing the element topology until the distortion rate of all elements is controlled within 5%.

[0046] The third step is assigning material properties. Material parameters such as elastic modulus, yield strength, Poisson's ratio, and hardening index are extracted from the design parameter list. A new material model is created in the Abaqus material module, and the above parameters are entered one by one into the corresponding property fields. Considering that skin stretching is a plastic deformation process, a bilinear isotropic hardening model is used to describe the plastic behavior of the material. This model can accurately reflect the hardening characteristics of the material after yielding, which conforms to the tensile deformation law of metallic materials. After assignment, the material model is linked to the finite element model of the skin to ensure that each element correctly inherits the material properties.

[0047] The fourth step is setting boundary conditions. Based on the equipment parameters in the forming constraint list, the clamping method and stretching direction of the clamps are defined. The two ends of the skin are set as the clamping areas, and the rotational degrees of freedom of the X, Y, and Z axes in these areas are constrained, allowing only the translational degree of freedom in the X-axis direction, to simulate the fixing and stretching effect of the clamps on the skin during the actual stretching process. The stretching direction is set to the length direction of the skin, i.e., the positive X-axis direction. At the same time, an upper limit value of the stretching force is set according to the maximum tonnage of the equipment to ensure that the stretching force does not exceed the load-bearing capacity of the equipment during the simulation. After the boundary conditions are set, the model is checked as a whole to confirm that the geometric dimensions, mesh quality, material properties, and boundary conditions are all correct, forming a complete finite element model of the sunken skin.

[0048] This step outputs a sunken skin-like finite element model containing geometric information, mesh information, material properties, and boundary conditions. This model will be directly used for the initial stretching path planning in S3, providing the structural property data required for path optimization in the algorithm; it is also the core model for simulation verification in S4, used to simulate the skin forming process under different stretching paths.

[0049] S3: Global planning of the initial stretching path based on the echo state network-cell mapping hybrid algorithm

[0050] The quality of the initial stretching path planning determines the efficiency of subsequent optimization work and the final molding quality. This step innovatively integrates two types of algorithms: echo state networks and cell mapping algorithms, such as... Figure 3 By achieving closed-loop collaboration of prediction, optimization, and iteration through bidirectional interaction, this approach solves the problems of insufficient global optimization accuracy and inaccurate defect prediction in traditional path planning. The echo state network excels at establishing nonlinear temporal correlation models, accurately predicting forming defect risks under different paths; the cell mapping algorithm excels at global optimization in complex state spaces, efficiently searching for the optimal path under the constraints of the echo state network. The fusion of these two approaches ensures that the initial stretching path possesses both global optimality and effectively avoids forming defects.

[0051] The input data for this step includes the forming constraint list output by S1 and the finite element model of the sunken skin type output by S2. The forming constraint list provides the algorithm with the range of path parameter values ​​and quality judgment criteria, while the finite element model provides the algorithm with data on the structural characteristics and deformation patterns of the skin.

[0052] The core function of the echo state network is to establish a nonlinear mapping relationship between stretching path parameters, molding defect risk, and sinking size error, providing precise constraints for the optimization process of the cell mapping algorithm. Its model construction, training, and application process are as follows:

[0053] The core of the model building phase is determining the network's structural parameters and mathematical model. The state update equation for the echo-state network is defined as follows:

[0054] ;

[0055] The output equation is:

[0056] ;

[0057] in, This represents the state vector of the echo state network reservoir at time t, with dimension . , The size of the reserve pool was determined through multiple experiments to ensure the network's fitting ability while avoiding excessive computation. is the echo state network forgetting factor, with a value of 0.95, used to balance the network's attention to historical states and current inputs; t is the time step index, with values ​​of 1, 2, ..., T, where T is the total number of time steps in the path; The hyperbolic tangent activation function is used to introduce nonlinear mapping relationships and improve the network's ability to fit complex problems. Input the weight matrix to the echo state network, with dimension . , The input features correspond to the clamp displacement, stretching speed, and segmented stretching sequence encoding, respectively. The matrix elements are randomly generated in the interval [-0.5, 0.5], with a sparsity of 0.1. The sparsity design can reduce the redundant computation of the network. Let be the input vector of the echo-state network at time t, with dimension . It includes the clamp displacement, stretching speed, and segment stretching sequence encoding value of the current path; The weight matrix for the echo state network's reservoir has dimensions of . The sparsity is 0.1, and the spectral radius is... A spectral radius less than 1 ensures network stability; Here is the bias vector of the echo state network, with dimension . The element takes a value of 0.1 and is used to adjust the network's output baseline. Let be the output vector of the echo-state network at time t, with dimension . Includes defect risk probability , depth of depression prediction error Predicted maximum principal stress These three outputs are the core indicators for evaluating the quality of a path; Output the weight matrix for the echo state network, with dimension . This is used to map the state of the reservoir to the input features and then to the output space. The noise predicted by the echo state network follows a pattern with a mean of 0 and a variance of . The Gaussian distribution is used to simulate random disturbances in the actual molding process.

[0058] During the model training phase, the core objective is to determine the output weight matrix through training on the dataset, ensuring the network possesses accurate predictive capabilities. First, a training dataset is constructed. Based on the S2 finite element model, 1000 initial path samples are generated using random sampling. Each sample contains an input vector. and the corresponding output label. Input vector The output labels consist of randomly generated clamp displacement, tensile velocity, and segmented tensile sequence codes. These labels are obtained through explicit dynamic simulation. Specifically, each set of path samples is input into the finite element model, and after running the simulation, the corresponding defect state, sink depth error, and maximum principal stress are extracted. The defect state is represented by 0 for no defect and 1 for a defect. The 1000 generated samples are divided into a training set (700 sets) and a validation set (300 sets) in a 7:3 ratio. The training set is used for model parameter learning, and the validation set is used for model accuracy verification.

