A Method for Strength Prediction and Bolt Layout Optimization of Four-Nail Connection Structures in Composite Materials Based on Physical Information Neural Networks
By using a physical information neural network-based approach, combined with refined simulation modeling and optimization algorithms, the strength analysis and bolt layout optimization problems of composite four-nail connection structures were solved, achieving efficient and reliable design and optimization. This approach breaks through the bottlenecks of traditional methods and improves design efficiency and prediction accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HARBIN INST OF TECH
- Filing Date
- 2025-11-03
- Publication Date
- 2026-07-17
Smart Images
Figure CN121502940B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for predicting the strength of a four-nail connection structure of composite materials and optimizing the bolt layout based on a physical information neural network, belonging to the field of composite material design technology. Background Technology
[0002] Composite materials, with their high specific strength, high specific stiffness, and lightweight properties, have become an irreplaceable core structural material in high-end equipment fields such as aviation, aerospace, and rail transportation. Among the typical connection forms of composite material components, the four-nail connection structure is widely used due to its compact structure and strong load-bearing capacity, and its connection strength directly determines the overall reliability and service life of the equipment.
[0003] Currently, the strength analysis of composite four-nail connection structures mainly adopts two technical approaches: finite element simulation and experimental testing. Although the finite element method can achieve high-precision analysis, it suffers from technical bottlenecks such as complex modeling process, high computational resource consumption, and long solution cycle. Experimental testing methods, on the other hand, require customized specimens, the construction of test platforms, and the completion of multi-condition loading tests, which are limited by long testing cycles, high costs, and difficulty in covering all working conditions.
[0004] In the application of data-driven neural network models, pure data-driven surrogate models improve computational efficiency by establishing a mapping relationship between input parameters and structural responses. However, such models rely on a large amount of high-quality labeled data as a training basis, which is costly to acquire and difficult to cover the entire parameter space. In addition, the prediction results may violate the basic conservation laws of material mechanics or boundary condition constraints, resulting in physically unreasonable predictions in areas not covered by training data, and insufficient generalization ability and reliability.
[0005] Meanwhile, the bolt layout optimization of composite four-nail connection structures needs to achieve the optimization goal of maximizing connection strength or minimizing weight by adjusting the bolt position distribution while satisfying multiple types of geometric constraints. However, traditional optimization methods often adopt a serial solution mode of separate surrogate models and optimization algorithms, which makes it difficult to achieve efficient collaboration between strength prediction models and layout optimization algorithms. This results in technical problems such as low optimization efficiency, poor convergence, and easy getting trapped in local optima, failing to meet the dual requirements of optimization efficiency and reliability in engineering applications. Summary of the Invention
[0006] To address the problems existing in the background technology, the present invention provides a method for strength prediction and bolt layout optimization of composite material four-nail connection structure based on physical information neural network.
[0007] To achieve the above objectives, the present invention adopts the following technical solution: a method for strength prediction and bolt layout optimization of a composite material four-nail connection structure based on a physical information neural network, the method comprising the following steps:
[0008] S1: Simulation modeling and verification of composite material four-nail connection structure;
[0009] S1 includes the following steps:
[0010] S101: Define the basic parameters required to construct the finite element model, including: geometric configuration, material properties, layup sequence, and contact boundary conditions;
[0011] S102: C3D8R three-dimensional solid element discrete composite laminate is used to ensure that each layer of material is divided into at least one mesh; local mesh refinement is performed on the stress concentration area around the bolt holes;
[0012] S103: Configure the damage assessment and evolution calculation model;
[0013] S103 includes the following steps:
[0014] S10301: Initial damage is determined for single-layer plates under different directions and stress modes using the three-dimensional hashin criterion, including:
[0015] Failure criterion for tensile damage in one direction of a single-layer plate:
[0016] (1)
[0017] Single-layer plate compressive damage failure criterion in one direction:
[0018] (2)
[0019] Failure criteria for single-layer plate under two-way tensile damage:
[0020] (3)
[0021] Single-layer plate two-way compressive damage failure criteria:
[0022] (4)
[0023] Three-directional tensile damage failure criteria for single-layer plates:
[0024] (5)
[0025] Three-directional compressive damage failure criteria for single-layer plates:
[0026] (6)
[0027] In equations (1)-(6):
[0028] , , These represent the normal stresses in three directions of a single-layer plate;
[0029] , , These represent the shear stresses in three directions of a single-layer plate;
[0030] , , These represent the tensile strengths of a single-layer plate in three directions.
[0031] , , These represent the compressive strength of a single-layer plate in three directions.
[0032] , , These represent the shear strengths of a single-layer plate in the 12, 13, and 23 directions, respectively.
[0033] This represents the weighting factor for the effect of shear on tension;
[0034] S10302: Calculation of damage variables based on a bilinear softening model using fracture energy:
[0035] (7)
[0036] In equation (7):
[0037] For damage variables;
[0038] The equivalent strength parameter for the type I fracture failure mode;
[0039] This represents the initial damage equivalent displacement under the Type I fracture failure mode;
[0040] The displacement is the equivalent of the final complete damage under the Type I fracture failure mode.
[0041] The value is in the Hashin criteria;
[0042] The fracture energy density is the fracture energy density under the type I fracture failure mode.
[0043] The initial damage equivalent stress is given under the Type I fracture failure mode.
[0044] S10303: Based on the Murakami-Ohno three-dimensional damage constitutive theory, the stiffness degradation matrix after damage can be obtained as follows:
[0045] (8)
[0046] In equation (8):
[0047] These are the single-direction stiffness degradation coefficients corresponding to the three directions;
[0048] These are the stiffness degradation coefficients for multi-directional coupling in the three directions, respectively;
[0049] These are the stiffness coefficients related to the elastic modulus in the three directions, respectively.
