Distributed measurement and full-field reconstruction method for deformation gap of large-scale composite part

Abstract

The invention discloses a large-scale composite member deformation gap distributed measurement and full-field reconstruction method, and the method comprises the following steps: setting a plurality of sets of technological parameters, and carrying out the mold pasting of a composite member based on the technological parameters, so as to enable the surface of the composite member to form a skin; determining an optimal arrangement scheme of the sensors, arranging the sensors according to the scheme, and obtaining a gap value matrix; obtaining a plurality of groups of gap value matrixes under different process parameters, and constructing a finite element model small sample training set; training the finite element model by using the finite element model small sample training set to obtain a full-field gap prediction finite element model; and generating a convolutional neural network large sample training set through the full-field gap prediction finite element model, and training the convolutional neural network by using the large sample training set to obtain a full-field gap prediction convolutional neural network model. The method has high systematicness and engineering implementability, and is more suitable for film pasting quality evaluation of a complex shell surface structure compared with a traditional method.

Description

Technical Field

[0001] This invention relates to the field of full-field reconstruction technology of profiles, specifically a method for distributed measurement and full-field reconstruction of deformation gaps in large composite parts. Background Technology

[0002] Currently, research on the molding gap problem formed during the assembly stage of large composite components mainly focuses on obtaining and analyzing the molding gap through methods such as feeler gauge measurement, optical 3D scanning, or finite element simulation. However, these methods mostly have limitations such as high measurement cost, limited applicability, and inability to monitor online. In practical engineering applications, the strong structural enclosure, limited measurement area, and the need for large-area high-resolution measurement make it difficult for traditional methods to meet the requirements for efficient and accurate evaluation of molding quality.

[0003] Some studies have attempted to indirectly reconstruct structural deformation using distributed gap sensor arrays combined with finite element inversion techniques, but these methods mostly employ apparent interpolation reconstruction, which cannot effectively address the multi-constraint, multi-degree-of-freedom coupled reconstruction problems in large, complex curved surface structures. Existing methods often use regular arrays or empirical point selection for sensor placement, lacking a systematic optimal design strategy, making it difficult to balance reconstruction accuracy and robustness under limited sensing point conditions.

[0004] Meanwhile, existing inverse finite element reconstruction methods are mostly designed for two-dimensional structures, but they are difficult to adapt to multi-degree-of-freedom coupling and complex boundary constraints in large-size shell structures, and are sensitive to gap data errors, exhibiting poor stability. In addition, existing deep learning-based prediction methods have failed to achieve joint modeling of process parameters and measured gap data, making it difficult to efficiently and accurately predict the full-field distribution of gaps, and lacking generalization ability and engineering applicability. Summary of the Invention

[0005] The purpose of this invention is to provide a method for distributed measurement and full-field reconstruction of deformation gaps in large composite parts, comprising the following steps:

[0006] S1. Set the process parameters and apply a mold to the composite component based on the current process parameters to form a skin on the surface of the composite component;

[0007] S2. Based on performance evaluation indicators and multi-objective particle swarm optimization algorithm, the optimal sensor layout scheme is confirmed; according to the optimal sensor layout scheme, a limited number of sensors are placed on the skin surface of the composite material component to obtain the gap value matrix.

[0008] S3. Repeat steps S1) to S2) to obtain multiple sets of gap value matrices under different process parameters, and construct a small sample training set for the finite element model.

[0009] S4. Train the finite element model using a small sample training set to obtain a full-field gap prediction finite element model with process parameters as input and full-field gap of the skin surface of composite material components as output.

[0010] S5. Generate a large sample training set for the convolutional neural network using the finite element model for full-field gap prediction; in the large sample training set for the convolutional neural network, the process parameters and the gap value matrix collected by the sensors are the inputs, and the full-field gap of the skin surface of the composite material component is the output.

[0011] S6. Train the convolutional neural network using a large sample training set to obtain a full-field gap prediction convolutional neural network model.

[0012] S7. Obtain the current process parameters and the corresponding sensor gap value matrix, and input them into the full-field gap prediction convolutional neural network model to obtain the full-field gap of the composite material component skin surface.

[0013] Furthermore, in step S1), the process parameters include hot-pressing process-related parameters, internal material process variables, and boundary conditions;

[0014] The parameters related to the hot-pressing process include curing temperature distribution or temperature gradient, pressurization time / pressure, cooling rate, and the difference in thermal expansion coefficients between the mold and the composite material.

[0015] The internal process variables of the material include local layup angle error and thickness distribution difference;

[0016] The boundary conditions include fixed, sliding, or elastic constraints between the skin and the supporting structure.

[0017] Furthermore, in step S2), the method for confirming the optimal sensor deployment scheme includes the following steps:

[0018] S2.1 Divide the skin surface into M nodes to form a candidate deployment set;

[0019] In the candidate deployment set, execute N P The selection operation generates N. P There are n sensor deployment schemes X, which are used as a candidate scheme set. Each sensor deployment scheme X includes n nodes.

[0020] S2.2. Based on reconstruction error and robustness, a dual objective function is established;

[0021] S2.3, Take the N generated in step S2.1) P Each sensor deployment scheme X is considered as a particle swarm, with each sensor deployment scheme X representing a single particle.

[0022] N non-repeating nodes are randomly selected from the candidate layout set as the initial solution X for each particle. i (0) and the initial optimal solution P i (0) And randomly generate a velocity vector V for each particle. i (0) Then create an empty external archive set; i = 1, 2, ..., N P N = n;

[0023] S2.4 Calculate X for each particle i The function values ​​on the two objectives yield the solution.