[0059] The ridge regression method was then used to solve for the output weight matrix. The solution formula is:

[0060] ;

[0061] in, Output a label matrix for the training set, with dimension 1. ; The training set reservoir state and input concatenation matrix has a dimension of . ; This is the ridge regression regularization coefficient, with a value of 0.01, used to prevent the model from overfitting. It is an identity matrix with dimension 1. .

[0062] After training, the validation set is input into the echo state network, and the prediction error of the model is calculated. The error calculation formula is as follows:

[0063] ;

[0064] in, The actual output labels for the validation set; This is a L2 norm operation used to quantify the deviation between predicted and actual values. If the calculated prediction error... If the prediction accuracy reaches 92% or higher, the model has good predictive ability and training is complete; if the prediction error is greater than 0.02, the size of the reserve pool should be adjusted. (Adjust by ±50 each time), and retrain until the accuracy requirements are met.

[0065] In the model application phase, the core is to utilize the trained network to predict the shaping characteristics of candidate paths. For any candidate stretching path, its corresponding clamp displacement, stretching speed, and segmented stretching sequence are encoded to form an input vector. The input is fed into the trained echo state network, and the defect risk probability corresponding to the path can be obtained through the state update equation and the output equation. , depth of depression prediction error Predicted maximum principal stress These outputs will serve as the core constraints for the cell mapping algorithm to find the optimal solution.

[0066] The core function of the cell mapping algorithm is to perform global optimization of the stretched path state space under the predictive constraints of the echo state network, and simultaneously feed the optimization results back to the echo state network to achieve iterative optimization of both. The model construction, optimization and interactive update process is as follows:

[0067] In the model building phase, the core task is to construct a three-dimensional state space that encompasses all possible path parameters. The three dimensions of the state space are clamp displacement, stretching velocity, and segmented stretching sequence: the clamp displacement ranges from 0 to the maximum clamp stroke obtained in S1. The step size is 0.05 mm to ensure the accuracy of displacement parameters; the stretching speed ranges from 0.5 mm / s to 5 mm / s, with a step size of 0.1 mm / s to balance speed accuracy and computational efficiency; the segmented stretching sequence involves four regions: edge region, non-sunken body region, sunken periphery region, and sunken core region. All possible sequences are permutations of the four regions, totaling 24. Each sequence is encoded as an integer from 1 to 24 to achieve a quantitative representation of the sequence.

[0068] The formula for calculating the total number of cells in the state space is:

[0069] ;

[0070] in, The total number of cells, each cell corresponds to a unique combination of path parameters, and is indexed. The identifiers are defined as follows: i is the displacement index, j is the velocity index, and k is the sequence index. Any set of path parameters can be quickly located using these indexes.

[0071] In the optimization preparation phase, the core task is to determine cell feasibility based on the prediction results of the echo state network and construct a fitness function. The key to cell feasibility determination is to select path parameter combinations that satisfy the forming constraints; the determination formula is as follows:

[0072] ;

[0073] in, Cellular The feasibility flag is 1 for feasibility and 0 for infeasibility. Cells output by the echo state network The corresponding defect risk probability is set as a defect constraint condition if the defect risk probability is less than 0.05 (i.e. 5%). Cellular The corresponding tensile force is calculated by inputting the path parameters of this cell into the finite element model of S2; The maximum tonnage of the tensioning equipment obtained in S1 serves as the upper limit constraint for the tensioning force.

[0074] The fitness function is used to quantify the merits of each path. Its construction requires comprehensive consideration of factors such as the accuracy of the depression dimensions, the uniformity of stress distribution, and the risk of defects. The formula is as follows:

[0075] ;

[0076] in, , , The weighting coefficient satisfies the condition that the sum of the weights is 1. This weighting is determined based on the priority of quality constraints. The accuracy of the recessed dimensions is crucial to product assembly, so it has the highest weight. Cells predicted for echo-state networks The corresponding depth error; Cells predicted for echo-state networks The corresponding maximum principal stress; Cellular The probability of defect risk. The smaller the fitness function value, the better the overall performance of the path.

[0077] In the global optimization phase, the core is to find the optimal path through cell transfer. First, an initial cell is selected, with its index as... ,in Corresponding displacement 0 mm Corresponding speed 1 mm / s The corresponding sequence is edge region → non-sunken body region → sunken surrounding region → sunken core region. This initial cell is set based on conventional stretching logic to ensure that optimization starts from a reasonable initial point.

[0078] Then the cell transition probability matrix is ​​calculated. Matrix elements Indicates from cell Transfer to cell unit The probability is calculated using the following formula:

[0079] ;

[0080] This formula uses an exponential function to enhance the transition probability of cells with small fitness function values, ensuring that the optimization process moves towards high-quality cells.

[0081] Set the number of optimization iterations In each iteration, the feasible cell with the highest transition probability is selected as the current optimal cell based on the transition probability matrix, and this process is repeated until the maximum number of iterations is reached. Finally, the fitness function value is selected from all iterations. The three smallest cell paths are selected as candidate initial stretching paths.

[0082] The core of the interactive update phase is to achieve bidirectional iteration between the echo state network and the cell mapping algorithm. The three selected optimal paths are then substituted back into the echo state network to calculate the prediction errors corresponding to these paths. The calculation method is consistent with the error calculation in the model validation phase. Based on this prediction error, the output weight matrix of the echo state network is updated using the following formula:

[0083] ;

[0084] in, This is the updated output weight matrix; This is the output weight matrix before the update; The learning rate of the echo state network is used to control the magnitude of weight updates; The prediction error for the back-substitution path; The training set is a concatenated matrix of the reservoir state and the input. It is the identity matrix; Here is the ridge regression regularization coefficient. This update will further improve the prediction accuracy of the echo state network, providing a more reliable basis for subsequent optimization.

[0085] Termination condition: When the cell mapping algorithm completes a preset number of iterations (e.g., 100 times), the optimal path selected is re-predicted by the echo state network. If the prediction error is less than the preset accuracy threshold for two consecutive times (e.g., error ≤ 0.02), or the change in the weight matrix output by the echo state network is less than the preset value (e.g., change ≤ 1%), the closed-loop interaction between the echo state network and the cell mapping algorithm terminates.

