A structure hysteretic behavior prediction method fusing meta-learning, pinns and meta-heuristic optimization

Abstract

This invention discloses a structural hysteresis behavior prediction method integrating meta-learning, PINN, and meta-heuristic optimization. It establishes a structural numerical model containing key stress nodes using vector finite element method, generates a multi-condition hysteresis curve dataset, and constructs a hybrid RNN-LSTM temporal network embedding Dropout layers and fully connected layers. The hysteresis model is introduced into the network as a hard physical constraint, and data loss, physical conservation loss, parameter regularization term, and gradient stabilization term are integrated to construct a collaboratively optimized total loss function. The AdamW optimizer and an improved StepLR learning rate scheduler are employed, utilizing a dual-loop collaborative mechanism to complete network training. This invention achieves deep integration of data-driven and physical mechanisms, improving prediction accuracy, physical consistency, small-sample generalization ability, and computational efficiency. It is suitable for structural hysteresis analysis, seismic assessment, and rapid engineering decision-making under seismic reciprocating loads.

Description

Technical Field

[0001] This invention relates to the technical fields of seismic analysis of building structures, physical information machine learning and intelligent optimization algorithms, and specifically to a method for predicting structural hysteresis behavior that integrates meta-learning-PINN-meta-heuristic optimization. Background Technology

[0002] Structural hysteresis behavior is a core indicator characterizing the nonlinear deformation, energy dissipation capacity, stiffness degradation, and damage evolution of building structures under cyclic loading. Accurate and efficient prediction of hysteresis behavior is a crucial prerequisite for seismic design, safety assessment, and toughness enhancement of structures. As building structures become increasingly taller, larger-span, more complex, and more functional, traditional hysteresis behavior analysis methods face insurmountable technical bottlenecks: physical testing methods are limited by model size, loading equipment, testing costs, and timelines, failing to cover systematic testing across multiple parameters, working conditions, and all stress stages, and struggling to achieve full-scale testing of complex structures, resulting in severely insufficient data representativeness and generalization; traditional numerical simulation methods rely on refined finite element modeling and extensive iterative calculations, easily encountering convergence difficulties when dealing with complex hysteresis characteristics such as strong nonlinearity, large deformation, and stiffness degradation, exhibiting extremely low computational efficiency and failing to support rapid decision-making and multi-scheme comparison in engineering scenarios; pure data-driven deep learning methods overly rely on massive amounts of high-quality labeled data, leading to a sharp decline in generalization ability under small sample conditions. Furthermore, the prediction results often violate fundamental physical laws such as momentum conservation, internal force balance, and hysteretic constitutive rules, exhibiting "non-physical prediction" defects and compromising the reliability of engineering applications. Traditional physical hysteresis models (such as the BWBN model) have parameters with strong coupling, high dimensionality, and non-convexity. Conventional parameter identification methods are highly sensitive to initial values, easily getting trapped in local optima, and cannot achieve fast, accurate, and robust parameter identification under multiple operating conditions. Moreover, they are difficult to characterize complex hysteresis details such as cumulative damage and pinching effects. Existing physical information neural network applications mostly employ uniform sampling and soft physical constraints, which suffer from problems such as blind sampling, physical constraint penetration, insufficient fitting accuracy in high gradient regions, and poor generalization ability for small samples under new operating conditions. They have not yet achieved deep collaboration with hysteresis model parameter identification and temporal feature extraction.

[0003] Metaheuristic optimization algorithms possess inherent advantages such as global optimization, strong robustness, and adaptability to high-dimensional non-convex problems, which can solve the core pain point of hysteresis model parameter identification. Meta-learning-enhanced PINN can achieve rapid generalization with small samples through prior learning, focus on high information density regions through adaptive sampling, and ensure the physical rationality of prediction results through hard physical constraints. However, existing technologies have not yet constructed an integrated technical framework of "vector finite element multi-condition data generation - adaptive hybrid metaheuristic global parameter identification - meta-learning-enhanced PINN physical constraint embedding - temporal network feature extraction - dual-loop collaborative optimization", which cannot achieve deep synergy among data-driven, physical mechanisms, and intelligent optimization, and cannot simultaneously meet the core requirements of engineering practice for hysteresis prediction of "high accuracy, high efficiency, strong generalization, and high reliability". Summary of the Invention

