Skin local rigidity self-adaptive dynamic optimization method based on flexible clamping

Abstract

The invention provides a skin local rigidity adaptive dynamic optimization method based on flexible clamping, and the method comprises the steps: firstly constructing a skin-flexible tool finite element model, carrying out the parameterization setting, and then carrying out the batch simulation analysis, and obtaining a simulated finite element sample data set; establishing an aircraft skin multi-point flexible clamping rigidity prediction model based on the simulated finite element sample data set, and training the aircraft skin multi-point flexible clamping rigidity prediction model; and carrying out multi-objective optimization by combining the trained aircraft skin multi-point flexible clamping rigidity prediction model, and finally obtaining an optimal clamping layout meeting constraint conditions. According to the method, finite element simulation, a neural network and a genetic algorithm are combined, and an effective solution is provided for rigidity control of the weak-rigidity skin in the machining process. According to the method, the precision and stability of skin machining are improved, the production cost is reduced, the production time is shortened, and wide application prospects are achieved.

Description

Technical Field

[0001] The invention belongs to the field of aircraft skins, and in particular relates to a method for adaptive dynamic optimization of local rigidity of skins based on flexible clamping. Background Art

[0002] In the field of aviation manufacturing, aircraft skin is a crucial component in the structure of the aircraft, and its processing quality and precision directly affect the aerodynamic performance and overall structural strength of the aircraft. Especially in the manufacturing process of large-sized skin, due to its complex shape, high dimensional accuracy requirements and diverse material properties, the processing becomes extremely complex and challenging.

[0003] As an advanced processing technology, mirror milling technology has been widely used in the manufacturing process of large-size aircraft skins. By processing both sides of the skin at the same time, mirror milling can reduce stress deformation during processing, thereby improving the shape accuracy and surface quality of the skin. In order to adapt to the shapes and sizes of different skins, flexible tooling technology has been adopted on mirror milling equipment. This technology can flexibly adjust the tooling to meet different processing requirements, greatly improving the flexibility and adaptability of processing.

[0004] However, although flexible tooling technology has achieved certain results in the processing of large-size skins, the existing flexible tooling layout design methods still have some limitations that need to be solved, mainly in the following aspects:

[0005] (1) Local areas with insufficient rigidity are difficult to predict accurately: Traditional design methods usually rely on experience and simplified mechanical models. It is difficult to accurately predict the local rigidity changes of the skin during the processing process, resulting in a lack of targeted layout design.

[0006] (2) Lack of efficient optimization methods: Most existing layout optimization methods are based on trial and error adjustment, which are inefficient and difficult to find the global optimal layout solution under complex working conditions.

[0007] (3) Insufficient dynamic adjustment capability: In the actual processing process, the deformation of the skin is affected by many factors. The existing layout method is difficult to achieve real-time dynamic optimization, resulting in the inability to adaptively adjust the local rigidity as the working conditions change.

[0008] These problems have become particularly prominent in modern aviation manufacturing, especially when faced with diverse aircraft models and complex processing environments. To this end, the present invention proposes a skin local rigidity adaptive dynamic optimization method based on flexible clamping, which optimizes the layout of multi-point flexible tooling for the skin by combining stiffness simulation, deep learning prediction and genetic algorithm optimization, thereby effectively improving the processing accuracy and efficiency of large-size skins and meeting the high requirements of modern aviation manufacturing. Summary of the invention

[0009] The purpose of the invention is to provide a skin local rigidity adaptive dynamic optimization method based on flexible clamping.

[0010] The technical solution of the present invention is as follows:

[0011] A skin local rigidity adaptive dynamic optimization method based on flexible clamping, the method comprising:

[0012] Firstly, the skin-flexible tooling finite element model is constructed and parameterized, and then batch simulation analysis is performed to obtain the finite element sample data set after simulation;

[0013] Based on the simulated finite element sample data set, a multi-point flexible clamping stiffness prediction model for aircraft skin was established and trained;

[0014] Multi-objective optimization is performed based on the trained aircraft skin multi-point flexible clamping stiffness prediction model, and finally the optimal clamping layout that meets the constraints is obtained.

[0015] Furthermore, the construction of the skin-flexible tooling finite element model is specifically as follows:

[0016] Establish the finite element model of the vacuum flexible suction cup, the skin finite element model and the mirror support finite element model;

[0017] The finite element model of the vacuum flexible suction cup, the skin finite element model and the mirror support finite element model are assembled as a whole. The layout position of each flexible suction cup is determined according to the design requirements and the geometric shape parameters of the skin to ensure that the center point of the suction cup is tangent to the curved surface of the skin, and the gap and interference in the assembly are checked to ensure that the center of the suction cup is accurately in contact with the skin surface; the position of the mirror support is determined. The processing point is the key area where the skin is subjected to force and support during the milling process. Ensure that the center of the mirror support coincides with the processing center point of the skin, and the top surface of the support should be tangent to the bottom surface of the skin.

[0018] Furthermore, the parameterized setting includes:

[0019] Set the skin size, curvature, local configuration, suction cup quantity, position, inclination, processing point and cutting force to adapt to different clamping and processing conditions.

[0020] Furthermore, the finite element simulation analysis specifically includes:

[0021] Set the properties of skin, suction cup and mirror support materials;

[0022] Determine the connection relationship between the skin and the support;

[0023] Set the analysis step mode type and parameters;

[0024] Set cutting load and boundary constraints;

[0025] Meshing the model;

[0026] Create a job and set solver parameters;

[0027] Submit the job for calculation.