[0050] These are the coupling stiffness coefficients in directions 13 and 23, respectively;
[0051] The stiffness coefficients are Poisson's ratio-related in 12 directions;
[0052] S10304: Introducing a viscosity regularization method:
[0053] (9)
[0054] In equation (9):
[0055] The damage variable after viscosity regularization;
[0056] The viscosity coefficient under the type I fracture failure mode;
[0057] This is the current time step;
[0058] For time step;
[0059] S10305: Zero-thickness cohesive elements are inserted at the ply interfaces to characterize interlayer delamination behavior, and a secondary stress criterion is used to determine the initiation of delamination.
[0060] (10)
[0061] In formula (10):
[0062] The normal direction of the element;
[0063] and These are the two shear directions of the unit;
[0064] The stress intensity is the material's normal direction.
[0065] and These represent the stress intensity in the two shear directions of the material, respectively.
[0066] S10306: Using a bilinear model for hierarchical evolution, stiffness-damage evolution parameters can be obtained. for:
[0067] (11)
[0068] In equation (11):
[0069] This refers to the opening displacement of the element node when the material is completely damaged and fails.
[0070] This represents the maximum opening displacement of the element node during the process;
[0071] This refers to the opening displacement of the unit nodes at the start of material layering.
[0072] S10307: Using the Black-K criterion to describe the hierarchical extension of hybrid modes:
[0073] (12)
[0074] In equation (12):
[0075] It exhibits composite fracture toughness;
[0076] This represents the total fracture energy release rate;
[0077] is the material constant of the BK criterion.
[0078] S104: Set contact boundary conditions: the bolt and the hole wall are in surface-to-surface contact, the normal direction is hard contact, and the tangential direction introduces Coulomb friction;
[0079] S105: Apply a symmetrical constraint to one side of the model and a displacement load to the other side of the model;
[0080] S106: Perform tensile tests on the composite material four-nail connection structure test specimen until the specimen fails. Compare the simulation results with the test results in multiple dimensions. If the ultimate load error is <10% and the failure mode predicted by the model is consistent with the experimental observation, the model is deemed reliable; otherwise, return to S101-S104 to adjust the modeling parameters, rebuild the model, and repeat the verification process.
[0081] S2: Based on the model obtained in S1, a parameterized method is used to generate a basic dataset, and a conditional generative adversarial network is used to expand the basic dataset;
[0082] S2 includes the following steps:
[0083] S201: The origin of the coordinate system is the geometric center of the composite material connection. A two-dimensional plane coordinate system is established, and the bolt layout of the composite material four-nail connection structure is parameterized into a 5-dimensional design variable vector, including: the coordinates of the bolt symmetry center. Bolts Spacing in direction Bolts Spacing in direction and standardized bolt types Based on the above parameters, the center coordinates of the four bolts are derived as follows: , , as well as ;
[0084] S202: Using the optimal Latin hypercube sampling method, W samples satisfying geometric constraints are generated in the 5-dimensional design space;
[0085] S202 includes the following steps:
[0086] S20201: Preset geometric constraints, including: minimum distance constraint between bolts, distance constraint from bolt center to plate edge, and length constraint of connection area;
[0087] S20202: Generate a large number of candidate points;
[0088] S20203: Select W sample points that simultaneously satisfy optimal space-filling performance and preset geometric constraints using a genetic algorithm.
[0089] S203: For each set of 5-dimensional design variables generated, parametric reconstruction is performed based on the model verified in S1. Simulation calculations are then executed after applying the same material parameters and boundary conditions to extract 5-dimensional response variables, forming the target output vector for training the physical information neural network, i.e., the basic dataset. The 5-dimensional response variables include:
[0090] Final failure load and the working load borne by each of the four bolts under 80% ultimate load. ;
[0091] S204: Introduce a conditional generative adversarial network to generate M groups of expanded datasets;
[0092] The construction and training of the conditional generative adversarial network described in S204 includes the following steps:
[0093] S20401: Input and Output Definitions:
[0094] The condition vector is a 5-dimensional design variable vector;
[0095] The random noise is a 10-dimensional random noise vector sampled from a standard normal distribution;
[0096] The target output is a 5-dimensional response variable vector;
[0097] S20402: Mesh structure:
[0098] Generator :
[0099] A fully connected neural network is used, whose input is a concatenation of a conditional vector and a noise vector, so the input layer has a dimension of 15. The network contains 3 hidden layers, all of which use the ReLU activation function, and the output layer has a dimension of 5 and uses a linear activation function.
[0100] Discriminator :
[0101] A fully connected neural network is used, whose input is the concatenation of the conditional vector and the response vector. Therefore, the input layer has a dimension of 10. The network contains 3 hidden layers and uses the LeakyReLU activation function. The output layer has a dimension of 1 and uses the Sigmoid activation function.
[0102] S20403: Training value function:
[0103] The conditional generative adversarial network is trained through mini-maximum games, with a value function... for:
[0104] (13)
[0105] In equation (13):
[0106] The distribution of real simulation data;
[0107] Noise distribution;
[0108] It is a conditional vector;
[0109] For the response vector;
[0110] This is the noise vector;
[0111] Generator The goal is to minimize ;
[0112] Discriminator The goal is to maximize the accuracy of the real data. of And minimize the impact on the generated data pairs of ;
[0113] S20404: Train the generator separately using the Adam optimizer. and discriminator In the early stages of training, the discriminator is updated multiple times before the generator is updated.
[0114] S205: Merge the base dataset and the augmented dataset to form a complete dataset, and divide the complete dataset into a training set, a validation set, and a test set in a ratio of 7:2:1.
[0115] S3: Construction and training of physical information neural network models;
[0116] S3 includes the following steps:
[0117] S301: Network architecture design and initialization, including:
[0118] The input layer consists of 5-dimensional design variables;
[0119] The output layer consists of 5-dimensional response variables;
[0120] The hidden layer employs a multilayer perceptron structure to progressively extract and combine high-order nonlinear representations of input features;
[0121] The hidden layers use the ReLU activation function, and the output layer uses the linear activation function.