[0004] In order to overcome the shortcomings and deficiencies of the existing technology, the purpose of this invention is to provide a structural hysteresis behavior prediction method that integrates meta-learning-PINN-meta-heuristic optimization.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A structural hysteresis behavior prediction method integrating meta-learning, PINN, and meta-heuristic optimization includes the following steps: S1. Based on the vector finite element method, a multi-scale structural numerical model is constructed, low-cycle repeated loads are applied, and a multi-condition hysteresis curve dataset covering the entire stress stage is generated. Preprocessing and dataset partitioning are then completed. S2 constructs an adaptive hybrid meta-heuristic optimization framework that integrates parallel genetic algorithm, adaptive particle swarm optimization and simulated annealing escape mechanism. Based on the multi-condition hysteresis curve, it performs global parallel optimization of the high-dimensional parameters of the BWBN hysteresis model (an improved Bouc-Wen hysteresis model) and outputs the parameter set of the multi-condition hysteresis model. S3, construct the meta-learning enhanced PINN network architecture, with RNN-LSTM hybrid network as the backbone for temporal feature extraction, embedding meta-learning adaptive sampling module and BWBN hysteresis differential equation hard physical constraint module, and connecting fully connected layer at the tail to output displacement prediction value; S4. Construct the total loss function, which integrates data fidelity loss, PINN physical conservation loss, metaheuristic parameter regularization loss, and training stability loss to provide multi-objective constraints for model optimization. S5 constructs a dual-loop collaborative optimization mechanism of "outer loop-inner loop". The outer loop iteratively updates the hysteresis model parameters through an adaptive hybrid meta-heuristic algorithm, while the inner loop iteratively updates the network parameters through meta-learning, AdamW optimizer and improved StepLR learning rate scheduler. The dual loops provide bidirectional feedback and synchronous iteration until convergence, thus completing model training. S6, based on the trained model, takes an external load sequence as input and outputs the structural hysteretic displacement response, thus completing the uncertainty quantification and performance verification of the prediction results.

[0007] Furthermore, in S1, the loading increment of the loading regime is determined by the formula... Calculate, where, For the final loaded amplitude, This is the initial loading amplitude. To load the loop count, To load the adjustment coefficient, This is the amount to adjust the number of iterations.

[0008] Furthermore, in S2, the fitness function of the adaptive hybrid metaheuristic optimization framework is: ,in, For the number of data points, For numerical simulation of load values, Identify load values ​​for the hysteresis model. These are the error weighting coefficients. The stability coefficient, The standard deviation of the parameter distribution. The boundary penalty coefficient, The penalty term is for parameters that exceed the physical reasonable boundary; the optimization framework adopts the MPI parallel computing architecture, with ≥8 parallel nodes, a population size of 200~500, 300~500 iterations, adaptive adjustment range of crossover probability of 0.5~0.9, adaptive adjustment range of mutation probability of 0.01~0.1, and the simulated annealing escape mechanism is triggered when the fitness does not decrease for 5 consecutive generations.

[0009] Furthermore, in S3, the formula for updating the hidden state of the RNN layer is as follows: ,in, The number of RNN layers. For the input weight matrix, Here is the hidden state weight matrix. For bias terms, For correction factor, This represents the state increment.

[0010] Furthermore, in S3, the sampling weight update formula of the meta-learning adaptive sampling module is as follows: ,in, For the first Sampling weights at each time step, The gradient magnitude of the physical loss at that time step. For smoothing coefficients, The total time step is denoted as ; the sampling weight is positively correlated with the gradient magnitude, enabling adaptive dense sampling of the high gradient region of the hysteresis curve.

[0011] Furthermore, in S4, the expression for the total loss function is as follows: ,in, The set of network weights and bias parameters. For the hysteresis model parameter set, To preserve data integrity, For PINN physical conservation loss, For metaheuristic parameter regularization loss, To train stable loss, , , These are the adaptive weighting coefficients for the corresponding loss term.

[0012] Furthermore, in S5, the learning rate update formula is as follows: ,in, The initial learning rate, Scaling factor To adjust the cycle length, The logarithmic adjustment coefficient is... For the number of iterations, The meta-learning decay coefficient, This represents the number of iterations in the inner loop of the MAML.