[0028] Furthermore, the batch simulation analysis specifically includes:

[0029] Write automated simulation scripts, use loops and conditional controls to systematically change input parameters, and call the finite element solver to perform large-scale simulations. Efficiently run finite element analysis under various parameter combinations to quickly obtain stress and deformation data of the skin under different conditions.

[0030] Furthermore, based on the simulated finite element sample data set, a multi-point flexible clamping stiffness prediction model for aircraft skin was established and trained, specifically:

[0031] Extract input features of neural network models from simulation datasets;

[0032] A fully connected neural network is used to construct a stiffness prediction model;

[0033] The mean square error (MSE) is used as the loss function and the Adam optimizer is used for training.

[0034] Furthermore, the stiffness prediction model is composed of an input layer, a hidden layer and an output layer, wherein the dimension of the input layer is determined according to the processing area and the number of suction cups, and is used to receive a multidimensional vector, and the hidden layer maps the input features into multidimensional features; finally, the dimension of the output layer is determined according to the number of skin nodes, and is used to convert the multidimensional features into multidimensional deformation prediction values.

[0035] Furthermore, the input features include a processing area, a number of suction cup rows, and a number of suction cup columns.

[0036] Furthermore, a multi-objective optimization is performed in combination with the trained aircraft skin multi-point flexible clamping stiffness prediction model, and finally the optimal clamping layout that meets the constraints is obtained, specifically:

[0037] The NSGA-II algorithm is used, with the geometric constraints of skin parametric modeling as constraints, the number of suction cup clamping points and the maximum deformation of the skin as optimization targets, and the trained aircraft skin multi-point flexible clamping stiffness prediction model is used to evaluate the maximum deformation performance of each individual, and the clamping layout with the least number of clamping points and the smallest deformation under the constraints is obtained.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] The present invention provides an effective solution for the stiffness control of weak rigid skin during processing by combining finite element simulation, neural network and genetic algorithm. The method not only improves the precision and stability of skin processing, but also reduces production cost and time, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The accompanying drawings generally illustrate various embodiments by way of example and not limitation, and together with the description and claims, serve to illustrate the embodiments of the invention. Where appropriate, the same reference numerals are used throughout the drawings to refer to the same or similar parts. Such embodiments are illustrative and are not intended to be exhaustive or exclusive embodiments of the present apparatus or method.

[0041] Figure 1 Shown is a framework flow chart of the present invention;

[0042] Figure 2 A schematic diagram of skin parameterized modeling of the present invention is shown;

[0043] Figure 3 An example of a fully connected neural network of the present invention is shown;

[0044] Figure 4 The fully connected neural network structure diagram of the present invention is shown;

[0045] Figure 5 The NSGA-II algorithm flow chart of the present invention is shown;

[0046] Figure 6 A schematic diagram of the mirror image support of the present invention is shown;

[0047] Figure 7 A simulation diagram of skin processing deformation for a conventional layout is shown.

[0048] Figure 8 Shows the optimized skin processing deformation simulation diagram DETAILED DESCRIPTION

[0049] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0050] Finite Element Modeling of Skin-Multi-Point Flexible Tooling Model

[0051] In the flexible tooling, the positioning, clamping and support of the tooling constitute an integral function and structure. This structure will contact the skin in the form of an adaptive surface, and the structure uses a limited number of support columns to form a spatial surface to clamp the skin. Finite element analysis software is used to complete the establishment of the finite element model of the skin-multi-point flexible tooling.

[0052] Finite element model building and simulation

[0053] In the flexible tooling structure, the vacuum suction cup is a structure that directly contacts the skin. The vacuum suction cup has a direct impact on the clamping deformation, and its sealing performance also directly affects the effect of air pressure clamping. The skin processing simulation supported by multi-point suction cups is carried out. This simulation aims to simulate the interaction between the suction cup and the skin surface at multiple contact points to evaluate the performance and stability of the skin processing process.

[0054] The modeling and finite element analysis process of the multi-point flexible suction cup is mainly as follows:

[0055] First, an accurate 3D geometric model of the suction cup is needed, including its shape, size and structural details, and material properties such as elastic modulus, Poisson's ratio and density are defined for the material used in the suction cup. Then, the finite element method is used to separate the suction cup into multiple small finite elements and generate a fine mesh to capture the complex deformation of the suction cup.

[0056] During the simulation process, several key factors are considered, including the contact and friction characteristics between the suction cup and the workpiece surface, the deformation of the suction cup, external process loading, and the influence of processing parameters. The simulation will simulate the deformation, force distribution and strain of the suction cup at multiple contact points to evaluate the performance, stability and workpiece quality during the processing. By adjusting the design parameters of the suction cup, such as the suction cup structure, material selection and suction cup arrangement, design optimization can be performed to maximize the efficiency and quality of skin processing, and the stress and deformation simulation results of the suction cup.

[0057] Skin finite element model establishment

[0058] Determine the skin size and select the model to obtain the skin geometric parameters, including curvature, lateral length, longitudinal length, and thickness. In order to better simulate the skin forming parameters, a shell unit model is used to draw the processing area on the skin surface, and the processing area is designed according to the original skin model to apply cutting force.