[0086] This step outputs three candidate initial stretching paths, each containing detailed clamp displacement-time curves, stretching velocity curves, and the segmented stretching sequence. These candidate paths will be input into the finite element simulation verification stage of S4. Through simulation comparison, the initial path with the best overall performance will be selected, laying the foundation for subsequent iterative optimization.

[0087] S4: Finite element simulation verification of the initial tension path

[0088] The merits of the candidate initial stretching paths need to be determined through simulation verification. This step is based on the finite element model of S2, and stretching simulations are performed on the three candidate paths output by S3 respectively. The forming effect of each path is comprehensively analyzed, providing accurate error data and defect information for the iterative optimization of S5.

[0089] The input data for this step includes the sunken skin-like finite element model output by S2 and the three candidate initial tension paths output by S3. The finite element model provides the structural basis for the simulation, while the candidate initial tension paths provide the loading conditions for the simulation.

[0090] The first step is to solve the parameter settings. Start the explicit dynamics module in Abaqus, import three candidate initial stretching paths, and create an independent simulation task for each path to avoid mutual interference. The simulation step size is set to 0.01 seconds per step, which ensures the accuracy of the simulation results while controlling the total computational load. Two simulation termination conditions are set; the simulation stops when either one is met: the clamp reaches the maximum stroke obtained in S1, and the skin's forming deformation reaches a stable state (i.e., the difference in deformation between two adjacent steps is less than 0.001 mm).

[0091] The second step is simulation execution. Simulation tasks for the three paths are launched sequentially. The explicit dynamics solver simulates the movement of the clamps based on the clamp displacement-time curves and tensile velocity curves within the paths, thereby driving the skin to undergo tensile deformation. During the simulation, the solver records the stress and strain distribution data of each element of the skin in real time, as well as the dimensional change history of the sunken area and the surface morphology data of the skin. To ensure the integrity of the simulation data, the data output frequency is set to once per step, covering all key physical quantities.

[0092] The third step is simulation result analysis. Based on the list of forming constraints output by S1, the simulation results for each path are analyzed from multiple dimensions. Regarding the analysis of the dimensional accuracy of the sunken area, the actual depth of the sunken area at the final simulation moment is extracted and compared with the design depth to calculate the depth error, determining whether the error meets the requirement of not exceeding ±0.1 mm. Regarding the stress distribution analysis, the maximum principal stress of the skin is extracted, determining whether it is less than or equal to the material yield strength obtained in S1, and simultaneously calculating the overall stress difference of the skin to determine whether it meets the requirement of not exceeding 50 MPa. Regarding the surface quality analysis, the surface morphology data is used to check for wrinkling and cracking defects in the skin. The criteria for wrinkling are a wrinkle height greater than or equal to 0.05 mm, and the criteria for cracking are an equivalent plastic strain greater than or equal to 0.2.

[0093] After the analysis is completed, a detailed simulation results report is generated for each path. The report includes stress cloud diagram, strain cloud diagram, sinking size error data, surface quality inspection results, and clearly indicates whether each path meets the forming constraint conditions.

[0094] This step outputs simulation result reports for three candidate paths, clearly showing the final result of each path. The path with the best overall performance (the path that satisfies the most constraints) will be used as the initial baseline path for S5 iterative optimization, and the error data and defect information found in the simulation results will serve as the core basis for optimization.

[0095] S5: Iterative Optimization of Stretching Path Based on Fractional Kalman Filter-Cuckoo Search Hybrid Algorithm

[0096] The optimal candidate path obtained after S4 simulation verification may still contain a small amount of error or potential defects, requiring further optimization. This step integrates two types of algorithms: fractional-order Kalman filtering and cuckoo search algorithm. Figure 4This approach achieves a closed loop of error purification, precise optimization, and parameter update through bidirectional interaction, solving the problems of large simulation noise interference and insufficient optimization accuracy in traditional optimization methods. Fractional-order Kalman filtering can accurately extract the pure error signal from the simulation results, filtering out simulation noise such as mesh discretization and numerical solution; the Cuckoo Search algorithm can adaptively adjust path parameters with the pure error as the target, achieving precise path optimization.

[0097] The input data for this step includes the simulation results report output by S4, the candidate initial stretching paths output by S3, and the list of forming constraints output by S1. The simulation results report provides the error and defect data required for optimization, the candidate initial stretching paths provide the benchmark for optimization, and the list of forming constraints provides the optimization objectives and boundaries.

[0098] The core function of fractional-order Kalman filtering is to extract clean error features from noisy simulation results, providing a precise optimization target for the Cuckoo Search algorithm. Its model construction, filtering, and application process are as follows:

[0099] In the model building phase, the core focus is on establishing a filtering model based on fractional calculus theory to improve the processing capability for nonlinear and non-stationary error signals. The fractional state equation is defined as follows:

[0100] ;

[0101] The fractional observation equation is:

[0102] ;

[0103] in, It is a Caputo-type fractional calculus operator. The order is a fractional order, which was determined through cross-validation. Different orders in the range of 0.6 to 1.0 were tested, and 0.8, which had the smallest filtering error, was finally selected. Let be the state vector of the fractional-order Kalman filter at time t, with dimension . Including displacement adjustment Speed ​​adjustment amount Order adjustment factor These three variables are the core parameters for path optimization; Here is the state transition matrix, with dimension 1. The value is a diagonal matrix. , used to describe the time evolution of the state vector; The input matrix has dimensions of . The value is taken as the identity matrix to ensure that the input signal can be completely transmitted to the state equation; The input vector for the fractional-order Kalman filter has dimension . This includes displacement error, velocity error, and sequence error extracted from the S4 simulation results; The noise is the process noise, which follows a mean of 0 and a variance of . The Gaussian distribution is used to simulate random disturbances during the filtering process; The observation vector is a fractional-order Kalman filter with dimension . This includes the measured depth error of the depression, stress difference, and defect observation values; The observation matrix has dimensions of . The value is the identity matrix, ensuring that the state vector can be accurately mapped to the observation space; To observe the noise, it follows a mean of 0 and a variance of . The Gaussian distribution is used to simulate noise interference during the observation process.