[0013] Further, S2 includes: S21, determining the core parameters and physical boundary range of the BWBN hysteresis model, and determining the upper and lower limits of each parameter based on engineering experience and experimental data; S22, initializing the adaptive hybrid meta-heuristic optimization framework, using Latin hypercube sampling to complete population initialization, setting parallel computing nodes, population size, number of iterations, initial values ​​of adaptive crossover and mutation probabilities, and triggering conditions for the simulated annealing escape mechanism; S23, parallel computing the hysteresis model output corresponding to each individual in the population, calculating its deviation from the numerical simulation hysteresis curve, and obtaining the fitness value by combining the boundary penalty term; S24, adaptively switching optimization strategies: the first 1 / 3 of the iteration cycle mainly uses particle swarm optimization to quickly converge to the neighborhood of the optimal solution; the middle 1 / 3 of the iteration cycle mainly uses parallel genetic algorithm to deepen global optimization; the last 1 / 3 of the iteration cycle introduces the simulated annealing escape mechanism to avoid getting trapped in local optima; S25, iterating until the preset number of iterations or the fitness value is lower than the convergence threshold, selecting the parameters corresponding to the individual with the smallest fitness as the optimal identification parameters of the hysteresis model under this condition, and organizing them into a multi-condition parameter set.

[0014] Further, S3 includes: S31, constructing a 4-layer RNN temporal feature extraction network, with the first layer having an input dimension of 1 and an output dimension of 256, and the other three layers having input and output dimensions of 256, with dropout layers between layers and a dropout rate of 0.3; S32, cascading a 3-layer LSTM network, with input and output dimensions of 256, and dropout layers with the same dropout rate between layers, capturing the long-term temporal dependencies of hysteresis behavior through input gates, forget gates, and output gates to solve the gradient vanishing problem; S33, embedding meta-learning adaptive... The sampling module dynamically updates the sampling weights at each time step based on the gradient magnitude of the physical loss, updating the sampling distribution every 10 iterations to focus on high-gradient feature regions; S34 embeds a hard physical constraint module for BWBN hysteresis differential equations, directly integrating the hysteresis constitutive control equations into the network's forward propagation, requiring the network's output displacement response to synchronously satisfy the hysteresis differential equations, replacing traditional soft loss constraints; S35 connects two fully connected layers at the tail, with 128 and 64 neurons in the hidden layers and 1 neuron in the output layer, completing the network architecture.

[0015] Further, S5 includes: S51, using the multi-condition data of the meta-training set as the source domain, pre-training is performed using the MAML algorithm, the inner loop updates the network parameters to adapt to the single-condition, and the outer loop updates the initial weights of the network to learn the general feature priors of hysteresis behavior, thus completing the pre-training weight initialization; S52, initializing the outer loop meta-heuristic optimization population and the inner loop network training hyperparameters, setting the convergence threshold and the maximum number of iterations; S53, based on the current hysteresis model parameter set output by the outer loop, updating the PINN physical constraint module, using the total loss function as the optimization objective, and performing network training using the AdamW optimizer and the improved StepLR learning rate scheduler, iteratively updating the network parameters; S54, using the total loss function value obtained from the inner loop training as fitness feedback, performing population iteration through the adaptive hybrid meta-heuristic algorithm, and updating the hysteresis model parameter set; S55, repeating steps S53 to S54 until the total loss function is lower than the preset threshold or the maximum number of iterations is reached, triggering the early stopping mechanism, and saving the optimal model parameters.

[0016] A structural hysteresis behavior prediction method integrating meta-learning, PINN, and meta-heuristic optimization is implemented through cascaded functional units, including: a multi-condition hysteresis data generation unit, used to construct multi-scale numerical models based on vector finite element method and generate a standardized hysteresis dataset covering all stress stages; a meta-heuristic parameter global identification unit, with a built-in adaptive hybrid meta-heuristic optimization framework, used for parallel global optimization of hysteresis model parameters under multiple conditions, outputting a highly robust physical parameter set; a meta-learning-PINN network construction unit, used to build an RNN-LSTM hybrid backbone network, a meta-learning adaptive sampling module, and a hard physical constraint module to form a complete prediction network architecture; a collaborative optimization loss function construction unit, used to construct a multi-objective total loss function that integrates data fidelity, physical conservation, parameter regularization, and training stability, providing objective guidance for collaborative optimization; a dual-loop collaborative training unit, used to realize bidirectional feedback and synchronous iteration between meta-heuristic parameter optimization and meta-learning-PINN network training, completing efficient and accurate model training; and a hysteresis behavior prediction and verification unit, used to receive external load input, output hysteresis displacement response and uncertainty quantification results, and simultaneously complete model performance verification.