[0059] The skin size is selected from model 5341C05003G73 as a reference, with a curvature of 2833mm, a horizontal length of 1972.2mm, a longitudinal length of 862.5mm, and a thickness of 6mm.

[0060] Mirror support finite element model establishment

[0061] The mirror support finite element model is established according to the actual mirror support geometry and parameters.

[0062] Mirror support structure such as Figure 6As shown in (a), the support end surface is composed of several groups of concentric circles. The outer circle has a diameter of 18 mm and a thickness of 3 mm. The innermost circle has a diameter of 8 mm and a thickness of 2 mm. There is a 3 mm wide water groove between the two thick circles. The mirror support finite element model is established as follows: Figure 6 (b) as shown.

[0063] Carry out finite element assembly of skin, multi-point flexible suction cup and mirror support. Determine the layout position of each flexible suction cup according to design requirements and the geometric shape of the skin, ensure that the center point of the suction cup is tangent to the curved surface of the skin, check the gap and interference in the assembly, and ensure that the center of the suction cup is accurately in contact with the skin surface; determine the position of the mirror support. The processing point is the key area where the skin is subjected to force and support during the milling process. Ensure that the mirror support coincides with the processing center point of the skin, and the top surface of the support should be tangent to the bottom surface of the skin.

[0064] Simulation of stiffness distribution of skin under flexible clamping state

[0065] Finite element analysis software was used to complete the simulation study of the stiffness distribution of the skin during mirror milling under different flexible clamping conditions. By constructing an accurate skin-flexible suction cup finite element model and performing simulation analysis, the stress and deformation characteristics of the skin during processing under different flexible clamping conditions were explored.

[0066] During the simulation process, several key factors need to be considered, including: (1) setting the material properties of the skin and mirror support; (2) defining the connection between the skin and the support; (3) setting the analysis step mode type and parameters; (4) setting the cutting load and boundary constraints; and (5) dividing the model network.

[0067] ① Setting the properties of skin and mirror support materials

[0068] The skin is made of aluminum alloy, which is widely used in aerospace and high-performance engineering applications and has excellent performance. Its elastic modulus is 71.049 GPa and Poisson's ratio is 0.28; the mirror support material is polytetrafluoroethylene, which is known for its excellent chemical resistance and low friction coefficient. It is very suitable for support and sliding contact applications. Its elastic modulus is 1.4 GPA and Poisson's ratio is 0.4; the suction cup material is rubber, which is widely used in application scenarios requiring cushioning and adsorption due to its high elasticity and good flexibility. Its elastic modulus is 6 MPa and Poisson's ratio is 0.47.

[0069] ② Definition of the connection relationship between skin and support

[0070] There is surface contact between the skin model and the positioning part, which belongs to area contact. The contact area is manually set. The lower surface of the skin is set as the contact body in the surface contact relationship, the positioning part is set as the target body, and the friction coefficient between the contact surfaces is 0.3.

[0071] ③Analysis step mode type and parameter settings

[0072] ABAQUS has multiple analysis modes such as static structure, modal analysis and random vibration. Skin processing deformation belongs to static large deformation. Select the static structure mode that allows large deformation. In parameter setting, modify the incremental step parameters, increase the upper limit of the incremental step number, and reduce the incremental step size.

[0073] ④Load and boundary constraints

[0074] Cutting force determination

[0075] After consulting relevant literature, the cutting force is shown in Table 1 when the feed speed is 6000 mm / min and the tool speed is 8000 r / min. The concentrated force is applied to the processing point for simulation.

[0076] Table 1 Tool cutting force

[0077] Cutting force size direction X-axis cutting force -300N Cutting width direction Y-axis cutting force -150N Tool feed direction Z-direction cutting force 60N Tool axial direction

[0078] Boundary Constraints

[0079] Boundary constraints are set for the flexible suction cup and mirror support to simulate actual processing conditions. Fixed constraints are imposed on the top of the flexible suction cup and on the screw hole position of the mirror support.

[0080] ⑤ Division of skin model network

[0081] The skin uses the S4R unit, which is a four-node curved shell unit that is particularly suitable for thin shell structures. The S4R unit can accurately simulate the bending and twisting characteristics of thin-walled structures such as skin. The reduced integration technology of the S4R unit effectively reduces the calculation cost, and prevents unit distortion through the hourglass control function to maintain calculation stability. At the same time, this unit allows finite membrane strain, which enables it to capture the larger deformation that may occur in the actual processing of the skin. Since the skin needs to withstand complex loads and deformations in practical applications, the S4R unit provides the necessary accuracy and efficiency, making it the best choice for simulating the mechanical behavior of the skin.

[0082] The multi-point flexible suction cup uses the C3D10 element, which is a ten-node quadratic tetrahedron element. Suction cups usually have complex three-dimensional geometries and require detailed meshing to accurately simulate their flexibility and contact behavior. Due to its high geometric adaptability, the C3D10 element can fit the complex shape of the suction cup well and provide a fine mesh distribution. At the same time, as a quadratic element, C3D10 provides higher computational accuracy, especially in capturing bending and local stress concentration. These characteristics enable the C3D10 element to accurately simulate the stress distribution and deformation response of the suction cup under different flexible clamping states.