[0104] In the filtering calculation stage, the core is to purify the error signal through prediction-update iteration. The specific steps are as follows:

[0105] The first step is state prediction, which predicts the current state based on the state estimate from the previous time step. The formula is:

[0106] ;

[0107] in, The prior state estimate at time t; Let be the posterior state estimate at time t-1.

[0108] The second step is error covariance prediction, which involves calculating the error covariance of the prior state estimate using the following formula:

[0109] ;

[0110] in, The prior error covariance; Let be the posterior error covariance.

[0111] The third step is to calculate the Kalman gain, which determines the correction weights of the observations to the state estimate. The formula is as follows:

[0112] ;

[0113] in, This represents the Kalman gain of the fractional-order Kalman filter.

[0114] The fourth step is state update, which involves revising the prior state estimate based on the observed values ​​to obtain the posterior state estimate, using the following formula:

[0115] ;

[0116] in, Let t be the posterior state estimate at time t, i.e., the purified purity error estimate.

[0117] The fifth step is to update the error covariance, correcting the posterior error covariance, using the following formula:

[0118] ;

[0119] in, It is a 3×3 identity matrix.

[0120] Through the iterative calculations described above (five steps), a clean error estimate, including the displacement adjustment estimate, can be extracted from the noisy simulation results. Speed ​​adjustment amount estimate , Sequential adjustment factor estimate .

[0121] In the model application phase, the core is to use the refined error estimates as the optimization target of the Cuckoo Search algorithm, clarifying the direction and magnitude of path adjustments. These error estimates accurately reflect the deviation between the current path and the ideal path, providing a clear basis for subsequent parameter optimization.

[0122] The core function of the Cuckoo Search algorithm is to adaptively adjust the stretching path parameters based on the purity error extracted by the fractional-order Kalman filter, while simultaneously feeding the optimization results back to the fractional-order Kalman filter to achieve iterative optimization of both. The model construction, optimization, and interactive update process is as follows:

[0123] The core of the model building phase is constructing a population containing all possible adjustable parameters. This involves defining the population size for the cuckoo search algorithm. Each individual in the population (m=1,2,...,50) is a 3-dimensional vector, corresponding to the displacement adjustment, speed adjustment, and sequence adjustment factor, respectively. The value range strictly follows the forming constraints: the displacement adjustment is [-0.2 mm, 0.2 mm] to avoid excessive adjustment leading to forming failure; the speed adjustment is [-1 mm / s, 1 mm / s] to ensure that the adjusted speed is within the allowable range of the equipment; and the sequence adjustment factor is [-1, 1], used to fine-tune the stretching priority of each region.

[0124] The initial population is estimated by the posterior state of a fractional-order Kalman filter. Random expansion generation, the generation formula is:

[0125] ;

[0126] in, is the initial population expansion coefficient, used to control the dispersion of the initial population and ensure that the population covers a sufficient search space; It is a 3-dimensional standard normal distribution random vector used to introduce random perturbations.

[0127] The core of the optimization preparation phase is to construct a fitness function to quantify the optimization performance of each individual. The fitness function targets the purity error extracted by the fractional-order Kalman filter, and the formula is:

[0128] ;

[0129] in, , , The weighting coefficients are such that the sum of the weights is 1. The weighting is determined based on the degree of influence of the error on the molding quality. The displacement error has the greatest impact on the accuracy of the depression size, so it has the highest weight. This is the estimated fractional-order Kalman filter shift adjustment value corresponding to the m-th individual; This is the estimated fractional-order Kalman filter velocity adjustment value for the m-th individual; This is the estimated fractional-order Kalman filter order adjustment factor for the m-th individual. A smaller fitness function value indicates better adjustment parameters for that individual, resulting in less path error.

[0130] In the global optimization phase, the core is to search for the optimal adjustment parameters through Lévy flight and the elimination of inferior solutions. The first step is individual update, which uses the Lévy flight strategy to generate new individuals, with the following formula:

[0131] ;

[0132] in, This refers to the m-th individual after the update. This refers to the m-th individual before the update. This is the step size factor, used to control the magnitude of individual updates; For Lévy flight distribution, This distribution has long-distance jump characteristics, which can effectively prevent the algorithm from getting trapped in local optima; The individual with the smallest fitness function value in the current population is the current best individual.

[0133] The second step is to eliminate inferior solutions, defining the discovery probability. For individuals in the population whose fitness function value is greater than a threshold (the threshold is 1.2 times the average fitness function value of the current population), a probability is used to... Replace with a new random solution to ensure population diversity and avoid premature convergence of the algorithm.

[0134] Set the number of optimization iterations Through the iterative process of individual updating and elimination of inferior solutions described above, the individual with the smallest fitness function value is finally output. This individual parameter represents the optimal adjustment parameter, which includes the optimal displacement adjustment amount. Optimal speed adjustment amount Optimal order adjustment factor .

[0135] The core of the interactive update phase is to achieve bidirectional iteration between the fractional-order Kalman filter and the cuckoo search algorithm. The optimal adjustment parameters output by the cuckoo search algorithm are then used. The data is fed back to the fractional-order Kalman filter to update its state estimate and process noise variance. The state estimate update formula is:

[0136] ;

[0137] in, These are the fractional-order Kalman filter state correction coefficients, used to control the magnitude of state updates; For the updated state estimate; This is the state estimate before the update.

[0138] The process noise variance update formula is:

[0139] ;

[0140] in, This is the updated process noise variance; The process noise variance before the update; This represents the fitness function value of the optimal individual. This represents the maximum fitness function value of the population. This update further improves the filtering accuracy of the fractional-order Kalman filter, providing more accurate error data for subsequent iterative optimization.