[0017] Compared with the prior art, the present invention has the following substantial breakthroughs and beneficial effects: 1. Breaking through the bottleneck of traditional parameter identification, achieving global and accurate identification of high-dimensional hysteresis parameters: The constructed adaptive hybrid metaheuristic optimization framework integrates the advantages of multiple metaheuristic algorithms. Through parallel computing, adaptive policy switching and simulated annealing escape mechanism, it solves the problems of traditional algorithms being sensitive to initial values, easily getting trapped in local optima, and having poor robustness. The parameter identification accuracy is improved by more than 40%, and the computational efficiency is improved by more than 3 times, providing accurate constitutive priors for physical constraint embedding.

[0018] 2. Addressing the shortcomings of purely data-driven non-physical predictions and achieving hard constraint embedding of physical laws: The proposed meta-learning enhanced PINN architecture directly integrates the BWBN hysteresis differential equation into the network forward propagation, achieving hard physical constraints and fundamentally avoiding non-physical prediction results; through meta-learning adaptive sampling, it focuses on the high gradient feature region of the hysteresis curve, solving the problems of blind sampling and insufficient fitting accuracy in high gradient regions in traditional PINN, and the prediction results strictly follow the laws of conservation of mechanics and the hysteresis constitutive rules.

[0019] 3. Construct a dual-loop collaborative optimization mechanism to achieve deep integration of data, physics, and optimization: Breaking through the traditional serial mode of "parameter identification first, network training later", a dual-loop collaborative mechanism of "outer loop parameter optimization - inner loop network training" is constructed to achieve bidirectional feedback and synchronous optimization of physical model parameters and network weights. This solves the problem of disconnect between parameter identification and network training and the inability to make bidirectional corrections in traditional methods, and greatly improves the prediction accuracy and multi-condition adaptability of the model.

[0020] 4. Achieve strong generalization ability under small sample conditions and significantly reduce the threshold for engineering applications: Through pre-training with the MAML algorithm, the model learns the general feature priors of hysteresis behavior. In small sample scenarios with new structures and new working conditions, only a small amount of data is needed to complete the rapid adaptation, and the generalization ability is improved by more than 50%. It does not need to rely on a large amount of physical test data, which greatly reduces the cost and threshold of engineering applications.

[0021] 5. Balancing efficiency and accuracy to fully meet engineering practice needs: While maintaining 99% prediction accuracy, the method of this invention improves the prediction speed of single-condition hysteresis response by two orders of magnitude compared with traditional finite element simulation. It can be widely used in engineering scenarios such as structural seismic design, performance evaluation, post-disaster assessment, and parameter inversion, and has strong engineering practicality and promotion value. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention. Figure 2 This is a flowchart of the method step S1 of the present invention; Figure 3 This is a flowchart of method step S2 of the present invention; Figure 4 This is a flowchart of method step S3 of the present invention; Figure 5 This is a flowchart of method step S4 of the present invention; Figure 6 This is a flowchart of step S5 of the method of the present invention; Figure 7 This is a flowchart of step S6 of the method of the present invention; Figure 8 This is a diagram showing the unit composition for implementing the method of the present invention. Detailed Implementation

[0023] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The described embodiments are only some embodiments of the present invention, and not all embodiments. The present application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0024] like Figure 1 As shown in the figure, this embodiment discloses a structural hysteresis behavior prediction method that integrates meta-learning, PINN, and meta-heuristic optimization. The specific implementation steps are as follows: S1, Constructing a multi-scale, multi-condition hysteresis dataset based on vector finite element method. This step provides high-quality benchmark data support for the entire method. The specific implementation process is as follows: Figure 2As shown; S11, based on vector finite element theory, a three-story, three-span self-resetting frame overall numerical model was built. The model includes cross-shaped beam-column nodes and T-shaped column base nodes, fully restoring the mechanical properties of the nodes such as semi-rigidity and self-resetting energy dissipation. Vector finite element theory uses point-value description and rigid body motion decomposition, which can accurately capture the large deformation and strong nonlinear behavior of the structure under cyclic loads, avoiding the mesh distortion and convergence difficulties of traditional finite element theory. S12, using a force-controlled loading method, a low-cycle cyclic load was applied to the top layer of the frame, with the loading rate controlled at 0.01 mm / s to ensure the synchronization of load and displacement response. Twelve sets of gradient loading regimes were designed, with loading amplitude ranging from 0.1 mm to 2.0 mm and loading cycles from 3 to 8, covering... The simulation covers all stress stages of the structure, including elasticity, yielding, plasticity, and ultimate failure. In S13, five sets of gradient beam-column section parameters are designed, and the material yield strength, reinforcement ratio, and axial compression ratio are adjusted simultaneously to form 60 independent simulation cases. In S14, each case undergoes independent numerical simulation with a mesh density of 5 elements per unit length and a data sampling frequency of 100Hz. Load-displacement time history data and hysteresis curves for each case are output, forming an original dataset containing 60 samples. In S15, the original dataset is preprocessed, including outlier removal, time-series alignment, and maximum / minimum standardization. It is then divided into training, validation, and test sets in a 7:1:2 ratio to provide standardized data for subsequent model training and validation.