[0083] C3D10 elements are also used for mirror supports to simulate their supporting and fixing functions during the machining process. Since support structures usually have complex geometries, especially in areas in contact with the skin, high-precision meshing is required to accurately simulate their forces. The C3D10 element can effectively adapt to these complex shapes due to its ability to adapt to complex geometries. In addition, support structures require accurate stress analysis when subjected to machining loads, and the high-precision characteristics of C3D10 meet this requirement, ensuring the stability and effectiveness of the support during machining. Using the same type of elements as the suction cup also helps to achieve good compatibility and a unified analysis method in the overall model.

[0084] The simulation results show that the stress of the skin is mainly concentrated in the processing area and the mirror support contact area. Stress concentration occurs near the processing point of the skin, indicating that these areas are the main parts of the force. In the clamping area of ​​the flexible suction cup, although the suction cup is in contact with the skin, the stress distribution is relatively low, which shows that the flexible support of the suction cup is obviously effective. The suction cup can avoid excessive local stress concentration while providing support. The high flexibility of the suction cup allows good contact and support effects to be maintained under large deformation. The mirror support is subjected to large stress in the area in contact with the skin, especially at the processing point. The support structure at these locations undergoes moderate elastic deformation, which fully utilizes the low elastic modulus characteristics of the polytetrafluoroethylene material and provides effective flexible support. During the entire simulation process, the overall deformation of the skin is also kept within the theoretical expected range, ensuring its structural stability and processing accuracy.

[0085] In summary, the simulation results are consistent with the actual processing conditions, which can provide a solid theoretical basis and data support for further optimization of the flexible clamping system.

[0086] Parametric modeling and batch simulation

[0087] In modern aviation manufacturing, the processing and support of skins face a variety of complex clamping conditions, especially when clamped by multiple suction cups. In order to effectively analyze and optimize the mechanical behavior under these conditions, it is necessary to carry out parametric modeling and batch simulation of skins facing variable constraints. These works not only provide data support for understanding the response of skins under different working conditions, but also lay the foundation for subsequent stiffness prediction and layout optimization.

[0088] 1. Parametric Modeling

[0089] Parametric modeling is the key to achieving effective simulation under variable constraints. By establishing a flexible finite element model, multiple influencing factors can be systematically adjusted and controlled. Specifically, the model includes the setting of key parameters such as skin size, curvature, local configuration, number of suction cups, position coordinates, inclination angle, processing point and cutting force. In this way, the model can adapt to different clamping and processing conditions, providing strong flexibility and adaptability for simulation under different working conditions.

[0090] Given the skin curvature R, lateral length L, and longitudinal length W, a coordinate system is established with the center point of the skin as the origin, such as Figure 2 shown.

[0091] The diameter of the suction cup is D, the center of the suction cup is tangent to the skin, and the coordinates of the center of the suction cup (X sucker ,Y sucker ,Z sucker ), angle α sucker is a variable, the minimum distance between the suction cups X coordinates min , minimum distance Y between suction cups Y coordinates min Satisfy geometric constraints:

[0092]

[0093] The tool processing point is on the skin surface, and the processing area AF corresponds to the processing point coordinates (X tool ,Y tool ,Z tool ) is the independent variable, the tool cutting force F(F x ,F y ,F z ) is a fixed constant, and the local configuration of the skin (regional thickness d) is the independent variable.

[0094] The skin deformation δ is the output of finite element simulation, the stiffness K is obtained by calculation, and the overall stiffness of the skin is the tool cutting force F and the average deformation The ratio of the skin processing area stiffness K zone is the tool cutting force F and the maximum deformation of the processing area δ max Ratio.

[0095]

[0096] 2. Batch simulation

[0097] Based on parametric modeling, batch simulation further improves the efficiency of data generation. By writing automated simulation scripts, finite element analysis can be efficiently run under various parameter combinations to quickly obtain stress and deformation data of the skin under different conditions. These scripts use loops and conditional controls to systematically change input parameters and call finite element solvers to perform large-scale simulations, which improves the speed of simulation data generation and enables the acquisition of large amounts of data in a short period of time.

[0098] ABAQUS software mainly consists of two parts: one is the CAE system for pre- and post-processing, which includes the GUI module and the Kernel module; the other is the solver system, including ABAQUS / standard, ABAQUS / explicit, etc., which reads the data file and performs mathematical calculations after the pre-processing step is completed. The GUI and Kernel modules are responsible for collecting finite element model parameters to form INP files, or opening ODB files to extract data from stress cloud maps.

[0099] Based on parametric modeling, batch simulation further improves the efficiency of data generation. By writing automated simulation scripts, finite element analysis can be efficiently run under various parameter combinations to quickly obtain stress and deformation data of the skin under different conditions. These scripts use loops and conditional controls to systematically change input parameters and call finite element solvers to perform large-scale simulations. This method significantly improves the speed of simulation data generation and can obtain a large amount of data in a short period of time, thus providing a rich data foundation for in-depth mechanical analysis and model training.

[0100] The batch simulation script aims to use Python and ABAQUS finite element analysis software to realize the automatic generation and simulation of multiple suction cup distribution schemes. The core functions of the script are to generate the position distribution of the suction cups, submit simulation tasks, and process simulation results. It is used to study the influence of the multi-point suction cup clamping system on the skin deformation and the subsequent creation of the stiffness prediction model training data set, as follows:

[0101] (1) Suction cup position generation

[0102] Random position distribution: The script randomly generates suction cup positions that meet the minimum spacing requirements based on the specified number of suction cup rows and the number of suction cups in each row, avoiding specific restricted areas such as processing points. The randomly generated suction cup positions are intended to build a diverse stress and deformation sample data set to support subsequent neural network model training.