[0024] Solution for all particles external archives Merge to form a temporary solution set The initial value of t1 is 0, and when t1 is 0, It is an empty set;

[0025] S2.5, Remove temporary solution sets Find identical solutions in the database, then select the non-dominated solutions and store them in an external archive set. Middle; Determine external archives If the number of solutions is greater than the capacity threshold h, proceed to step 2.6); otherwise proceed to step 2.7.

[0026] 2.6 Calculate the crowding distance of solutions in the external archive set, sort the solutions in the external archive set according to the size of the crowding distance, and then select the top h solutions with the largest crowding distances as the external archive set. Proceed to step 2.7);

[0027] 2.7 Determine the solution for each particle. Is the optimal solution dominable for each particle? like Dominate Then let

[0028] like Dominate Then let

[0029] If they do not dominate each other, then the solution with the higher crowding degree is retained as the optimal solution.

[0030] 2.8. Based on crowding distance, from external archives For each particle X i Choose a facilitator Then based on the optimal solution and guide Update Particle X i speed and location

[0031] Determine if the iteration number t1 is less than the maximum iteration number T. If so, set t1 = t1 + 1 and return to step S2.4; otherwise, output the external archive set. As a set of optimal candidate solutions;

[0032] 2.9. Based on the objectives of the plan, select the optimal deployment plan from the set of superior candidate plans.

[0033] Further, in step S2.1), the candidate deployment set is candidate set = {P1, P2, ..., P...} j ,…,P M}, where each P j Represents the position of a three-dimensional node (x) j ,y j ,z j ).

[0034] Further, in step S2.2), the biobjective function Index(X) is expressed as: min Index(X)=[RRMSE(X), -RBI(X)], stdet(K(X))≠0 (1)

[0035]

[0036] RBI(X)=min(θ c ), c=1,2,…,m1 (3)

[0037] In the formula: RBI(X) is the robustness index;

[0038] RRMSE(X) is the relative root mean square error, used to measure reconstruction error;

[0039] K(X) is the global stiffness matrix corresponding to the sensor deployment scheme;

[0040] n is the number of verification points, i.e., the number of nodes in sensor deployment scheme X;

[0041] This is the reference displacement obtained by scanning with an optical measuring device at the b-th verification point; The displacement at the b-th verification point is obtained using sensor deployment scheme X and interpolation method.

[0042] θ c Let c be the c-th non-zero singular value in the singular value decomposition.

[0043] m1 represents the degree of freedom dimension of the node.

[0044] Further, in step S2.8), the particle X i The velocity and position update formulas are:

[0045]

[0046] In the formula: ω is the inertia weight;

[0047] These represent the velocities of the i-th particle before and after the update at the t1-th iteration;

[0048] c1 and c2 are the individual learning factor and the group learning factor, respectively.

[0049] r1 and r2 are random numbers that follow a uniform distribution;

[0050] This represents the optimal solution for the i-th particle at the t1-th iteration.

[0051] It is the guide of the i-th particle at the t1-th iteration.

[0052] Furthermore, in step S4), constructing the finite element model for full-field gap prediction includes the following steps:

[0053] S4.1 Establish the optimization objective function

[0054] The objective function The formula is:

[0055]

[0056] In the formula: n is the number of sensors;

[0057] This represents the gap value at the a-th sensor location calculated using finite element analysis.

[0058] The gap value measured by the a-th sensor;

[0059] S4.2, Process parameters The data is input into the finite element model to obtain the full-field gap on the skin surface of the composite component, including the gap values ​​at the sensor placement locations. The initial value of t2 is 1, representing the gap value between the sensorless area and the area without a sensor.

[0060] S4.3, Output-based gap value Calculate the objective function based on the actual gap value measured in step S2). judge If the value is less than a threshold, output the finite element model as the full-field gap prediction finite element model; otherwise, calculate the objective function. The gradient is calculated, and then proceed to step S4.4);

[0061] S4.4, Based on the objective function The gradient direction is determined, and the parameters are updated in the opposite direction of that gradient. Let t2 = t2 + 1, and then return to step S4.2);

[0062] The parameter update formula is:

[0063]

[0064] In the formula: This is the parameter vector at the t2th iteration;

[0065] α is the learning rate;

[0066] For the objective function For parameters The gradient.

[0067] Furthermore, in step S4.1), the objective function is constructed. Regularization terms are introduced to limit the range of parameter variation;

[0068] Objective function with regularization term The formula is:

[0069]

[0070] In the formula: λ is the regularization coefficient; m2 is the parameter dimension.

[0071] Furthermore, in step S6), constructing the full-field gap prediction convolutional neural network model includes the following steps:

[0072] S6.1, respectively, the input process parameters and gap value matrix Perform a linear transformation;

[0073] S6.2, based on the processed process parameters As the first channel, the processed gap value matrix As the second channel, an auxiliary mask channel is generated based on the validity of the process parameters and the gap value matrix, and the auxiliary mask channel is used as the third channel;

[0074] The input data of the three channel groups are used as the input data in the large sample training set of the convolutional neural network;

[0075] S6.3 Build a convolutional neural network, including setting the activation function, the number of layers in the network, the number of convolution kernels in each convolutional layer, the size of the convolution kernels and pooling windows, the stride and padding method of convolution and transposed convolution, and the processing strategy of the output layer;

[0076] S6.4 Input the input data from step S6.2) into the constructed convolutional neural network; in the encoding stage, extract local and global features through multiple convolutional and pooling layers; in the feature transformation stage, use convolutional kernels to fuse multi-scale features; in the decoding stage, use transposed convolutional layers to sample and restore high-dimensional features to the full-field gap of the composite material component skin surface with the same output size; the initial value of t3 is 1;

[0077] S6.5 Calculate the mean square error between the full-field gap output in step S6.4) and the full-field gap in the large sample training set in step S5); determine whether the mean square error is less than the threshold. If so, use the current convolutional neural network model as the full-field gap prediction convolutional neural network model; otherwise, proceed to step S6.6.