[0141] The core of the path update and iterative verification phase is to update the path based on the optimal adjustment parameters and verify the effectiveness of the updated path. First, the path parameters are updated using the following formulas:

[0142] ;

[0143] ;

[0144] ;

[0145] in, , , For the updated clamp displacement, stretching speed, and segmented stretching sequence; , , The path parameters before the update; , , These are the optimal adjustment parameters output by the cuckoo search algorithm.

[0146] The updated path is then input into the finite element simulation verification stage of S4 for re-simulation analysis. If the simulation results of three consecutive iterations meet all quality constraints (i.e., sink depth error ≤ ±0.1 mm, stress difference ≤ 50 MPa, no wrinkling or cracking defects), the iteration stops, and the current path becomes the optimized final stretching path. If the iteration count reaches 50 and all constraints are still not met, the process returns to S1 to re-verify the design parameters and forming constraints, and to investigate any possible errors in parameter acquisition.

[0147] Termination condition: When the Cuckoo Search algorithm completes a preset number of iterations (e.g., 100 times), the optimal adjustment parameters output are re-filtered by the fractional Kalman filter, and the extracted error estimate is less than the preset error threshold (e.g., error ≤ 0.01), or the stable value after the noise variance update in the fractional Kalman filter process remains unchanged for 3 consecutive times, the closed-loop interaction between the fractional Kalman filter and the Cuckoo Search algorithm terminates.

[0148] This step outputs the optimized final stretching path, which includes the adjusted clamp displacement-time curve, stretching speed curve, and segmented stretching sequence. All performance parameters meet the forming constraints. This path will serve as the core basis for S6 to generate control commands for the stretching equipment, directly guiding the actual stretching forming process.

[0149] In some embodiments, to further improve the initial accuracy of error extraction, the optimal candidate initial path of the cell mapping algorithm can interact with the fractional-order Kalman filter: the optimal candidate initial path parameters output by the cell mapping algorithm (denoted as...) , , , which are respectively the optimal clamp displacement, optimal stretching speed, and optimal segmented stretching sequence encoding, and serve as the initial state estimation benchmark for fractional-order Kalman filtering.

[0150] The specific interaction formula is as follows:

[0151] ;

[0152] ;

[0153] in, Let be the initial state estimation vector for the fractional-order Kalman filter. , , These are the initial displacement adjustment, initial velocity adjustment, and initial sequence adjustment factor, respectively. , , The displacement, velocity, and sequence parameters for the design reference path (derived from the design parameter list); Let Variance be the initial process noise variance for fractional-order Kalman filtering. This is the baseline process noise variance (preset constant) for fractional-order Kalman filtering. The fitness value of the optimal path in the cell mapping algorithm. is the maximum fitness value among all feasible paths in the cell mapping algorithm.

[0154] After receiving the initial parameters, the fractional-order Kalman filter performs the first filtering based on the simulation results, thus achieving preheating optimization for error extraction.

[0155] When the fractional-order Kalman filter completes its first filtering operation, and the initial posterior error covariance of the output... satisfy ( For matrix trace operations, The interaction terminates when the preset covariance threshold (derived from the error accuracy requirements in the forming constraints) or when the cell mapping algorithm passes parameters to the fractional Kalman filter and completes 3 filtering iterations, and subsequent fractional Kalman filters iterate independently according to conventional logic.

[0156] In some embodiments, to enhance the model's generalization ability, the optimal adjustment parameters of the Cuckoo Search algorithm can be fed back to the Echo State Network as new training samples to optimize the prediction accuracy of the Echo State Network: the optimal adjustment parameters output by the Cuckoo Search algorithm (denoted as...) , , ) and the corresponding simulation verification results (denoted as , , The new training samples consist of actual defect risk, actual subsidence depth error, and actual maximum principal stress, respectively. ,in ( , , (Path parameters before optimization) .

[0157] The formula for updating the output weights of an echo-state network is:

[0158] ;

[0159] in, Output the weight matrix for the updated echo state network. ( (The output matrix of the original training set). ( The original training set reservoir state - input concatenation matrix, (The state of the echo state network reserve pool corresponding to the newly added sample). The ridge regression regularization coefficient is... It is an identity matrix.

[0160] The validation error of the echo-state network after adding new samples satisfy ( (For the preset target prediction error), or the number of new samples cumulatively fed back to the echo state network by the Cuckoo Search algorithm reaches a certain threshold. When the maximum number of new samples is preset, which is set according to the initial training set size, the interaction terminates, and the echo state network will no longer receive parameter feedback from the cuckoo search algorithm.

[0161] In some embodiments, to narrow the optimization range of the cuckoo search algorithm, the echo state network can output the high-optimal interval prediction results of the path parameters to the cuckoo search algorithm: the echo state network identifies the path parameter interval with the smallest prediction error based on historical training data (denoted as...). , , , which are the high-optimal intervals for displacement, velocity, and order, respectively, and are used as the generation constraints for the initial population of the Cuckoo Search algorithm.

[0162] The formula for generating the initial population in the Cuckoo Search algorithm is adjusted as follows:

[0163] ;

[0164] in, For the m-th individual in the cuckoo search algorithm, , , These are the displacement, velocity, and sequence adjustment parameters for each individual. , , The high-optimal range is the output of the echo state network. For expansion coefficient, Let be a standard normally distributed random vector. This constraint allows the initial population of the Cuckoo Search algorithm to focus on a range of high-quality parameters, reducing ineffective optimization.

[0165] When the cuckoo search algorithm completes the initial population initialization, and the average fitness value of the initial population is... satisfy ( This is a preset proportional coefficient. The interaction terminates when the initial average fitness value of the population is the value of the population under the constraint of the echoless state network, or when the Cuckoo Search algorithm has completed 3 iterations of optimization. Subsequent Cuckoo Search algorithms update the population according to the normal logic.