[0103] Uniform position distribution: Within a fixed rectangular boundary, the script evenly generates suction cup positions according to the specified number of rows and columns. This ensures that the outermost suction cup positions remain consistent in all configurations, which is used to study the stress and deformation laws of the skin under the multi-point suction cup clamping system.

[0104] (2) ABAQUS simulation operation

[0105] Instantiation and position adjustment: The script automatically creates the suction cup instance in ABAQUS and rotates and translates it according to the calculated coordinates to reflect the actual position and attitude of the suction cup.

[0106] Boundary condition setting: Set fixed boundary conditions for each suction cup instance to simulate actual clamping conditions.

[0107] Task submission and result processing: The script automatically generates simulation tasks and submits them. After the simulation is completed, the results are automatically processed, including deleting temporary instances and boundary conditions, and preparing for the next round of simulation.

[0108] (3) ODB file post-processing

[0109] Batch processing of ODB files: Traverse all ODB files in the specified directory and process each file. After opening each file, the program will locate all instances of a specific part and extract the data of the target node for these instances.

[0110] Extract node coordinates and displacement data: The program extracts the three-dimensional coordinates and displacement information of each specified node. For each node, record its coordinates in the X, Y, and Z directions, as well as the displacement data in the X direction.

[0111] Data storage and statistics: The extracted data will be written to CSV files for subsequent analysis. For each processed ODB file, a CSV file containing all target node coordinates and displacements is generated. In addition, the average and maximum displacements of the nodes for all files are calculated and summarized, and these statistics are saved to a total table.

[0112] Through the above functions, the script realizes the automation of the whole process from suction cup position generation to simulation result processing, and can efficiently generate suction cup distribution schemes under different configurations and perform stress deformation analysis. This not only supports the design optimization of multi-point suction cup clamping system, but also provides a rich data set for the training of neural network models.

[0113] Construction of a stiffness prediction model for aircraft skin multi-point flexible clamping

[0114] Skin stiffness distribution dataset preparation and feature extraction

[0115] 1. Dataset Preparation

[0116] In the early stage of the example setting, 1250 sets of samples under different working parameters were collected. Each sample had a different processing area and suction cup position distribution. The processing area was randomly generated within the specified range through parametric modeling, and the suction cup position distribution was generated within 5 rows and 5 columns through a batch random distribution simulation script.

[0117] For each suction cup center point coordinate (X sucker ,Y sucker ,Z sucker ), according to formula (3), Z sucker Available through X sucker Calculated, so each suction cup has two independent variables X sucker , Y sucker , there are 25 X sucker , Y sucker , and the processing area AF is an independent variable, so the neural network prediction has a total of 51 input dimensions. Each finite element sample in the example contains 2146 nodes, which is the output dimension after the neural network prediction.

[0118] From the data set level, for five rows and five columns with a total of 25 suction cups, the X coordinate of each suction cup is randomly generated in the range of [-954.6, 954.6], the Y coordinate of the suction cup is randomly generated in the range of [-399.75, 399.75], and the processing area is selected between AF. The composition of the stress data set is shown in Table 2 below.

[0119] Table 2 Composition of the skin stiffness distribution sample data set

[0120]

[0121] 2. Feature extraction

[0122] In order to build an effective stiffness prediction model, it is necessary to accurately extract and process a large amount of data from the finite element simulation samples, including the coordinate distribution of all suction cups in each sample, the deformation and stress distribution of skin nodes, the node coordinates of the skin, etc. Therefore, the suction cup coordinate reading function, deformation and stress distribution reading function, and skin node coordinate reading function are written to improve the efficiency of data processing.

[0123] (1) Suction cup coordinate reading function

[0124] Function: Read the XYZ coordinates of the suction cup center point of all ODB files in the specified folder in sequence, and save them into TXT files respectively.

[0125] accomplish:

[0126] Traverse all ODB files in the specified directory.

[0127] For each file, extract the center point coordinates of the suction cup.

[0128] Store these coordinates in corresponding TXT files respectively.

[0129] (2) Deformation and stress distribution reading function

[0130] Function: Read the deformation and stress distribution data of all nodes of the skin of all ODB files in the specified folder, save them in the specified folder in the form of TXT files, calculate the average value and find the maximum value.

[0131] accomplish:

[0132] Open each ODB file and read the deformation (U) and stress (S) data of the skin nodes.

[0133] Store deformation and stress data in two different TXT files.

[0134] Calculate and record the average deformation value, maximum deformation value, average stress value, and maximum stress value for each file and store these statistics in a summary CSV file.

[0135] (3) Skin node coordinate reading function

[0136] Function: Read the XYZ coordinates of each node of skin 1-2146.

[0137] accomplish:

[0138] Open the ODB file and iterate through all instances to find the skin instance.

[0139] Extract the node coordinates within the specified node range.

[0140] Store these coordinates in a TXT file for later analysis and visualization.

[0141] Skin stiffness prediction model construction and training

[0142] 1. Model Principle

[0143] The skin stiffness prediction model uses a fully connected neural network. The fully connected neural network is one of the earliest deep learning networks, which evolved from the multi-layer perceptron in machine learning. The fully connected neural network is usually a deep neural network composed of a sufficient number of fully connected layers. These fully connected layers are usually divided into input layers, hidden layers, and output layers. For example, Figure 3 As shown, each layer is composed of several neuron nodes. The neurons in the same layer are not connected to each other, and the neurons in adjacent layers are fully connected.