[0078] S6.6 Determine whether the current iteration number t3 is equal to the maximum iteration number t. 3max If so, adjust the learning rate of the Adam optimizer and set t3 = 1, then return to step S6.1; otherwise, based on the Adam optimizer, adjust the parameters of the convolutional neural network and set t3 = t3 + 1, then return to step S6.3.

[0079] Furthermore, in step S6.5), the formula for calculating the mean square error is:

[0080]

[0081] In the formula: H and W are the spatial dimensions of the image;

[0082] These are the gap values ​​predicted by the convolutional neural network;

[0083] G i,j The gap reference value for the reconstruction of the finite element model.

[0084] The technical effects of this invention are undeniable, and its beneficial effects are as follows:

[0085] 1. This invention provides a complete set of micro-gap detection and prediction schemes applicable to large composite skin structures, covering the entire process of sensor layout optimization, inverse finite element reconstruction and deep learning prediction. It has a high degree of systematicity and engineering feasibility, and is more suitable for the quality assessment of molding of complex shell structures compared with traditional methods.

[0086] 2. The sensor deployment strategy based on dual-target multi-particle swarm optimization proposed in this invention can balance reconstruction accuracy and robustness under limited sensing point conditions, which is significantly better than the traditional equidistant point deployment or empirical point selection method. It achieves more stable displacement reconstruction effect in multiple verification models.

[0087] 3. The deep learning gap prediction network proposed in this invention, based on the joint input of process parameters and gap, can simultaneously model the coupling relationship between structural response and manufacturing process, and realize rapid prediction of gaps across the entire field of large composite materials. Attached Figure Description

[0088] Figure 1 Flowchart of a method for distributed measurement and full-field reconstruction of deformation gaps in large composite parts;

[0089] Figure 2 This diagram illustrates the optimal layout method for micro-gap sensors.

[0090] Figure 3 This is a gap full-field reconstruction algorithm based on inverse finite element analysis;

[0091] Figure 4 This is a deep learning method for process-induced deformation based on convolutional neural networks. Detailed Implementation

[0092] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0093] Example 1:

[0094] A method for distributed measurement and full-field reconstruction of deformation gaps in large composite components includes the following steps:

[0095] S1. Set the process parameters and apply a mold to the composite component based on the current process parameters to form a skin on the surface of the composite component;

[0096] S2. Based on performance evaluation indicators and multi-objective particle swarm optimization algorithm, the optimal sensor layout scheme is confirmed; according to the optimal sensor layout scheme, a limited number of sensors are placed on the skin surface of the composite material component to obtain the gap value matrix.

[0097] S3. Repeat steps S1) to S2) to obtain multiple sets of gap value matrices under different process parameters, and construct a small sample training set for the finite element model; the small sample training set for the finite element model contains approximately several hundred samples, and the specific number is determined according to the actual situation.

[0098] S4. Train the finite element model using a small sample training set to obtain a full-field gap prediction finite element model with process parameters as input and full-field gap of the skin surface of composite material components as output.

[0099] S5. Generate a large sample training set for the convolutional neural network using the finite element model for full-field gap prediction; in the large sample training set for the convolutional neural network, the process parameters and the gap value matrix collected by the sensors are the inputs, and the full-field gap of the skin surface of the composite material component is the output.

[0100] The large training set of the convolutional neural network contains approximately several thousand samples, with the exact number determined based on the actual situation.

[0101] S6. Train the convolutional neural network using a large sample training set to obtain a full-field gap prediction convolutional neural network model.

[0102] S7. Obtain the current process parameters and the corresponding sensor gap value matrix, and input them into the full-field gap prediction convolutional neural network model to obtain the full-field gap of the composite material component skin surface.

[0103] Example 2:

[0104] The main structure of this embodiment is the same as that of Embodiment 1. Further, in step S1), the process parameters include hot-pressing process-related parameters, internal process variables of the material, and boundary conditions.

[0105] The parameters related to the hot-pressing process include curing temperature distribution or temperature gradient, pressurization time / pressure, cooling rate, and the difference in thermal expansion coefficients between the mold and the composite material.

[0106] The internal process variables of the material include local layup angle error and thickness distribution difference.

[0107] The boundary conditions include fixed, sliding, or elastic constraints between the skin and the supporting structure.

[0108] Example 3:

[0109] The main structure of this embodiment is the same as any one of embodiments 1 to 2. Furthermore, in step S2), the method for confirming the optimal sensor deployment scheme includes the following steps:

[0110] S2.1 Divide the skin surface into M nodes to form a candidate deployment set;

[0111] In the candidate deployment set, execute N P The selection operation generates N. P There are n sensor deployment schemes X, which are used as a candidate scheme set. Each sensor deployment scheme X includes n nodes.

[0112] S2.2. Based on reconstruction error and robustness, a dual objective function is established;

[0113] S2.3, Take the N generated in step S2.1) p Each sensor deployment scheme X is considered as a particle swarm, with each sensor deployment scheme X representing a single particle.

[0114] N unique nodes are randomly selected from the candidate layout set as the initial solution for each particle. and the initial optimal solution P i (0) And randomly generate a velocity vector V for each particle. i (0) Then create an empty external archive set; i = 1, 2, ..., N P N = n;

[0115] S2.4 Calculate X for each particle i The function values ​​on the two objectives yield the solution.