[0122] All network weights are initialized using the He normal distribution method, with bias initialized to zero.
[0123] S302: Obtain the total loss function using a composite weighted method. :
[0124] (14)
[0125] In equation (14):
[0126] For data fitting loss;
[0127] Loss due to global force balance constraints;
[0128] This is a regularization term for physical laws;
[0129] , The hyperparameters are used to balance the weights of various losses;
[0130] S303: Data fitting loss measures the difference between network predictions and high-fidelity simulation data.
[0131] (15)
[0132] In equation (15):
[0133] The number of samples;
[0134] and These are the weighting coefficients;
[0135] The first The actual final failure load and the predicted final failure load of each sample;
[0136] The first The first sample The actual working load and the predicted working load of each bolt;
[0137] S304: The force balance constraint loss forced model follows the global force balance principle, ensuring that the sum of the working loads of the four bolts equals 80% of the failure load.
[0138] (16)
[0139] S305: Physical law regularization terms include gradient terms based on automatic differentiation calculations.
[0140] (17)
[0141] In equation (17):
[0142] , , Here, represents the gradient regularization coefficient.
[0143] S306: Training strategy and convergence control.
[0144] S4: The prediction accuracy and generalization ability of the physical information neural network model are systematically calibrated and verified using experimental data;
[0145] S4 includes the following steps:
[0146] S401: Select experimental samples of composite four-nail connection structures from group J that did not participate in simulation and model training as independent test data for model calibration and validation; clarify that the hyperparameter optimization objective is to minimize the mean relative error (MRE) on the validation set, and the hyperparameters to be optimized include: physical constraint weight coefficients. , Gradient regularization coefficient , , And the number of neurons in the hidden layer;
[0147] S402: Automatically tune the hyperparameters in the physical information neural network using Bayesian optimization method;
[0148] S403: Three indicators are used to evaluate the model's prediction accuracy, including:
[0149] Mean relative error:
[0150] (18)
[0151] Coefficient of determination:
[0152] (19)
[0153] Maximum relative error:
[0154] (20)
[0155] In equations (18)-(20):
[0156] These are the model's predicted values;
[0157] The actual value;
[0158] The average of the true values;
[0159] S404: After Bayesian optimization and hyperparameter tuning, the model must meet the following accuracy requirements:
[0160] (twenty one)
[0161] S5: Construct an automatic optimization framework for bolt layout of composite material four-nail connection structure and output the optimal bolt layout parameters.
[0162] S5 includes the following steps:
[0163] S501: Define the optimization variables as 5-dimensional design variables, and the objective function is to maximize the final failure load predicted by the physical information neural network model. The constraints include:
[0164] Bolt distance constraint: Center-to-center distance between adjacent bolts Minimum distance constraint between adjacent bolt centers ;
[0165] Edge distance constraint: Distance from bolt center to plate edge Minimum edge distance constraint from bolt center to plate edge ;
[0166] Connectivity region length constraint: Minimum constraint on the length of the connectivity region ≤Connection region length Maximum constraint ≤ connection region length ;
[0167] Standardized bolt types ;
[0168] S502: Formulating the bolt layout optimization problem into a constrained optimization model:
[0169] (twenty two)
[0170] S503: Configures the parameters of the improved non-dominated sorting genetic algorithm, including: population size, crossover probability, mutation probability, and selection mechanism; and adopts the penalty function method to incorporate constraint violation quantities into the fitness function, which is:
[0171] (twenty three)
[0172] In equation (23):
[0173] Violation is the degree to which a candidate solution does not satisfy the constraints.
[0174] As a penalty factor;
[0175] S504: Start the iterative process of the improved non-dominated sorting genetic algorithm, perform population evolution according to the configured parameters, and handle constraint violations by using the penalty function method; when the improvement of the optimal solution for 50 consecutive generations is less than 0.0001, the algorithm is considered to have converged and the optimal bolt layout parameters are output.
[0176] Compared with the prior art, the beneficial effects of the present invention are:
[0177] This invention embeds force balance equations and gradient regularization terms into a physical information neural network to ensure that prediction results strictly adhere to basic mechanical principles. This solves the problem of illogical predictions in sparse data regions by purely data-driven models, improving generalization ability and reliability. A 5D parametric description method is used to reduce the dimensionality of the four-nail connection structure variables. Combined with an improved non-dominated sorting genetic algorithm and penalty function constraints, efficient collaborative optimization is achieved while satisfying geometric constraints such as bolt spacing and edge distance, overcoming the shortcomings of traditional optimization methods, such as low efficiency and susceptibility to local optima. By expanding the dataset through a conditional generative adversarial network, the data bottleneck of finite element simulation and experimental testing is overcome, constructing an automated design framework of simulation-physical information neural network-optimization. This achieves a complete closed loop from rapid strength assessment to automatic layout optimization, significantly improving the design efficiency and reliability of composite material four-nail connection structures. Furthermore, the method is highly versatile and can be extended to the analysis and optimization of similar mechanical connection structures. Attached Figure Description
[0178] Figure 1 This is a flowchart of the present invention;
[0179] Figure 2 This is a schematic diagram of the physical information neural network framework of the present invention;
[0180] Figure 3 This is a schematic diagram of a four-nail connection structure made of composite materials;
[0181] Figure 4 This is a schematic diagram of the finite element model mesh with symmetry constraints applied in this invention. Detailed Implementation
[0182] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0183] A method for strength prediction and bolt layout optimization of a composite material four-nail connection structure based on a physical information neural network, the method comprising the following steps:
[0184] S1: Refined simulation modeling and verification of composite material four-nail connection structure;
[0185] S1 includes the following steps:
[0186] S101: Define the basic parameters required to construct the finite element model, including: geometric configuration, material properties, layup sequence, and contact boundary conditions;
[0187] S102: C3D8R three-dimensional solid element discrete composite laminate is used to ensure that each layer of material is divided into at least one mesh; local mesh refinement is performed on the stress concentration area around the bolt holes;
[0188] S103: Configure the damage assessment and evolution calculation model;
[0189] S103 includes the following steps:
[0190] S10301: Initial damage is determined for single-layer plates under different directions and stress modes using the three-dimensional hashin criterion, including:
[0191] Failure criterion for tensile damage in one direction of a single-layer plate:
[0192] (1)
[0193] Single-layer plate compressive damage failure criterion in one direction:
[0194] (2)
[0195] Failure criteria for single-layer plate under two-way tensile damage:
[0196] (3)
[0197] Single-layer plate two-way compressive damage failure criteria:
[0198] (4)
[0199] Three-directional tensile damage failure criteria for single-layer plates:
[0200] (5)
[0201] Three-directional compressive damage failure criteria for single-layer plates:
[0202] (6)
[0203] In equations (1)-(6):
[0204] , , These represent the normal stresses in three directions of a single-layer plate;
[0205] , , These represent the shear stresses in three directions of a single-layer plate;
[0206] , , These represent the tensile strengths of a single-layer plate in three directions.