[0144] The neurons in any network layer of the fully connected neural network are connected to all neurons in the previous network layer. The information transmission between nodes in different network layers is calculated by weighted sum combined with the bias term, as shown in formula (7). The output of the kth neuron in the j+1th layer is the bias term b plus the weighted sum of the outputs of all neurons in the jth layer. The calculation of the fully connected network layer is usually expressed as a matrix operation, as shown in formula (8), where X represents the information of the neurons in the network layer, W is the weight matrix, and B is the bias matrix.

[0145]

[0146] X (j+1) =X (j) W (j) +B (j) (8)

[0147] In actual use, an activation function is introduced between the latter layer of the network and the previous layer of the network to achieve nonlinear information processing capabilities, as shown in formula (9), where h(·) represents the activation function. In addition, the activation function helps the neural network determine which neurons should be activated. A suitable activation function can improve the accuracy and training efficiency of the network. The activation function selected in this method is the ReLU function.

[0148] The ReLU function has high computational efficiency and solves the problem of gradient disappearance. The formula is shown in (10).

[0149] X (j+1) =h(X (j) W j +B (j) ) (9)

[0150] ReLU(x)=max(0,x) (10)

[0151] 2. Model building

[0152] According to the data set features in Table 2, the input features are suction cup X coordinate * 25, suction cup Y coordinate * 25, and processing area, so the number of input feature channels is 51; the number of output channels is 2146, corresponding to the deformation values ​​of 2146 skin nodes. The architecture of the fully connected neural network is as follows Figure 4 As shown. The input layer has 51 neurons for receiving 51-dimensional vectors; four hidden layers with neurons map the feature vectors into 1024-dimensional features; finally, the output layer converts the features into 2146-dimensional deformation prediction values. Except for the output layer, the other layers use the ReLU activation function. The activation function formula is shown in (10).

[0153] 3. Model training

[0154] The hyperparameters, loss function, optimizer and other information of the neural network are shown in Table 3. 80% of the data set is used for training and 20% for testing; the training batch is 64; the initial learning rate is set to 0.001. The optimizer uses the Adam (Adaptive Moment Estimation) optimizer. Adam is essentially RMSprop with a momentum term. It uses the first-order moment estimation and second-order moment estimation of the gradient to dynamically adjust the learning rate of each parameter. Its advantage is that the parameters change smoothly during the adaptive adjustment of the learning rate, and the memory requirement is small, which is suitable for large data sets and high-dimensional spaces.

[0155] Table 3. Fully connected neural network parameter settings

[0156]

[0157] The training loss of the network uses the mean squared error (MSE), which is defined as shown in formula (11). The MSE function curve is smooth and continuous, and has the characteristic of being differentiable everywhere, which is suitable for applying the gradient descent algorithm. In addition, as the error decreases, its gradient also decreases accordingly, which helps the convergence of the training model. In order to facilitate comparison with the true value to measure the accuracy of the prediction, the test set uses the mean relative error (MRE) to measure the prediction effect of the extreme stress value, as shown in formula (12); the regression model determination coefficient R 2 It measures the overall prediction level of the model, as shown in formula (13). 2 It indicates the relative error between the model prediction value and the actual observation value, and its value is usually between 0 and 1. 2 The closer the value is to 1, the stronger the predictive power of the model is and the better the model explains the data.

[0158]

[0159] Among them, y i is the true value of stress for each sample; is the corresponding predicted value; ε is a small value to avoid the calculation error of the true stress value being 0, and ε is taken as 1×10 -8 .

[0160] The network construction and training code are written in the PyTorch framework. The PyTorch deep learning framework is a software tool for implementing deep learning algorithms. It provides various high-level and low-level APIs, allowing users to quickly build and train deep learning networks without understanding the underlying details, or use the low-level APIs to freely design and debug models. The training environment configuration table of the fully connected neural network model in this paper is shown in Table 4.

[0161] Table 4 Fully connected neural network training environment configuration table

[0162]

[0163] 4. Model Performance Evaluation

[0164] The performance of the trained network is evaluated using an independent validation dataset to ensure that it can accurately predict skin stiffness on unseen data.

[0165] The average relative error of the prediction results of the skin deformation (stiffness) of the fully connected neural network built in this example compared with the actual finite element simulation results is 5.2%. This means that the neural network model can meet the needs of fast calculation of skin deformation and provide support for the fast calculation of the subsequent skin local rigidity adaptive multi-objective optimization algorithm.

[0166] Adaptive multi-objective optimization of skin local rigidity during machining based on flexible clamping

[0167] 1. Basic principles of NSGA-II algorithm

[0168] Multi-objective optimization usually involves multiple conflicting objectives, and there is no feasible solution to minimize or maximize all objectives at the same time. At present, there are two main methods for solving multi-objective optimization problems. One is to convert the multi-objective optimization problem into a single-objective optimization problem by linearly weighting multiple objective functions; the other is to use a population-based intelligent optimization algorithm. The result of this solution method is a set of trade-off solutions between different objectives. The set of these trade-off points is called the Pareto optimal solution set, and the corresponding objective value is called the Pareto frontier. Of the above two methods, the former is simple and efficient to implement when the weights of each objective function are determined. However, in most engineering optimization problems, the weights of each objective function are usually unclear or even dynamically changing. At this time, this method is more difficult to implement and requires multiple optimization operations based on different weights. The latter results in a set of solutions, and the optimal solution can be selected according to engineering requirements without multiple operations. The non-textual sorting genetic algorithm with elite strategy can converge to the real Pareto frontier and maintain good population diversity on the final Pareto optimal solution set. Therefore, NSGA-Ⅱ is used to search for the Pareto optimal solution set of the clamping layout.