[0166] In some embodiments, to improve the optimization efficiency of the cuckoo search algorithm, the set of feasible cells in the cell mapping algorithm can be used as the optimization boundary constraint for the cuckoo search algorithm: the parameter range of all feasible cells output by the cell mapping algorithm (denoted as...) , , , which are the sets of feasible displacements, feasible velocities, and feasible sequences, respectively. During iterative updates, the Cuckoo Search algorithm forces the parameters of newly generated individuals to fall within these feasible sets.

[0167] The individual update formula for the Cuckoo Search algorithm has been adjusted as follows:

[0168] ;

[0169] ;

[0170] in, This is the updated m-th individual in the cuckoo search algorithm. , , For the updated individual parameters, , , This is the set of feasible parameters output by the cell mapping algorithm. Step size factor For Lévy flight distribution, This is the current optimal individual.

[0171] When the cuckoo search algorithm iterates to the individual with the best fitness... The corresponding parameters stably fall within the feasible set of the cell mapping algorithm (the parameters do not exceed the limit in 5 consecutive iterations), or the cuckoo search algorithm reaches the preset maximum number of iterations. When this happens, the interaction terminates, and even if the subsequent Cuckoo Search algorithm generates a small number of individuals that exceed the feasible set, they can be eliminated through the inferior solution elimination mechanism.

[0172] S6: Generation and transmission of control commands for tensioning equipment

[0173] The final stretching path needs to be converted into control commands that the stretching equipment can recognize in order to achieve precise control over the actual forming process. This step will generate, verify, and transmit commands based on the final stretching path output by S5 and the stretching equipment parameters output by S1, ensuring the accuracy and compatibility of the commands.

[0174] The input data for this step are the final stretching path output by S5 and the stretching device parameters output by S1. The final stretching path provides the motion parameters required by the command, and the device parameters provide the format and range constraints of the command.

[0175] The first step is format conversion. Launch Matlab software and import the clamp displacement-time curve and stretching speed curve from the final stretching path. Based on the stretching equipment type obtained from S1, select the corresponding instruction format: If it is a CNC stretching equipment, convert the path parameters into G-code. The G-code must include instructions such as G01 (linear interpolation) and G90 (absolute coordinates), specifying the displacement and speed values ​​at each time step; if it is a hydraulic stretching equipment, convert the path parameters into PLC instructions. The PLC instructions must include logic control statements and analog output statements, specifying the stretching force threshold and the logical sequence of clamp movements.

[0176] Regardless of the instruction format, it must include the clamp start signal, the core parameters for each time step, the tensile force threshold (not exceeding the maximum tonnage of the equipment), and the emergency stop triggering conditions (such as tensile force exceeding the threshold or excessive displacement deviation) to ensure that the equipment can safely and accurately perform the tensile action.

[0177] The second step is command verification. The generated control commands are imported into an offline simulation system that matches the actual stretching equipment model. This system can accurately simulate the equipment's operating status. The offline simulation is started, and the virtual clamp movement trajectory, stretching speed, and stretching force are observed to ensure they match the final stretching path. The commands are checked for syntax errors, parameters exceeding the equipment's range, or other issues. If any anomalies are found, the command parameters are adjusted in the Matlab software, and verification is repeated until the offline simulation results fully meet expectations.

[0178] This step outputs verified stretching equipment control commands, which are the key bridge connecting path planning and actual forming. These commands will be directly transmitted to the S7 stretching equipment control system to guide the actual stretching and forming of the skin.

[0179] S7: Actual Stretching and Process Monitoring of Depressed Skin

[0180] Actual stretch forming is the core step in implementing the solution and must be strictly executed according to control instructions. Simultaneously, multi-dimensional monitoring is crucial to ensure the stability and safety of the forming process. This step will complete equipment debugging, skin clamping, forming execution, and process monitoring, allowing for real-time control of forming quality.

[0181] The input data for this step consists of the stretching equipment control command output by S6 and the forming constraint list output by S1. The control command guides the specific operation of the equipment, while the forming constraint list provides quality judgment criteria for process monitoring.

[0182] The first step is equipment debugging. Transmit the tensioning equipment control commands to the tensioning equipment control system via data cable, turn on the equipment power, and enter manual debugging mode. Debug the initial position of the clamps, ensuring it matches the initial position in the command; debug the tensioning direction, ensuring tension is along the positive X-axis; test the emergency stop function, ensuring the equipment can stop quickly in abnormal situations. After debugging, switch to automatic mode and wait for the skin to be clamped.

[0183] The second step is to clamp the skin. Select a recessed skin blank that matches the design parameters, and accurately place both ends of the blank into the clamping area of ​​the equipment clamp according to the boundary conditions in the S2 finite element model. Activate the clamping function to ensure a firm grip, and at the same time check the position of the recessed area of ​​the blank through the positioning device to ensure that it is consistent with the design position, avoiding clamping deviations that may lead to forming defects.

[0184] The third step is to initiate the forming process and monitor it. The automatic operation function of the equipment is activated, and the equipment will execute the stretching forming action according to the control commands. During the process, four types of equipment are used for real-time monitoring: a displacement sensor monitors the actual displacement of the clamps with an accuracy of ±0.01 mm, comparing the actual displacement with the commanded displacement in real time. If the deviation exceeds 0.05 mm, the control system will automatically adjust the clamp speed to correct the deviation; a tension sensor monitors the actual tensile force with an accuracy of ±1 kN, ensuring that the tensile force does not exceed the maximum tonnage of the equipment obtained in S1; an infrared thermometer monitors the surface temperature of the skin, with a monitoring range of 20°C to 150°C. When the temperature exceeds 100°C, the equipment automatically reduces the stretching speed to avoid the high temperature affecting the material properties; and an industrial camera captures images of the skin surface in real time, using image recognition algorithms to monitor for defects such as wrinkles and cracks. Once a defect is detected, an emergency stop is immediately triggered, terminating the forming process.

[0185] After molding is completed, the equipment automatically stops running and records complete process monitoring data, including displacement, tension, temperature data and defect records at each time point.