[0116] Solution for all particles external archives Merge to form a temporary solution set The initial value of t1 is 0, and when t1 is 0, It is an empty set;

[0117] S2.5, Remove temporary solution sets Find identical solutions in the database, then select the non-dominated solutions and store them in an external archive set. Middle; Determine external archives If the number of solutions is greater than the capacity threshold h, proceed to step 2.6); otherwise proceed to step 2.7.

[0118] 2.6 Calculate the crowding distance of solutions in the external archive set, sort the solutions in the external archive set according to the size of the crowding distance, and then select the top h solutions with the largest crowding distances as the external archive set. Proceed to step 2.7);

[0119] 2.7 Determine the solution for each particle. Is the optimal solution dominable for each particle? like Dominate Then let

[0120] like Dominate Then let

[0121] If they do not dominate each other, then the solution with the higher crowding degree is retained as the optimal solution.

[0122] 2.8. Based on crowding distance, from external archives For each particle X i Choose a facilitator Then based on the optimal solution and guide Update Particle X i speed and location

[0123] Determine if the iteration number t1 is less than the maximum iteration number T. If so, set t1 = t1 + 1 and return to step S2.4; otherwise, output the external archive set. As a set of optimal candidate solutions;

[0124] 2.9. Based on the objectives of the plan, select the optimal deployment plan from the set of superior candidate plans.

[0125] Example 4:

[0126] The main structure of this embodiment is the same as any one of embodiments 2 to 3. Further, in step S2.1), the candidate deployment set is candidate set = {P1, P2, ..., P...} j ,…,P M}, where each P j Represents the position of a three-dimensional node (x) j ,y j ,z j ).

[0127] Example 5:

[0128] The main structure of this embodiment is the same as any one of embodiments 2 to 4. Further, in step S2.2), the bi-objective function Index(X) is expressed as:

[0129] min Index(X)=[RRMSE(X),-RBI(X)],stdet(K(X))≠0 (1)

[0130]

[0131] RBI(X)=min(θ c ), c=1,2,…,m1 (3)

[0132] In the formula: RBI(X) is the robustness index;

[0133] RRMSE(X) is the relative root mean square error, used to measure reconstruction error;

[0134] K(X) is the global stiffness matrix corresponding to the sensor deployment scheme;

[0135] n is the number of verification points, i.e., the number of nodes in sensor deployment scheme X;

[0136] This is the reference displacement obtained by scanning with an optical measuring device at the b-th verification point;

[0137] The displacement at the b-th verification point is obtained using sensor deployment scheme X and interpolation method.

[0138] θ c Let c be the c-th non-zero singular value in the singular value decomposition.

[0139] m1 represents the degree of freedom dimension of the node.

[0140] Example 6:

[0141] The main structure of this embodiment is the same as any one of embodiments 2 to 5. Further, in step S2.8), the particle X... i The velocity and position update formulas are:

[0142]

[0143] In the formula: ω is the inertia weight;

[0144] These represent the velocities of the i-th particle before and after the update at the t1-th iteration;

[0145] c1 and c2 are the individual learning factor and the group learning factor, respectively.

[0146] r1 and r2 are random numbers that follow a uniform distribution;

[0147] This represents the optimal solution for the i-th particle at the t1-th iteration.

[0148] The guide for the i-th particle at the t1-th iteration;

[0149] Example 7:

[0150] The main structure of this embodiment is the same as any one of embodiments 1 to 6. Further, in step S4), constructing the finite element model for full-field gap prediction includes the following steps:

[0151] S4.1 Establish the optimization objective function

[0152] The objective function The formula is:

[0153]

[0154] In the formula: n is the number of sensors;

[0155] This represents the gap value at the a-th sensor location calculated using finite element analysis.

[0156] The gap value measured by the a-th sensor;

[0157] S4.2, Process parameters The data is input into the finite element model to obtain the full-field gap on the skin surface of the composite component, including the gap values ​​at the sensor placement locations. The initial value of t2 is 1, representing the gap value between the sensorless area and the area without a sensor.

[0158] S4.3, Output-based gap value Calculate the objective function based on the actual gap value measured in step S2). judge If the value is less than a threshold, output the finite element model as the full-field gap prediction finite element model; otherwise, calculate the objective function. The gradient is calculated, and then proceed to step S4.4);

[0159] S4.4, Based on the objective function The gradient direction is determined, and the parameters are updated in the opposite direction of that gradient. Let t2 = t2 + 1, and then return to step S4.2);

[0160] The parameter update formula is:

[0161]

[0162] In the formula: This is the parameter vector at the t2th iteration;

[0163] α is the learning rate;

[0164] For the objective function For parameters The gradient.

[0165] Example 8:

[0166] The main structure of this embodiment is the same as that of embodiment 7. Further, in step S4.1), the objective function is constructed. Regularization terms are introduced to limit the range of parameter variation;

[0167] Objective function with regularization term The formula is:

[0168]

[0169] In the formula: λ is the regularization coefficient; m2 is the parameter dimension.

[0170] Example 9:

[0171] The main structure of this embodiment is the same as any one of embodiments 1 to 8. Further, in step S6), constructing the full-field gap prediction convolutional neural network model includes the following steps:

[0172] S6.1, respectively, the input process parameters and gap value matrix Perform a linear transformation;

[0173] S6.2, based on the processed process parameters As the first channel, the processed gap value matrix As the second channel, an auxiliary mask channel is generated based on the validity of the process parameters and the gap value matrix, and the auxiliary mask channel is used as the third channel;

[0174] The input data of the three channel groups are used as the input data in the large sample training set of the convolutional neural network;

[0175] S6.3 Build a convolutional neural network, including setting the activation function ReLU, the number of network layers, the number of convolution kernels in each convolutional layer, the size of the convolution kernels and pooling windows, the stride and padding method of convolution and transpose convolution, and the processing strategy of the output layer;

[0176] S6.4 Input the input data from step S6.2) into the constructed convolutional neural network; in the encoding stage, extract local and global features through multiple convolutional and pooling layers; in the feature transformation stage, use convolutional kernels to fuse multi-scale features; in the decoding stage, use transposed convolutional layers to sample and restore high-dimensional features to the full-field gap of the composite material component skin surface with the same output size; the initial value of t3 is 1;

[0177] S6.5 Calculate the mean square error between the full-field gap output in step S6.4) and the full-field gap in the large sample training set in step S5); determine whether the mean square error is less than the threshold. If so, use the current convolutional neural network model as the full-field gap prediction convolutional neural network model; otherwise, proceed to step S6.6.