[0169] The selection, crossover and mutation operators of the non-dominated sorting genetic algorithm are the same as those of the ordinary genetic algorithm. The main difference is that before the selection operation, each individual in the population is stratified according to the dominant and non-dominated relationship, which increases the probability of excellent individuals being retained and achieves multi-objective optimization. In order to improve the convergence speed, Deb et al. proposed the NSGA-II algorithm by introducing the elite strategy. The flowchart of the algorithm is shown in the figure below. Figure 5 As shown, the specific implementation process is as follows:

[0170] Step 1: Initialize the population and set the evolutionary generation Gen = 1;

[0171] Step 2: Determine whether the first generation sub-population is generated. If it is generated, set the evolutionary number Gen = 2. Otherwise, perform non-dominated sorting, selection, crossover and mutation on the initial population to generate the first generation sub-population and set the evolutionary number Gen = 2:

[0172] Step 3: Merge the parent population and the offspring population into a new population;

[0173] Step 4: Determine whether to generate a new parent population. If not, calculate the objective function of each individual in the new population, and perform operations such as fast non-dominated sorting, calculation of congestion, and elite strategy to generate a new parent population; otherwise, proceed to step 5;

[0174] Step 5: Perform selection, crossover, and mutation operations on the generated parent population to generate a new child population. Step 6: Determine whether the convergence condition is met. If not, the evolutionary generation number Gen = Gen + 1 and return to step 3; otherwise, the algorithm ends.

[0175] 2. Multi-objective optimization solution strategy

[0176] Considering that the optimization generation problem of the operation mode of the flexible tooling system is a multi-variable, multi-constrained optimization problem, and the traditional optimization algorithms are mostly local optimization, with large amount of calculation and slow convergence speed, it is not easy to achieve good results for multi-variable, multi-constrained structural optimization problems, and the time cost of finite element calculation is large, especially when the number of units or the number of calculations is large, the present invention proposes a skin local rigidity adaptive dynamic optimization method combining stiffness prediction and NSGA-II, with the skin parameterized modeling geometric constraints as constraints, the minimum number of suction cup clamping points and the minimum maximum deformation of the skin as optimization goals, and the trained stiffness prediction model is used to evaluate the maximum deformation performance of each individual, and the clamping layout with the minimum number of clamping points and the minimum deformation under the constraints is obtained. In the optimization process, the deformation and stress of the skin in the flexible clamping process are comprehensively considered, and the powerful ability of neural networks in processing complex pattern recognition and the high efficiency of genetic algorithms in global search and optimization are fully utilized.

[0177] 3. NSGA-II Optimization Process

[0178] Initial population generation: The initial population is randomly generated, where each individual represents a suction cup clamping layout scheme, including parameters such as suction cup position and quantity. The maximum deformation performance of each individual is evaluated using the trained stiffness prediction model.

[0179] Fitness evaluation: Taking the minimum number of suction cup clamping points and the minimum maximum deformation of the skin as multiple objectives, calculate the fitness value of each individual.

[0180] Non-dominated sorting and congestion calculation:

[0181] Non-dominated sorting: Sort the population according to the Pareto dominance relationship and divide the individuals into different non-dominated frontier layers. The first layer contains all non-dominated individuals.

[0182] Crowding calculation: The crowding degree is calculated for each individual in the non-dominated front layer to maintain the diversity of the population. Individuals with large crowding degrees are more likely to be retained.

[0183] Selection, crossover and mutation:

[0184] Selection: A tournament selection method is used to select individuals with higher fitness from the population for reproduction.

[0185] Crossover: The simulated binary crossover (SBX) method is used to generate offspring individuals, and new suction cup clamping layout schemes are generated by mixing the gene combinations of parent individuals.

[0186] Mutation: Polynomial mutation method is used to introduce random mutations in offspring individuals to increase the diversity of solutions.

[0187] Constraint processing: In each iteration, constraints are checked on the newly generated individuals to ensure that all individuals meet constraints such as tooling strength, tooling stability, and processing path.

[0188] Population update and convergence judgment: merge the newly generated offspring with the current population, update the population, and retain individuals with high fitness based on non-dominated sorting and crowding. After multiple generations of iterations, when the Pareto front no longer changes significantly, the optimization process converges and a non-dominated solution set for multi-objective optimization is obtained.

[0189] 4. Optimization results verification and adjustment:

[0190] Finite element simulation verification: The optimal suction cup clamping layout solution obtained by the NSGA-II algorithm is input into the finite element simulation software to verify its maximum deformation performance under actual working conditions. If the simulation results deviate from expectations, they can be corrected by adjusting the stiffness prediction model or retraining the neural network.

[0191] Experimental verification and parameter adjustment: In the actual production process, the optimized suction cup clamping layout is experimentally verified to monitor the deformation distribution of the skin during processing. If there is a situation that does not meet the design requirements, it can be solved by fine-tuning the suction cup position or re-optimizing.