[0207] , , These represent the compressive strength of a single-layer plate in three directions.
[0208] , , These represent the shear strengths of a single-layer plate in the 12, 13, and 23 directions, respectively.
[0209] This represents the weighting factor for the effect of shear on tension;
[0210] S10302: Calculation of damage variables based on a bilinear softening model using fracture energy:
[0211] (7)
[0212] In equation (7):
[0213] The damage variable ranges from 0 to 1, representing a change from no damage to complete failure.
[0214] The equivalent strength parameter for the type I fracture failure mode;
[0215] This represents the initial damage equivalent displacement under the Type I fracture failure mode;
[0216] The displacement is the equivalent of the final complete damage under the Type I fracture failure mode.
[0217] The value is in the Hashin criteria;
[0218] The fracture energy density is the fracture energy density under the type I fracture failure mode.
[0219] The initial damage equivalent stress is given under the Type I fracture failure mode.
[0220] S10303: Based on the Murakami-Ohno three-dimensional damage constitutive theory, the stiffness degradation matrix after damage can be obtained as follows:
[0221] (8)
[0222] In equation (8):
[0223] These are the single-direction stiffness degradation coefficients corresponding to the three directions;
[0224] These are the stiffness degradation coefficients for multi-directional coupling in the three directions, respectively;
[0225] These are the stiffness coefficients related to the elastic modulus in the three directions, respectively.
[0226] These are the coupling stiffness coefficients in directions 13 and 23, respectively;
[0227] The stiffness coefficients are Poisson's ratio-related in 12 directions;
[0228] S10304: To improve computational convergence, a viscosity regularization method is introduced:
[0229] (9)
[0230] In equation (9):
[0231] The damage variable after viscosity regularization;
[0232] The viscosity coefficient under the type I fracture failure mode;
[0233] This is the current time step;
[0234] For time step;
[0235] S10305: Zero-thickness cohesive elements are inserted at the ply interfaces to characterize interlayer delamination behavior, and a secondary stress criterion is used to determine the initiation of delamination.
[0236] (10)
[0237] In formula (10):
[0238] The normal direction of the element corresponds to the material undergoing Type I fracture.
[0239] and These represent the two shear directions of the element, corresponding to type П and type Ш fractures of the material, respectively.
[0240] The stress intensity is the material's normal direction.
[0241] and These represent the stress intensity in the two shear directions of the material, respectively.
[0242] S10306: Using a bilinear model for hierarchical evolution, stiffness-damage evolution parameters can be obtained. for:
[0243] (11)
[0244] In equation (11):
[0245] This refers to the opening displacement of the element node when the material is completely damaged and fails.
[0246] This represents the maximum opening displacement of the element node during the process;
[0247] This refers to the opening displacement of the unit nodes at the start of material layering.
[0248] S10307: Using the Black-K criterion to describe the hierarchical extension of hybrid modes:
[0249] (12)
[0250] In equation (12):
[0251] It exhibits composite fracture toughness;
[0252] This represents the total fracture energy release rate;
[0253] These are the material constants according to the BK criterion;
[0254] S104: Set contact boundary conditions: the bolt and the hole wall are in surface-to-surface contact, the normal direction is hard contact, and the tangential direction introduces Coulomb friction (the friction coefficient is 0.3).
[0255] S105: Apply symmetrical constraints to one side of the model to simplify the calculation, and apply displacement loads to the other side of the model to simulate tensile conditions;
[0256] S106: To verify the reliability of the model, a tensile test was conducted on the composite four-nail connection structure specimen at a loading rate of 1 mm / min until the specimen failed. The simulation results were compared with the test results in multiple dimensions, including load-displacement curves, ultimate load, and damage morphology. The verification results showed that if the ultimate load error was <10% and the failure mode predicted by the model was consistent with the experimental observation, the model was deemed reliable; otherwise, return to S101-S104 to adjust the modeling parameters, rebuild the model, and repeat the verification process.
[0257] S2: Based on the model obtained in S1, a parameterized method is used to generate a basic dataset. In order to overcome the limitation of the basic dataset size on the fine simulation, a conditional generative adversarial network is used to expand the basic dataset.