[0178] S6.6 Determine whether the current iteration number t3 is equal to the maximum iteration number t. 3maxIf so, adjust the learning rate of the Adam optimizer and set t3 = 1, then return to step S6.1; otherwise, based on the Adam optimizer, adjust the parameters of the convolutional neural network and set t3 = t3 + 1, then return to step S6.3.

[0179] Example 10:

[0180] The main structure of this embodiment is the same as that of Embodiment 9. Further, in step S6.5, the formula for calculating the mean square error is:

[0181]

[0182] In the formula: H and W are the spatial dimensions of the image;

[0183] These are the gap values ​​predicted by the convolutional neural network;

[0184] The gap reference value for the reconstruction of the finite element model.

[0185] Example 11:

[0186] The main structure of this embodiment is the same as any one of embodiments 1 to 10. Furthermore, to achieve efficient and accurate detection and modeling of micro-gaps generated during the molding and application process of large composite material skins, this invention proposes a complete scheme consisting of three parts: an optimal layout method for micro-gaps sensors, a gap full-field reconstruction algorithm based on inverse finite element analysis, and a modeling method for rapid gap prediction combined with deep learning, as shown in the appendix. Figure 1 As shown. This method can achieve high-precision estimation of the gap distribution on the entire skin surface under limited measurement points, and has scalable real-time prediction capabilities, making it suitable for assembly quality control and service condition assessment of large composite structures.

[0187] 1. Optimal Layout Method for Micro-Gap Sensors

[0188] To achieve high-precision modeling of the gap distribution after molding large composite material skins, a limited number of sensors must first be deployed on the skin surface, and their optimal spatial combination must be determined through optimization algorithms. The overall process is shown in the attached figure. Figure 2 As shown. Suppose the skin surface has been divided into M candidate nodes, forming a candidate set = {P1, P2, ..., P}. j ,…,P M}, where each P j Represents the position of a three-dimensional node (x) j ,y j ,z j Select n points from these to form a sensor deployment scheme:

[0189]

[0190] Next, we will minimize two performance evaluation metrics: reconstruction error and robustness. First, we define the accuracy metric RRMSE (Relative Root Mean Square Error), which represents the ratio of the prediction error to the maximum reference displacement, and is used to measure reconstruction accuracy.

[0191]

[0192] in, The reference displacement at the b-th calibration point (obtained by scanning with an optical measuring device) is... The displacement is obtained by interpolation of the entire surface using scheme X, where N is the total number of verification points.

[0193] The Reconstruction Robustness Index (RBI) measures a system's sensitivity to sensor errors, and its definition is as follows:

[0194]

[0195] Where A(X) is the displacement-gap transformation matrix, which depends on the sensor position; It is the sensor measurement gap vector; θ c It is the c-th non-zero singular value in the singular value decomposition; n1 is the degree of freedom dimension of the node.

[0196] The two objectives can be combined into a bi-objective optimization problem as follows:

[0197] min Index(X)=[RRMSE(X),-RBI(X)],stdet(K(X))≠0

[0198] Where K(X) is the global stiffness matrix corresponding to the layout scheme.

[0199] To solve the aforementioned bi-objective optimization problem, a multi-objective particle swarm optimization algorithm (MOPSO) is used to search for sensor deployment schemes. This algorithm defines each particle as a specific sensor combination scheme. That is, it is an integer sequence of length n, corresponding to the candidate node index.

[0200] Each step of the optimization process is as follows:

[0201] (1) Initialize the population and set the particle swarm size to N. p The initial solution for each particle is formed by randomly selecting n non-repeating nodes from the candidate point set. At the same time, a velocity vector V is randomly generated for each particle. i (0) Its dimensions are consistent with the particle positions, and its elements are integer variables representing the direction of index movement. All particles constitute the initial population. Next, the velocity update strategy and position update formula are defined. In each iteration, the velocity update of the i-th particle is performed according to the following formula:

[0202]

[0203] in ω represents the current velocity; ω is the inertia weight, which is gradually decreased to enhance convergence; c1 and c2 are the individual learning factor and the group learning factor, respectively; r1 and r2 ∈ [0,1] are random numbers following a uniform distribution. It is the historical optimal solution for particle i; It is the guiding particle in the current external non-dominated solution set (selected as the one with the minimum crowding on the Pareto boundary). Position is updated after velocity update:

[0204]

[0205] Here, round represents the rounding operation and performs a validity check on the result to ensure that the index is still within the range of the candidate set and that there are no duplicates.

[0206] (2) In each iteration, for all particles Decode the solution and calculate its corresponding biobjective function values, namely RRMSE(Xi) and RBI(Xi), to construct the target vector set of the current solution set.

[0207] The solutions for all particles are unified and incorporated into the external archive. Pareto optimality and distribution breadth of the solution set are maintained through non-dominated sorting and crowding distance calculation. If the solution set exceeds the capacity, the solution with the lowest crowding is discarded.