[0192] 5. Example results explanation

[0193] By comparing the deformation of the skin processing between the suction cup layout after the NSGA-II optimization algorithm and the conventional layout, combined with finite element simulation verification, the effectiveness of the optimization algorithm was verified. Among them, the conventional layout of the suction cup is a grid layout of five rows and five columns, with a total of 25 suction cups evenly distributed on the skin surface. The position of each suction cup is fixed on a regular grid point to provide basic support and clamping. The skin deformation under this layout is as follows Figure 7 As shown in the figure, the maximum deformation is 0.75 mm. The suction cup layout is significantly improved by the NSGA-II optimization algorithm. The optimized suction cup layout is reduced to 18 suction cups. The distribution is no longer limited to grid points, but is finely adjusted based on the stiffness and deformation characteristics of the skin. Under this layout, the suction cups are concentrated in the area with larger deformation. The skin deformation after the optimized layout is shown in the figure below. Figure 8 As shown in the figure, the maximum deformation is reduced to 0.35 mm, a reduction of 53%. This proves that the optimized suction cup layout of NSGA-II can effectively reduce the deformation of the skin and improve the processing accuracy under actual working conditions.

[0194] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A skin local rigidity adaptive dynamic optimization method based on flexible clamping, characterized in that: The method comprises: Firstly, the skin-flexible tooling finite element model is constructed and parameterized, and then batch simulation analysis is performed to obtain the finite element sample data set after simulation; Based on the simulated finite element sample data set, a multi-point flexible clamping stiffness prediction model for aircraft skin was established and trained; Multi-objective optimization is performed based on the trained aircraft skin multi-point flexible clamping stiffness prediction model, and finally the optimal clamping layout that meets the constraints is obtained.

2. The method for adaptive dynamic optimization of skin local rigidity based on flexible clamping according to claim 1 is characterized in that: The construction of the skin-flexible tooling finite element model is specifically as follows: Establish the finite element model of the vacuum flexible suction cup, the skin finite element model and the mirror support finite element model; The finite element model of the vacuum flexible suction cup, the skin finite element model and the mirror support finite element model are assembled as a whole. The layout position of each flexible suction cup is determined according to the design requirements and the geometric shape parameters of the skin to ensure that the center point of the suction cup is tangent to the curved surface of the skin, and the gap and interference in the assembly are checked to ensure that the center of the suction cup is accurately in contact with the skin surface; the position of the mirror support is determined. The processing point is the key area where the skin is subjected to force and support during the milling process. Ensure that the center of the mirror support coincides with the processing center point of the skin, and the top surface of the support should be tangent to the bottom surface of the skin.

3. The method for adaptive dynamic optimization of skin local rigidity based on flexible clamping according to claim 1 is characterized in that: The parameterization settings include: Set the skin size, curvature, local configuration, suction cup quantity, position, inclination, processing point and cutting force to adapt to different clamping and processing conditions.

4. The method for adaptive dynamic optimization of skin local rigidity based on flexible clamping according to claim 1 is characterized in that: The finite element simulation analysis specifically includes: Set the properties of skin, suction cup and mirror support materials; Determine the connection relationship between the skin and the support; Set the analysis step mode type and parameters; Set cutting load and boundary constraints; Meshing the model; Create a job and set solver parameters; Submit the job for calculation.

5. The method for adaptive dynamic optimization of skin local rigidity based on flexible clamping according to claim 1 is characterized in that: The batch simulation analysis specifically includes: Write automated simulation scripts, use loops and conditional controls to systematically change input parameters, and call the finite element solver to perform large-scale simulations. Efficiently run finite element analysis under various parameter combinations to quickly obtain stress and deformation data of the skin under different conditions.

6. The method for adaptive dynamic optimization of skin local rigidity based on flexible clamping according to claim 1 is characterized in that: Based on the simulated finite element sample data set, the aircraft skin multi-point flexible clamping stiffness prediction model is established and trained, specifically: Extract input features of neural network models from simulation datasets; A fully connected neural network is used to construct a stiffness prediction model; The mean square error (MSE) is used as the loss function and the Adam optimizer is used for training.

7. The method for adaptive dynamic optimization of skin local rigidity based on flexible clamping according to claim 6 is characterized in that: The stiffness prediction model consists of an input layer, a hidden layer and an output layer, wherein the dimension of the input layer is determined according to the processing area and the number of suction cups, and is used to receive multidimensional vectors, and the hidden layer maps the input features into multidimensional features; finally, the dimension of the output layer is determined according to the number of skin nodes, and is used to convert multidimensional features into multidimensional deformation prediction values.

8. The method for adaptive dynamic optimization of skin local rigidity based on flexible clamping according to claim 6 is characterized in that: The input features include processing area, number of suction cup rows and number of suction cup columns.

9. The method for adaptive dynamic optimization of skin local rigidity based on flexible clamping according to claim 1 is characterized in that: Combined with the trained aircraft skin multi-point flexible clamping stiffness prediction model, multi-objective optimization is performed to finally obtain the optimal clamping layout that meets the constraints, specifically: The NSGA-II algorithm is used, with the geometric constraints of skin parametric modeling as constraints, the number of suction cup clamping points and the maximum deformation of the skin as optimization targets, and the trained aircraft skin multi-point flexible clamping stiffness prediction model is used to evaluate the maximum deformation performance of each individual, and the clamping layout with the least number of clamping points and the smallest deformation under the constraints is obtained.

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