[0186] This step outputs the formed sunken skin-like workpiece and process monitoring data. The skin-like workpiece will then enter the S8 quality inspection stage, and the process monitoring data will serve as an auxiliary basis for quality inspection, helping to analyze the causes of forming defects.

[0187] S8: Molding Quality Inspection and Path Validation

[0188] Quality inspection is the final step in evaluating the molding effect and the rationality of the path planning. This step involves a comprehensive inspection of the molded skin workpiece according to the design parameters and molding constraints to determine its qualification, while also verifying the feasibility of the path planning scheme.

[0189] The input data for this step includes the sunken skin-like workpiece after molding (output from S7), process monitoring data, and the design parameter list and molding constraint list (output from S1). The skin-like workpiece is the object of inspection, the process monitoring data is the basis for auxiliary analysis, and the design parameters and molding constraints are the inspection standards.

[0190] The first step is dimensional inspection. A coordinate measuring machine (CMM) is used to precisely measure the skin workpiece, covering all key dimensions: the length, width, and thickness of the skin body; the location of the recessed area, focusing on measuring its X / Y coordinates to determine if the deviation is no greater than ±0.2 mm; the shape of the recess, comparing the measured contour with the design drawings to determine if the contour deviation is no greater than ±0.15 mm; the depth of the recess, measuring the depth at multiple points and calculating the error compared to the designed depth to determine if the error is no greater than ±0.1 mm; and the radius of the rounded corners at multiple locations on the recessed edges to determine if the error is no greater than ±0.1 mm. All measurement data are recorded in the inspection report.

[0191] The second step is surface quality inspection. A surface roughness meter is used to measure the roughness of the skin surface. Multiple measurement points are selected to ensure the representativeness of the results, determining whether the roughness meets the requirement of Ra ≤ 1.6 micrometers. Simultaneously, the skin surface is inspected visually using a magnifying glass, focusing on wrinkles, cracks, and scratches. The criterion for scratches is a depth not exceeding 0.05 millimeters. If any of these defects are found, the surface quality is deemed unacceptable.

[0192] The third step is performance testing. The hardness of the molded skin workpiece is tested using a Rockwell hardness tester, measuring hardness values ​​at multiple points. The error between the measured hardness and the design hardness is calculated, and it is determined whether the error is no greater than ±5%. Simultaneously, a portion of the sample is taken for tensile testing, performed according to GB / T 228.1-2010 standard (or the latest standard). The elastic modulus and yield strength of the sample are measured, and it is determined whether their deviation from the S1 design parameters is no greater than ±3%.

[0193] Based on the results of comprehensive dimensional inspection, surface quality inspection, and performance inspection, if all inspection indicators meet the forming constraints of S1, the forming is deemed qualified, and the path planning scheme is deemed feasible. At this point, a qualified sunken skin product is output, along with the final stretching path optimized in S5, as the standard forming path for subsequent mass production of similar skins.

[0194] If any of the test indicators fails to meet the constraints, the molding process is deemed unqualified. In this case, it is necessary to analyze the reasons for the unqualified process by combining the process monitoring data and test results, return to the path iteration optimization stage of S5, readjust the path parameters based on the analysis results, and then execute steps S6 to S8 in sequence until a qualified skin product is produced.

[0195] The core innovation of this scheme lies in the bidirectional fusion and collaborative work of four types of algorithms, forming a complete technology chain of prediction-optimization-filtering-optimization. The fusion of the echo state network and the cell mapping algorithm solves the problems of insufficient global optimization accuracy and inaccurate defect prediction in traditional initial path planning. The accurate predictions of the echo state network provide constraints for the cell mapping algorithm, and the optimization results of the cell mapping algorithm further optimize the echo state network, enabling the initial path to possess both global optimality and defect avoidance capabilities. The fusion of fractional-order Kalman filtering and the cuckoo search algorithm solves the problems of simulation noise interference and insufficient optimization accuracy. The clean error extracted by the fractional-order Kalman filter provides a precise target for the cuckoo search algorithm, and the optimization results of the cuckoo search algorithm feed back into the fractional-order Kalman filter, achieving precise iterative optimization of the path. This scheme enables high-precision planning of the stretching and forming path for sunken skin-like structures, significantly improving forming quality and production efficiency.

Claims

1. A method for planning the stretching and forming path of a sunken skin, characterized in that, include: S1. Obtain the design parameters and molding constraints of the sunken skin, and generate a list of design parameters and a list of molding constraints; S2. Based on the design parameter list and forming constraint list, establish a sunken skin-like finite element model containing geometric information, mesh information, material properties and boundary conditions; S3. Based on the forming constraint list and the finite element model of the sunken skin, a hybrid algorithm with bidirectional interaction between the echo state network and the cell mapping algorithm is used to perform global planning of the initial stretching path and generate candidate initial stretching paths. The echo state network is used to predict the forming defect risk, sunken size error and maximum principal stress of the candidate paths. The cell mapping algorithm performs global optimization under the predictive constraints of the echo state network, and the optimization result is fed back to the echo state network to update the model parameters. S4. Input the candidate initial stretching path into the sunken skin finite element model for simulation verification and generate a simulation result report; S5. Based on the simulation result report, candidate initial stretching paths, and the list of forming constraints, a hybrid algorithm combining fractional Kalman filtering and the Cuckoo Search algorithm is used to iteratively optimize the stretching path and generate the final stretching path. The fractional Kalman filtering is used to extract the pure error features in the simulation results, and the Cuckoo Search algorithm optimizes the parameters with the error features as the target. The optimization results are fed back to the fractional Kalman filtering to update the filtering parameters.