[0208] The above process iterates for T rounds (e.g., 200 generations), eventually returning the set of non-dominated solutions retained in the external solution set. This represents the optimal candidate solution set for all available sensor deployments.

[0209] The optimal candidate set typically contains multiple options, representing a combination of sensor layouts that strikes a balance between two objectives: minimizing Reconstruction Reduction (RRMSE) and maximizing Reconstruction Bias (RBI). If reconstruction accuracy is a primary concern, the option with the lowest RRMSE (minimum prediction error and most accurate mold gap reconstruction) can be selected. If system robustness (e.g., the presence of measurement noise or sensor susceptibility) is a primary concern, the option with the highest RBI (least sensitive to gap errors and highest system stability) can be chosen. We usually select a balanced option that strikes a middle ground, achieving a high level of both accuracy and stability.

[0210] 2. Gap Full-Field Reconstruction Algorithm Based on Inverse Finite Element Analysis

[0211] After the sensor deployment is completed, the gap value matrix of the deployed sensors can be obtained. In the optimization of the previous method, the obtained full-field gap of the surface shape was further reconstructed through interpolation, thereby selecting the optimal sensor layout. However, in order to obtain a more accurate full-field gap of the surface shape, a gap full-field reconstruction algorithm based on inverse finite element analysis will be introduced next, as shown in the appendix. Figure 3 As shown.

[0212] The approach of inverse finite element analysis (IEM) is to adjust the model's input parameters (such as layup angle error, curing temperature gradient, interface contact state, and boundary constraints) to make the model's calculation results as close as possible to the sensor's measurement data. The IEM process can be reduced to an optimization problem: by minimizing the error between the finite element model's calculation results and the sensor's measurement results, the global deformation that satisfies the gap condition is found. The objective function is defined using mean square error.

[0213]

[0214] in This represents the gap value at the a-th sensor position calculated by finite element analysis.

[0215] The actual measured value of the a-th sensor is represented by the gap value matrix. We obtain n, which is the number of sensors. This objective function measures the error between the simulation results and the measured values, and the goal of optimization is to minimize this error.

[0216] In numerical optimization, gradient descent is used to iteratively adjust the input parameters in the finite element model. The objective function value is reduced by shifting the parameters in the opposite direction of the gradient of the error function in each iteration. The basic formula for gradient descent is:

[0217]

[0218] in It is the parameter vector at the t2th iteration; α is the learning rate, which determines the step size of parameter updates in each iteration; It is the objective function For parameters The gradient of the objective function represents the direction and rate of change of the objective function with respect to the parameters. The parameters θ consist of the following three types of variables:

[0219] Hot-press process related parameters: curing temperature distribution or temperature gradient (temperature causes thermal deformation), pressurization process time / pressure (such as vacuum bag pressure or mold closure degree), cooling rate (affects residual stress), and difference in thermal expansion coefficient between mold and composite material (CTE mismatch).

[0220] Internal process variables of the material: local layup angle error, thickness distribution difference, etc.

[0221] Boundary conditions: such as fixed, sliding, or elastic constraints between the skin and the supporting structure.

[0222] Furthermore, inverse finite element problems often exhibit ill-posedness, meaning that small measurement errors can lead to large computational errors. To address this issue, a regularization term is incorporated into the optimization process, using L2 regularization to limit the range of parameter variation and prevent drastic parameter changes from causing physically unreasonable results. The objective function for regularization is expressed as:

[0223]

[0224] Where λ is the regularization coefficient, controlling the strength of regularization; m2 is the dimension of the parameter, which is 3 here considering three parameters. In the specific optimization steps, based on the experimental data from the previous finite element analysis model, including the hot-pressing process parameters, internal material process variables, and boundary conditions, a reverse finite element analysis is performed using these parameters to calculate the deformation at each sensor location. Then, based on the actual measured values ​​of the gap sensor, the objective function is calculated. This refers to the error between the simulated value and the actual measured value.

[0225] To update the parameters, the gradient of the objective function with respect to the parameter θ needs to be calculated. Since parameter θ includes multiple variables (hot-pressing process parameters, internal material process variables, and boundary conditions), the partial derivative of each parameter with respect to the objective function is calculated. The gradient is calculated using numerical differentiation.

[0226]

[0227] Where e j It is the unit vector in the direction of the j-th parameter; ∈ is a very small value used to calculate finite differences; This is the partial derivative of the objective function with respect to the j-th parameter. The influence of these three variables on the finite element results is calculated separately, and then based on the formula...

[0228]

[0229] Update the parameter vector based on gradient information.

[0230] An adaptive method is used to adjust the learning rate α to prevent the algorithm from diverging or converging too slowly. This step is then repeated, iteratively updating the parameters and recalculating the objective function each time, until the error of the objective function is reduced to a preset threshold.

[0231] When the objective function error converges to a small range, the optimized finite element model can accurately reflect the overall gap distribution of the skin. This method establishes an optimization problem, iteratively adjusts the input parameters of the finite element model, and ultimately matches the calculation results with the sensor measurements. It not only explains the deformation at the sensor location but also infers the gap information of other areas where no sensors are installed through the model.

[0232] 3. Modeling methods for fast gap prediction using deep learning

[0233] To achieve rapid assessment and prediction of gaps in composite skins, a deep learning modeling method is introduced based on sensor-reconstructed data. This method takes finitely measurable gap data and molding process parameters as input, and outputs a predicted gap distribution map of the entire skin through an end-to-end regression neural network.

[0234] First, a large sample reference set needs to be constructed based on the skin deformation and gap distribution maps under different working conditions generated by the finite element model. The specific process is as follows: record the process parameters such as curing temperature and cooling rate during the composite molding process under a certain environment, deploy gap sensors after molding to collect real gap information, and obtain a high-reliability full-field gap map through inverse finite element reconstruction, which serves as the real sample for training.