[0258] S2 includes the following steps:
[0259] S201: To comprehensively describe the bolt layout of a four-nail connection structure in composite materials, this invention employs a symmetry-based parameterization method, with the geometric center of the composite material connection portion as the coordinate origin. A two-dimensional plane coordinate system is established, and the composite material four-nail connection structure is distributed in a matrix of two rows and two columns. The bolt layout of the composite material four-nail connection structure is parameterized into a 5-dimensional design variable vector, including: the coordinates of the bolt symmetry center. Bolts Spacing in direction Bolts Spacing in direction and standardized bolt types Based on the above parameters, the center coordinates of the four bolts are derived as follows: , , as well as This parameterization method simplifies the original 8 bolt coordinate variables to 5, reducing the dimensionality of the problem and meeting the symmetrical layout requirements of composite material four-nail connection structures in actual working conditions.
[0260] S202: The optimal Latin hypercube sampling method is adopted to generate W=200 samples that meet the geometric constraints in the 5-dimensional design space. This method can ensure that the projection of all sample points is uniformly distributed in each dimension, avoid clustering, and thus better explore the entire design space to generate design variable combinations.
[0261] The sampling process is a constrained sampling, and step S202 includes the following steps:
[0262] S20201: Preset geometric constraints, including: minimum distance constraint between bolts, distance constraint from bolt center to plate edge, and length constraint of connection area;
[0263] S20202: Generate a large number of candidate points;
[0264] S20203: Select W sample points that simultaneously satisfy optimal space-filling performance and preset geometric constraints using a genetic algorithm.
[0265] S203: For each set of 5-dimensional design variables generated, parametric reconstruction is performed based on the model verified in S1. Simulation calculations are then executed after applying the same material parameters and boundary conditions to extract 5-dimensional response variables, forming the target output vector for training the physical information neural network, i.e., the basic dataset. The 5-dimensional response variables include:
[0266] Final failure load and the working load borne by each of the four bolts under 80% ultimate load. The working load can be calculated by extracting the resultant force of the contact force between the bolt and the hole wall in the model.
[0267] S204: Although W sets of high-confidence data were obtained through refined simulation, they are still insufficient for training complex physical information neural networks. To overcome this data bottleneck, a conditional generative adversarial network is introduced to intelligently augment the basic dataset, generating M=800 augmented datasets.
[0268] The construction and training of the conditional generative adversarial network described in S204 includes the following steps:
[0269] S20401: Input and Output Definitions:
[0270] The condition vector is a 5-dimensional design variable vector;
[0271] The random noise is a 10-dimensional random noise vector sampled from a standard normal distribution to introduce data diversity;
[0272] The target output is a 5-dimensional response variable vector;
[0273] S20402: Mesh structure:
[0274] Generator :
[0275] A fully connected neural network is employed, with its input being a concatenation of a conditional vector and a noise vector. The input layer dimension is 5 + 10 = 15 dimensions, hence the network has a total of 15 dimensions. The network contains three hidden layers with 64, 128, and 64 neurons respectively, all using the ReLU activation function to introduce non-linear transformation capabilities. The output layer has a 5-dimensional dimension and uses a linear activation function to ensure the generation of physically plausible continuous response values.
[0276] Discriminator :
[0277] A fully connected neural network is used, with its input being a concatenation of a conditional vector and a response vector (from a real dataset or a generator). The input layer has a dimension of 5 + 5 = 10, hence the network has a 10-dimensional input layer. The network contains three hidden layers with 128, 64, and 32 neurons respectively, using the LeakyReLU activation function (with a negative slope of 0.2) to alleviate the gradient vanishing problem. The output layer has a 1-dimensional dimension and uses the Sigmoid activation function to estimate the probability that the output input data comes from a real dataset.
[0278] S20403: Training value function:
[0279] The conditional generative adversarial network is trained through mini-maximum games, with a value function... for:
[0280] (13)
[0281] In equation (13):
[0282] The distribution of real simulation data;
[0283] Noise distribution;
[0284] It is a conditional vector;
[0285] For the response vector;
[0286] This is the noise vector;
[0287] Generator The goal is to learn the mapping from the condition space and noise space to the response space, generating response data sufficient to fool the discriminator, i.e., minimizing... ;
[0288] Discriminator The goal is to accurately distinguish between real data pairs and generated data pairs, that is, to maximize the accuracy of real data pairs. of And minimize the impact on the generated data pairs of ;
[0289] S20404: Train the generator separately using the Adam optimizer. and discriminator The initial learning rate is set to 2×10. -4 The first-order moment estimate has an exponential decay rate of 0.5. The training process lasts for 5000 training epochs, with a batch size of 32. To stabilize the training dynamics, the discriminator is updated multiple times in the early stages of training before updating the generator. Verification shows that the generated augmented data is consistent with the original dataset in terms of statistical distribution.
[0290] S205: Merge the 200 basic datasets and 800 supplementary datasets to form a complete dataset containing 1000 samples. Divide the complete dataset into training, validation, and test sets in a 7:2:1 ratio. The training set is used for learning the physical information neural network model, the validation set is used for parameter tuning and early stopping, and the test set is used for final evaluation.
[0291] S3: Construction and training of physical information neural network models;
[0292] S3 includes the following steps:
[0293] S301: Network architecture design and initialization, including:
[0294] The input layer consists of the 5-dimensional design variables defined in S2;
[0295] The output layer consists of the 5-dimensional response variables defined in S2;
[0296] The hidden layers adopt a multilayer perceptron structure, containing four hidden layers with 128, 256, 128 and 64 neurons in each layer, respectively, which are used to progressively extract and combine high-order nonlinear representations of input features;
[0297] The hidden layer uses the ReLU activation function to provide the necessary nonlinearity while effectively mitigating the gradient vanishing problem during training; the output layer uses a linear activation function to ensure that the output is a continuous mechanical response value, which meets the requirements of regression tasks.
[0298] All network weights are initialized using the He normal distribution method, with bias initialized to zero.
[0299] This initialization strategy is particularly well-suited for the ReLU activation function, which helps stabilize gradient propagation in the early stages of training and accelerates model convergence.