2. The method for planning the stretching and forming path of a sunken skin according to claim 1, characterized in that, Also includes: S6. Based on the final stretching path and the list of forming constraints, generate control instructions for the stretching equipment; S7. Transmit the control command of the stretching equipment to the stretching equipment, and perform actual stretching and forming of the sunken skin according to the final stretching path. During the forming process, process monitoring data is obtained through multi-dimensional monitoring equipment. S8. Based on the formed sunken skin workpiece, process monitoring data, design parameter list, and forming constraint list, perform forming quality inspection. If all inspection indicators meet the forming constraints, output the qualified skin finished product and the final stretching path as the standard forming path; otherwise, return to S5 for re-optimization.

3. The method for planning the stretching and forming path of a sunken skin according to claim 1, characterized in that, The model training process of the echo state network in S3 includes: randomly generating multiple sets of initial path samples based on the sunken skin finite element model, each set of samples containing clamp displacement, tensile velocity, and segmented tensile sequence parameters; obtaining the forming defect state, sunken size error, and maximum principal stress corresponding to each set of samples through explicit dynamic simulation, and constructing training and validation datasets; solving the output weight matrix of the echo state network using the ridge regression method, training the model using the training dataset, calculating the prediction error using the validation dataset, until the prediction error meets the preset accuracy requirements, and completing the model training.

4. The method for planning the stretching and forming path of a sunken skin according to claim 1, characterized in that, The state space construction and feasible cell selection process of the S3 cell mapping algorithm includes: constructing a state space with clamp displacement, stretching speed, and segmented stretching sequence as three dimensions, where the segmented stretching sequence is a full permutation of edge region, non-sunken body region, sunken periphery region, and sunken core region; discretizing the three-dimensional state space into uniform cells with a preset step size, each cell corresponding to a unique set of path parameter combinations; based on the molding defect risk probability and maximum principal stress prediction value output by the echo state network, combined with the maximum tensile force limit in the molding constraints, determining the feasibility of each cell, and selecting feasible cells with defect risk probability lower than a preset threshold and tensile force not exceeding the maximum tonnage.

5. The method for planning the stretching and forming path of a sunken skin according to claim 1, characterized in that, The bidirectional interaction process between the echo state network and the cell mapping algorithm in S3 includes: the echo state network outputs the forming defect risk probability, the predicted value of the sinking size error, and the predicted value of the maximum principal stress corresponding to each set of candidate path parameters to the cell mapping algorithm, which serves as the core basis for cell feasibility determination and the calculation parameters of the fitness function; the cell mapping algorithm selects several paths with optimal fitness through global optimization, substitutes these optimal paths back into the trained echo state network, calculates the prediction error corresponding to the path, and adjusts the output weight matrix of the echo state network based on the prediction error, thereby realizing the iterative update of the echo state network and forming a closed-loop interaction of prediction-optimization-update.

6. The method for planning the stretching and forming path of a sunken skin according to claim 1, characterized in that, The error extraction process of fractional Kalman filtering in S5 includes: defining a state vector containing displacement adjustment, velocity adjustment, and order adjustment factor, where the order adjustment factor is used to fine-tune the priority of the segmented stretching order; establishing fractional state equations and observation equations based on fractional calculus theory, whereby the state equations describe the time evolution of the state vector, and the observation equations correlate the state vector with the simulation observation data; and filtering out grid discretization noise and numerical solution noise in the simulation results through an iterative process of state prediction, error covariance prediction, Kalman gain calculation, state update, and error covariance update, thereby extracting pure estimates of displacement adjustment, velocity adjustment, and order adjustment factor.

7. The method for planning the stretching and forming path of a sunken skin according to claim 1, characterized in that, The optimization process of the cuckoo search algorithm in S5 includes: using the pure error estimate extracted by fractional-order Kalman filtering as a benchmark, generating an initial population by adding a random perturbation of a preset magnitude. Each individual in the population corresponds to a set of path adjustment parameters, and the parameter values ​​meet the shaping constraints. Constructing a fitness function with the goal of minimizing the error estimate, the fitness function comprehensively considers the weight ratio of displacement adjustment, velocity adjustment, and order adjustment factor. Updating the population individuals through the Lévy flight strategy, eliminating inferior solutions with poor fitness using a preset discovery probability, and after a preset number of iterations, selecting the individual with the best fitness as the optimal path adjustment parameter.

8. The method for planning the stretching and forming path of a sunken skin according to claim 1, characterized in that, The bidirectional interaction between the fractional-order Kalman filter and the cuckoo search algorithm in S5 includes: the pure error estimate output by the fractional-order Kalman filter is directly used as the basis for calculating the fitness function of the cuckoo search algorithm, clarifying the target direction and magnitude of path adjustment; the optimal adjustment parameters selected by the cuckoo search algorithm are fed back to the fractional-order Kalman filter to correct the state estimation results of the fractional-order Kalman filter, and the process noise variance is updated based on the fitness value corresponding to the optimal adjustment parameters, reducing noise interference in subsequent filtering processes and improving the accuracy of error extraction.

9. The method for planning the stretching and forming path of a sunken skin according to claim 1, characterized in that, During the simulation verification of S4, the simulation step size is set to a fixed value, and the simulation termination condition is that the clamp reaches the maximum stroke in the forming constraint condition or the skin forming deformation is less than the preset threshold. The specific analysis indicators included in the simulation result report are: sinking depth error, maximum principal stress, overall stress difference, surface wrinkling state and cracking state. The judgment criteria for each indicator are set according to the quality requirements in the forming constraint condition.

10. The method for planning the stretching and forming path of a sunken skin according to claim 2, characterized in that, The multi-dimensional monitoring equipment in the S7 includes displacement sensors, tension sensors, infrared thermometers, and industrial cameras. The displacement sensors are used to monitor the actual displacement of the clamps in real time and compare it with the displacement parameters in the final stretching path. When the deviation exceeds the preset range, the equipment is automatically adjusted. The tension sensors are used to monitor the actual tensile force to ensure that it does not exceed the maximum tonnage in the forming constraints. Infrared thermometers are used to monitor the surface temperature of the skin to prevent excessive temperature from affecting material properties; industrial cameras are used to capture images of the skin surface in real time, identify wrinkling and cracking defects, and trigger emergency stops.

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