[0235] The actual measured values ​​of the gap sensor and the process parameters are input into the neural network to obtain the predicted full-field gap diagram. The results are compared with the simulation results to continuously optimize the model and iterate repeatedly.

[0236] The model's input consists of two parts:

[0237] (1) Process parameters: including hot-pressing process parameters, internal material process variables, and boundary conditions, i.e., P = [α1, α2, ..., α k ]

[0238] (2) The measured value of the distributed gap sensor is ε = [ε1, ε2, ..., εn There are n sensors in total, selected according to the optimized deployment strategy, and their actual measurement values ​​are taken.

[0239] After the two inputs are linearly transformed (embedding) separately, they are concatenated to form a tensor input of a single-channel two-dimensional image (as shown in the attached image). Figure 4 (as shown in a). Here, sensor measurements are mapped to a discrete sampling map in space, and process parameters, after being broadcast, are embedded as channel vectors, which, together with the gap map, form a three-channel input tensor, in the form of:

[0240] X in ∈R H×W×3

[0241] Wherein, H and W represent the image spatial dimensions (consistent with the discrete mesh of the skin), and the number of channels 3 corresponds to the gap data channel, the process channel, and the auxiliary mask channel, respectively. The schematic diagram of the three-channel image convolution is attached. Figure 4 As shown in b.

[0242] The detailed network structure is attached. Figure 4 As shown in c, the encoding stage extracts local and global features from the input image through multiple convolutional and pooling layers, with the dimensions increasing sequentially from 20×20×3 to 512×20×20. The feature transformation stage performs 3×3 convolutions on the feature map to fuse multi-scale features. The decoding stage uses transposed convolutional layers (deconvolution) to progressively upsample the high-dimensional features, restoring them to a prediction map with the same size as the output. This represents the gap distribution predicted on the skin surface.

[0243] During the training phase, existing simulation results are used as supervision labels. Each training sample is mapped from (P,ε) to its corresponding reference gap map G(x,y), using mean squared error as the loss function.

[0244]

[0245] in, G represents the gap value predicted by the network. i,j These are reference values ​​obtained from simulation / reconstruction.

[0246] The Adam algorithm was chosen for optimization, with an initial learning rate of 0.001 and 100 training epochs. Each epoch used 64 samples for mini-batch updates. After training, the model can be saved for subsequent deployment.

[0247] After the model is deployed, the user can input any set of molding process parameters and the gap values ​​measured by the sensors in real time, and the trained network can directly predict the gap image.

Claims

1. A method for measuring and reconstructing the deformation gap distribution of a large composite part, characterized in that, The method comprises the following steps: S1, setting process parameters, and based on the current process parameters, the composite component is attached to the mold to form a skin on the surface of the composite component; S2, based on the performance evaluation index and the multi-objective particle swarm optimization algorithm, the optimal sensor arrangement scheme is determined; according to the optimal sensor arrangement scheme, a limited number of sensors are arranged on the skin surface of the composite material component, so as to obtain a gap value matrix; S3, repeating steps S1)~S2), obtaining a plurality of gap value matrices under different process parameters, and constructing a finite element model small sample training set; S4, training the finite element model using the finite element model small sample training set to obtain a full-field gap prediction finite element model taking process parameters as input and composite material component skin surface full-field gap as output; S5, generating a convolutional neural network large sample training set through the full-field gap prediction finite element model; in the convolutional neural network large sample training set, the process parameters and the gap value matrix collected by the sensor are input, and the composite material component skin surface full-field gap is output; S6, training the convolutional neural network using the convolutional neural network large sample training set to obtain a full-field gap prediction convolutional neural network model; S7, obtaining the current process parameters and the sensor collected gap value matrix corresponding to the current process parameters, and inputting them into the full-field gap prediction convolutional neural network model to obtain the composite material component skin surface full-field gap.

2. The method of claim 1, wherein: In step S1), the process parameters include hot-pressing process related parameters, material internal process variables and the boundary conditions; The hot-pressing process related parameters include curing temperature distribution or temperature gradient, pressurization process time / pressure, cooling rate, and difference in thermal expansion coefficient between the mold and the composite material; The material internal process variables include local layer angle error, thickness distribution difference; The boundary conditions include fixing, sliding or elastic constraint between the skin and the support structure.

3. The method of claim 1, wherein: In step S2), the method for confirming the optimal sensor arrangement scheme comprises the following steps: S2.1, dividing the surface of the skin into M nodes to form a candidate arrangement set; In the candidate deployment set, perform N P sub-selection operations to generate N P sensor deployment schemes X as a candidate scheme set, wherein each sensor deployment scheme X includes n nodes; S2.2, establishing a double objective function based on reconstruction error and robustness; S2.3, generating N P sensor deployment schemes X as a swarm of particles, each sensor deployment scheme X representing a particle; Randomly select N non-repeating nodes from the candidate deployment set as the initial solution of each particle and the initial optimal solution and randomly generate a velocity vector for each particle Then create an empty external file set; i = 1, 2, …, N P ; N = n; S2.4, compute each particle X i The function value on two targets, get the solution solving for all particles with the external file set merge, forming a temporary solution set t1 has an initial value of 0, and when t1 is 0, is an empty set; S2.5, removing the temporary set identical solutions, and then selecting from among them the non-dominated solutions to be stored in the external archive whether the number of solutions in the external archive is greater than the capacity threshold h, and if so, proceeding to step 2.6), otherwise proceeding to step 2.7); 2.6, calculate the crowded distance of solutions in the external archive, and sort the solutions in the external archive according to the size of the crowded distance, and then screen out the first h solutions with the largest crowded distance as the external archive go to step 2.7); 2.7, solution of each particle whether the optimal solution of each particle is disposable If disposable Let If dominate then let If not, the solution with the higher congestion is retained as the optimal solution 2.