[0300] S302: Obtain the total loss function using a composite weighted method. :
[0301] (14)
[0302] In equation (14):
[0303] For data fitting loss;
[0304] Loss due to global force balance constraints;
[0305] This is a regularization term for physical laws;
[0306] , To balance the hyperparameters of the various loss weights, Bayesian optimization was subsequently used to determine them.
[0307] S303: Data fitting loss measures the difference between network predictions and high-fidelity simulation data.
[0308] (15)
[0309] In equation (15):
[0310] The number of samples;
[0311] =0.6 and =0.1 is a weighting coefficient, assigned to emphasize the importance of predicting failure loads. Higher weight;
[0312] The first The actual final failure load and the predicted final failure load of each sample;
[0313] The first The first sample The actual working load and the predicted working load of each bolt;
[0314] S304: The force balance constraint loss forced model follows the principle of global force balance, ensuring that the sum of the working loads of the four bolts equals 80% of the failure load (based on engineering experience, the structure is still in the elastic stage under this load).
[0315] (16)
[0316] S305: The physical regularization term includes a gradient term based on automatic differentiation calculation, to force the network output response to change more smoothly and continuously with the input design variables, conforming to the general laws of physical fields and avoiding violent non-physical oscillations.
[0317] (17)
[0318] In equation (17):
[0319] , , This is the gradient regularization coefficient, which will be determined subsequently using Bayesian optimization.
[0320] S306: Training strategy and convergence control.
[0321] The network was trained using the Adam optimizer with an initial learning rate of 2×10⁻⁶. -4 The first-order moment estimate has an exponential decay rate of 0.9. The training process lasts for 5000 epochs, with a fixed batch size of 32 to balance gradient update stability and memory efficiency. To prevent overfitting and ensure model convergence, an early stopping mechanism based on the validation set is introduced: model performance is evaluated on an independent validation set every 100 epochs; if the validation set loss does not decrease by more than a preset threshold of 1×10⁻⁶ within 200 consecutive epochs, the model is stopped out. -5 If so, training will be terminated early.
[0322] This strategy ensures the model's generalization ability while effectively avoiding unnecessary computational costs, ultimately causing the total loss function to converge to a stable plateau, thus ensuring the model's reliability and repeatability.
[0323] S4: The prediction accuracy and generalization ability of the physical information neural network model are systematically calibrated and verified using experimental data;
[0324] S4 includes the following steps:
[0325] S401: Select J=15 experimental samples of composite four-nail connection structures that did not participate in simulation and model training as independent test data for model calibration and validation; clarify that the optimization objective of hyperparameters (physical constraint weights, gradient regularization coefficients, number of hidden layer neurons) is to minimize the mean relative error (MRE) on the validation set. The hyperparameters to be optimized include: physical constraint weight coefficients. , Gradient regularization coefficient , , And the number of neurons in the hidden layer (optimized among 128, 256, and 512).
[0326] S402: The hyperparameters in the physical information neural network are automatically tuned using the Bayesian optimization method. The optimization process is set to a maximum of 50 iterations. The model performance is evaluated on the validation set (200 sets) for each iteration, and the loss function value is recorded.
[0327] S403: Three indicators are used to evaluate the model's prediction accuracy, including:
[0328] Mean relative error:
[0329] (18)
[0330] Coefficient of determination:
[0331] (19)
[0332] Maximum relative error:
[0333] (20)
[0334] In equations (18)-(20):
[0335] These are the model's predicted values;
[0336] The actual value;
[0337] The average of the true values;
[0338] S404: After Bayesian optimization and hyperparameter tuning, the model must meet the following accuracy requirements:
[0339] (twenty one)
[0340] The verification results show that the calibrated model meets the above indicators on all test samples, confirming that it has good prediction accuracy and engineering applicability.
[0341] S5: Construct an automatic optimization framework for bolt layout of composite material four-nail connection structure and output the optimal bolt layout parameters.
[0342] Although the single objective is to maximize the final failure load, the framework described in this invention is also applicable to multi-objective optimization problems involving failure load, weight, cost, etc. Therefore, this invention employs an improved non-dominated sorting genetic algorithm. Step S5 includes the following steps:
[0343] S501: Define the optimization variables as 5-dimensional design variables, and the objective function is to maximize the final failure load predicted by the physical information neural network model. The constraints include:
[0344] Bolt distance constraint: Center-to-center distance between adjacent bolts Minimum distance constraint between adjacent bolt centers ;
[0345] Edge distance constraint: Distance from bolt center to plate edge Minimum edge distance constraint from bolt center to plate edge ;
[0346] Connectivity region length constraint: Minimum constraint on the length of the connectivity region ≤Connection region length Maximum constraint ≤ connection region length ;
[0347] Standardized bolt types ;
[0348] S502: Formulating the bolt layout optimization problem into a constrained optimization model:
[0349] (twenty two)
[0350] S503: Configures the parameters of the improved non-dominated sorting genetic algorithm, including: population size of 100, crossover probability of 0.8 (simulated binary crossover), mutation probability of 0.1 (polynomial mutation), and tournament selection mechanism (size = 3); and adopts a penalty function method to incorporate constraint violation into the fitness function, the fitness function being:
[0351] (twenty three)
[0352] In equation (23):
[0353] Violation is the degree to which a candidate solution does not satisfy the constraints.
[0354] =1000 is the penalty factor;
[0355] S504: Initiate the iterative process of the improved non-dominated sorting genetic algorithm, perform population evolution (crossover, mutation, selection) according to the configured parameters, and handle constraint violations through the penalty function method; when the improvement of the optimal solution for 50 consecutive generations is less than 0.0001, the algorithm is determined to have converged, and the optimal bolt layout parameters are output.
[0356] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.
[0357] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.