8. Based on the crowding distance, select one leader from the external archive set for each particle X i select a leader then update the velocity and position of the particle X i based on the best solution and the leader determining whether the iteration number t1 is smaller than the maximum iteration number T, if yes, setting t1 = t1 + 1 and returning to step S2.4), otherwise outputting the external profile set as the optimal candidate set; 2.9, selecting the optimal arrangement scheme from the optimal candidate scheme set based on the scheme target.

4. The method of claim 3, wherein the method further comprises: determining the deformation gap distribution of the large composite part based on the measured deformation gap distribution of the large composite part. In step S2.1), the candidate set is candidate set = {P1, P2,..., P j ,…,P M} where each P j represents a three-dimensional node position (x j ,y j ,z j ).

5. The method of claim 3, wherein the method further comprises: determining the deformation gap distribution of the large composite part based on the measured deformation gap distribution of the large composite part. In step S2.2), the double objective function Index(X) is represented as: min Index(X)=[RRMSE(X),-RBI(X)],s.t.det(K(X))≠0 (1) RBI(X) = min(θ c ), c = 1, 2,..., m1 (3) In the formula: RBI(X) is a robustness index; RRMSE(X) is a relative root mean square error for measuring reconstruction error; K(X) is a global stiffness matrix corresponding to the sensor arrangement scheme; b is a check point, that is, the number of nodes in the sensor arrangement scheme X; is the reference displacement obtained by scanning with the optical measuring device at the b-th check point; Displacement at the bth checkpoint obtained using sensor layout X and interpolation method; θ c is the cth non-zero singular value in the singular value decomposition; m1 is the node freedom dimension.

6. The method of claim 3, wherein: In step S2.8) the particles X i The velocity and position update equations are: In the formula: ω is an inertia weight; respectively the velocity of the i-th particle before and after the update at the t1-th iteration. c1 and c2 are individual learning factors and group learning factors, respectively; r1 and r2 are random numbers obeying uniform distribution; is the optimal solution for the i-th particle at the t1-th iteration; is the leader of the ith particle at the tth iteration.

7. The method of claim 1, wherein: In step S4), constructing the full-field gap prediction finite element model comprises the following steps: S4.1, establishing an optimization objective function The objective function The formula is: In the formula: n is the number of sensors; gapafor the finite element analysis calculation at the a-th sensor position; a gap value measured for the ath sensor; S4.2, the process parameters Input into the finite element model to obtain the full-field gap of the composite component skin surface, including the gap value at the sensor layout position And the gap value u2;t2 of the area without sensor is 1; S4.3, based on the output gap value and the actual gap value measured in step S2), a target function is calculated a decision is made whether it is smaller than a threshold value, if yes, the finite element model is output as a full-field gap prediction finite element model, otherwise the gradient of the target function is calculated and step S4.4) is entered; ​ S4.4, updating the parameters in the opposite direction of the gradient direction of the objective function based on the gradient direction, along the opposite direction of the gradient and let t2 = t2 + 1, then return to step S4.2); The parameter update formula is: In the formula: is the parameter vector at the t2th iteration; α is the learning rate; for the objective function the gradient of the parameters .

8. The method of claim 7, wherein: In step S4.1), an objective function is constructed a regularization term is introduced to limit the range of variation of the parameters; Objective function with regularization term The formula is: In the formula, λ is a regularization coefficient; and m2 is a parameter dimension.

9. The method of claim 1, wherein: In step S6), the constructing the full-field gap prediction convolutional neural network model comprises the following steps: S6.1, performing a linear transformation on the input process parameters and the gap value matrix respectively; S6.2, with the processed process parameters as a first channel, a processed gap value matrix as a second channel, generating an auxiliary mask channel from the process parameters and the validity of the gap value matrix, and taking the auxiliary mask channel as a third channel; The input data of the three channel groups is taken as input data in the large sample training set of the convolutional neural network; S6.3, building a convolutional neural network, including setting an activation function, a number of layers of the network, a number of convolution kernels of each convolution layer, a size of the convolution kernel and the pooling window, a step and a padding mode of the convolution and the transposed convolution, and a processing strategy of the output layer; S6.4, inputting the input data of step S6.2) to the built convolutional neural network; in the encoding stage, extracting local spatial and global features through a plurality of convolution layers and pooling layers; in the feature transformation stage, fusing multi-scale features by convolution kernel convolution; in the decoding stage, using a transposed convolution layer to sample, restoring high-dimensional features to a full-field gap of a composite material component skin surface with the same output size as the initial value of t3; S6.5, calculating a mean square error of the full-field gap output by step S6.4) and the full-field gap in the large sample training set of step S5); judging whether the mean square error is less than a threshold value, if yes, taking the current convolutional neural network model as the full-field gap prediction convolutional neural network model, otherwise, entering step S6.6); S6.6, judging whether the current iteration number t3 is equal to the maximum iteration number t 3max If yes, adjusting the learning rate of the Adam optimizer, and letting t3 = 1, returning to step S6.1); otherwise, adjusting the parameters of the convolutional neural network based on the Adam optimizer, and letting t3 = t3 + 1, returning to step S6.3).

10. The method of claim 9, wherein: In step S6.5, the formula for calculating the mean square error is: In the formula, H and W are image space dimensions; gap value predicted for the convolutional neural network; G i,j The gap reference value is for finite element model reconstruction.

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