Claims
1. A method for strength prediction and bolt layout optimization of a composite material four-nail connection structure based on a physical information neural network, characterized in that: The method includes the following steps: S1: Simulation modeling and verification of composite material four-nail connection structure; S1 includes the following steps: S101: Define the basic parameters required to construct the finite element model, including: geometric configuration, material properties, layup sequence, and contact boundary conditions; S102: C3D8R three-dimensional solid element discrete composite laminate is used to ensure that each layer of material is divided into at least one mesh; local mesh refinement is performed on the stress concentration area around the bolt holes; S103: Configure the damage assessment and evolution calculation model; S104: Set contact boundary conditions: the bolt and the hole wall are in surface-to-surface contact, the normal direction is hard contact, and the tangential direction introduces Coulomb friction; S105: Apply a symmetrical constraint to one side of the model and a displacement load to the other side of the model; S106: Perform tensile tests on the composite material four-nail connection structure test specimen until the test specimen fails. Compare the simulation results with the test results in multiple dimensions. If the ultimate load error is <10% and the failure mode predicted by the model is consistent with the experimental observation, the model is deemed reliable; otherwise, return to S101-S104 to adjust the modeling parameters, rebuild the model and repeat the verification process. S2: Based on the model obtained in S1, a parameterized method is used to generate a basic dataset, and a conditional generative adversarial network is used to expand the basic dataset; S3: Construction and training of physical information neural network models; S4: The prediction accuracy and generalization ability of the physical information neural network model are systematically calibrated and verified using experimental data; S5: Construct an automatic optimization framework for bolt layout of composite material four-nail connection structure and output the optimal bolt layout parameters.
2. The method for strength prediction and bolt layout optimization of a composite material four-nail connection structure based on a physical information neural network according to claim 1, characterized in that: S103 includes the following steps: S10301: Initial damage is determined for single-layer plates under different directions and stress modes using the three-dimensional hashin criterion, including: Failure criterion for tensile damage in one direction of a single-layer plate: (1) Single-layer plate compressive damage failure criterion in one direction: (2) Failure criteria for single-layer plate under two-way tensile damage: (3) Single-layer plate two-way compressive damage failure criteria: (4) Three-directional tensile damage failure criteria for single-layer plates: (5) Three-directional compressive damage failure criteria for single-layer plates: (6) In equations (1)-(6): , , These represent the normal stresses in three directions of a single-layer plate; , , These represent the shear stresses in three directions of a single-layer plate. , , These represent the tensile strengths of a single-layer plate in three directions. , , These represent the compressive strength of a single-layer plate in three directions. , , These represent the shear strengths of a single-layer plate in the 12, 13, and 23 directions, respectively. This represents the weighting factor for the effect of shear on tension; S10302: Calculation of damage variables based on a bilinear softening model using fracture energy: (7) In equation (7): For damage variables; The equivalent strength parameter for the type I fracture failure mode; This represents the initial damage equivalent displacement under the Type I fracture failure mode; The displacement is the equivalent of the final complete damage under the Type I fracture failure mode. The value is in the Hashin criteria; The fracture energy density is the fracture energy density under the type I fracture failure mode. The initial damage equivalent stress is given under the Type I fracture failure mode. S10303: Based on the Murakami-Ohno three-dimensional damage constitutive theory, the stiffness degradation matrix after damage can be obtained as follows: (8) In equation (8): These are the single-direction stiffness degradation coefficients corresponding to the three directions; These are the stiffness degradation coefficients for multi-directional coupling in the three directions, respectively; These are the stiffness coefficients related to the elastic modulus in the three directions, respectively. These are the coupling stiffness coefficients in directions 13 and 23, respectively; The stiffness coefficients are Poisson's ratio-related in 12 directions; S10304: Introducing a viscosity regularization method: (9) In equation (9): The damage variable after viscosity regularization; The viscosity coefficient under the type I fracture failure mode; This is the current time step; For time step; S10305: Zero-thickness cohesive elements are inserted at the ply interfaces to characterize interlayer delamination behavior, and a secondary stress criterion is used to determine the initiation of delamination. (10) In formula (10): The normal direction of the element; and These are the two shear directions of the unit; The stress intensity is the material's normal direction. and These represent the stress intensity in the two shear directions of the material, respectively. S10306: Using a bilinear model for hierarchical evolution, stiffness-damage evolution parameters can be obtained. for: (11) In equation (11): This refers to the opening displacement of the element node when the material is completely damaged and fails. This represents the maximum opening displacement of the element node during the process; This refers to the opening displacement of the unit nodes at the start of material layering. S10307: Using the Black-K criterion to describe the hierarchical extension of hybrid modes: (12) In equation (12): It exhibits composite fracture toughness; This represents the total fracture energy release rate; is the material constant of the BK criterion.
3. The method for strength prediction and bolt layout optimization of a composite material four-nail connection structure based on a physical information neural network according to claim 2, characterized in that: S2 includes the following steps: S201: The origin of the coordinate system is the geometric center of the composite material connection. A two-dimensional plane coordinate system is established, and the bolt layout of the composite material four-nail connection structure is parameterized into a 5-dimensional design variable vector, including: the coordinates of the bolt symmetry center. Bolts Spacing in direction Bolts Spacing in direction and standardized bolt types Based on the above parameters, the center coordinates of the four bolts are derived as follows: , , as well as ; S202: Using the optimal Latin hypercube sampling method, W samples satisfying geometric constraints are generated in the 5-dimensional design space; S203: For each set of 5-dimensional design variables generated, parametric reconstruction is performed based on the model verified in S1. Simulation calculations are then executed after applying the same material parameters and boundary conditions to extract 5-dimensional response variables, forming the target output vector for training the physical information neural network, i.e., the basic dataset. The 5-dimensional response variables include: Final failure load and the working load borne by each of the four bolts under 80% ultimate load. ; S204: Introduce a conditional generative adversarial network to generate M groups of expanded datasets; S205: Merge the base dataset and the augmented dataset to form a complete dataset, and divide the complete dataset into a training set, a validation set, and a test set in a ratio of 7:2:
1.
4. The method for strength prediction and bolt layout optimization of a composite material four-nail connection structure based on a physical information neural network according to claim 3, characterized in that: S202 includes the following steps: S20201: Preset geometric constraints, including: minimum distance constraint between bolts, distance constraint from bolt center to plate edge, and length constraint of connection area; S20202: Generate a large number of candidate points; S20203: Select W sample points that simultaneously satisfy optimal space-filling performance and preset geometric constraints using a genetic algorithm.
5. The method for strength prediction and bolt layout optimization of a composite material four-nail connection structure based on a physical information neural network according to claim 4, characterized in that: The construction and training of the conditional generative adversarial network described in S204 includes the following steps: S20401: Input and Output Definitions: The condition vector is a 5-dimensional design variable vector; The random noise is a 10-dimensional random noise vector sampled from a standard normal distribution; The target output is a 5-dimensional response variable vector; S20402: Mesh structure: Generator : A fully connected neural network is used, whose input is a concatenation of a conditional vector and a noise vector, so the input layer has a dimension of 15. The network contains 3 hidden layers, all of which use the ReLU activation function, and the output layer has a dimension of 5 and uses a linear activation function. Discriminator : A fully connected neural network is used, whose input is the concatenation of the conditional vector and the response vector. Therefore, the input layer has a dimension of 10. The network contains 3 hidden layers and uses the LeakyReLU activation function. The output layer has a dimension of 1 and uses the Sigmoid activation function. S20403: Training value function: The conditional generative adversarial network is trained through mini-maximum games, with a value function... for: (13) In equation (13): The distribution of real simulation data; Noise distribution; It is a conditional vector; For the response vector; This is the noise vector; Generator The goal is to minimize ; Discriminator The goal is to maximize the accuracy of the real data. of And minimize the impact on the generated data pairs of ; S20404: Train the generator separately using the Adam optimizer. and discriminator In the early stages of training, the discriminator is updated multiple times before the generator is updated.
6. The method for strength prediction and bolt layout optimization of a composite material four-nail connection structure based on a physical information neural network according to claim 5, characterized in that: S3 includes the following steps: S301: Network architecture design and initialization, including: The input layer consists of 5-dimensional design variables; The output layer consists of 5-dimensional response variables; The hidden layer employs a multilayer perceptron structure to progressively extract and combine high-order nonlinear representations of input features; The hidden layers use the ReLU activation function, and the output layer uses the linear activation function. All network weights are initialized using the He normal distribution method, with bias initialized to zero. S302: Obtain the total loss function using a composite weighted method. : (14) In equation (14): For data fitting loss; Loss due to global force balance constraints; This is a regularization term for physical laws; , The hyperparameters are used to balance the weights of various losses; S303: Data fitting loss measures the difference between network predictions and high-fidelity simulation data. (15) In equation (15): The number of samples; and These are the weighting coefficients; The first The actual final failure load and the predicted final failure load of each sample; The first The first sample The actual working load and the predicted working load of each bolt; S304: The force balance constraint loss forced model follows the global force balance principle, ensuring that the sum of the working loads of the four bolts equals 80% of the failure load. (16) S305: Physical law regularization terms include gradient terms based on automatic differentiation calculations. (17) In equation (17): , , Here, represents the gradient regularization coefficient. S306: Training strategy and convergence control.
7. The method for strength prediction and bolt layout optimization of a composite material four-nail connection structure based on a physical information neural network according to claim 6, characterized in that: S4 includes the following steps: S401: Select experimental samples of composite four-nail connection structures from group J that did not participate in simulation and model training as independent test data for model calibration and verification; The objective of hyperparameter optimization is to minimize the mean relative error (MRE) on the validation set. The hyperparameters to be optimized include: physical constraint weight coefficients. , Gradient regularization coefficient , , And the number of neurons in the hidden layer; S402: Automatically tune the hyperparameters in the physical information neural network using Bayesian optimization method; S403: Three indicators are used to evaluate the model's prediction accuracy, including: Mean relative error: (18) Coefficient of determination: (19) Maximum relative error: (20) In equations (18)-(20): These are the model's predicted values; The actual value; The average of the true values; S404: After Bayesian optimization and hyperparameter tuning, the model must meet the following accuracy requirements: (21)。 8. The method for strength prediction and bolt layout optimization of a composite material four-nail connection structure based on a physical information neural network according to claim 7, characterized in that: S5 includes the following steps: S501: Define the optimization variables as 5-dimensional design variables, and the objective function is to maximize the final failure load predicted by the physical information neural network model. The constraints include: Bolt distance constraint: Center-to-center distance between adjacent bolts Minimum distance constraint between adjacent bolt centers ; Edge distance constraint: Distance from bolt center to plate edge Minimum edge distance constraint from bolt center to plate edge ; Connectivity region length constraint: Minimum constraint on the length of the connectivity region ≤Connection region length Maximum constraint ≤ connection region length ; Standardized bolt types ; S502: Formulating the bolt layout optimization problem into a constrained optimization model: (22) S503: Configures the parameters of the improved non-dominated sorting genetic algorithm, including: population size, crossover probability, mutation probability, and selection mechanism; and adopts the penalty function method to incorporate constraint violation quantities into the fitness function, which is: (23) In equation (23): Violation is the degree to which a candidate solution does not satisfy the constraints. As a penalty factor; S504: Start the iterative process of the improved non-dominated sorting genetic algorithm, perform population evolution according to the configured parameters, and handle constraint violations by using the penalty function method; when the improvement of the optimal solution for 50 consecutive generations is less than 0.0001, the algorithm is considered to have converged and the optimal bolt layout parameters are output.