[0025] S2, Global Identification of Hysteresis Model Parameters Based on Adaptive Hybrid Metaheuristic Optimization: This step uses a metaheuristic optimization algorithm to solve the challenge of globally identifying high-dimensional, strongly coupled parameters in the BWBN hysteresis model. The specific implementation process is as follows... Figure 3As shown; S21, determine the governing differential equations and 8 core parameters of the BWBN hysteresis model, and determine the physical reasonable boundary range of each parameter based on engineering test data to avoid the identification results exceeding the engineering feasible domain; S22, build an MPI-based parallel computing architecture, set up 8 parallel computing nodes, each node is responsible for the parameter identification task of 7~8 working conditions; initialize the adaptive hybrid heuristic optimization framework: the population size is set to 300, the maximum number of iterations is set to 400, the initial value of crossover probability is 0.7, the initial value of mutation probability is 0.05, the adaptive adjustment range of crossover probability is 0.5~0.9, the adaptive adjustment range of mutation probability is 0.01~0.1, the initial temperature of simulated annealing is set to 100, the cooling coefficient is set to 0.95, and the escape mechanism is triggered when the fitness does not decrease for 5 consecutive generations; S23, use Latin hypercube sampling to complete the population initialization to ensure that the initial population is uniformly distributed in the parameter space and covers the entire parameter boundary range; calculate the BWBN model hysteresis output corresponding to each individual in parallel, and calculate its correlation with the numerical value. The mean square error of the simulated hysteresis curve is combined with the parameter boundary penalty term, and the fitness value of each individual is calculated through the fitness function. In S24, an adaptive strategy is adopted to switch the optimization mode: in the early stage of iteration (generations 1-150), adaptive particle swarm optimization is mainly used, and the population is guided to converge quickly to the neighborhood of the optimal solution through individual optimality and global optimality, thus accelerating the optimization speed; in the middle stage of iteration (generations 151-300), parallel genetic algorithm is mainly used, and global optimization is deepened and the population search range is expanded through roulette wheel selection, single-point crossover, and adaptive mutation operations; in the late stage of iteration (generations 301-400), a simulated annealing escape mechanism is introduced, which accepts individuals with poor fitness with a certain probability, escapes local optima, and ensures the global optimality of the optimization results; in S25, when the iteration reaches the maximum number of iterations or the fitness value is lower than the convergence threshold of 1e-4, the 8 parameters corresponding to the individual with the smallest fitness in each working condition are selected as the optimal identification parameters for that working condition, and 60 sets of hysteresis model parameter sets for working conditions are organized to provide accurate constitutive priors for subsequent PINN physical constraints.

[0026] S3, Building the Meta-Learning Enhanced PINN Network Architecture: This step constructs a meta-learning-PINN network architecture that integrates temporal feature extraction, adaptive sampling, and hard physical constraints. The specific implementation process is as follows... Figure 4As shown in S31, construct the RNN-LSTM hybrid temporal feature extraction backbone network: build a 4-layer RNN network, the first layer has an input dimension of 1 (corresponding to the load input) and an output dimension of 256, the other three layers have input and output dimensions of 256, and each hidden layer has 256 neurons; set a Dropout layer between adjacent RNN layers, with a neuron dropout rate of 0.3 to suppress overfitting; cascade 3 layers of LSTM network after the RNN network, with input and output dimensions of 256 and a cell state dimension of 256, each layer containing three gating units: input gate, forget gate, and output gate, to capture the long-term temporal dependencies of hysteresis behavior and solve the gradient vanishing problem of RNN; set Dropout layers with the same dropout rate between LSTM layers to form a continuous overfitting suppression mechanism; S32, embed a meta-learning adaptive sampling module: the module dynamically updates the sampling weights at each time step based on the gradient magnitude of the physical loss, and updates the sampling distribution every 10 iterations; for high gradient regions such as the yield segment, unloading segment, and stiffness degradation segment, higher gradients are assigned. S33: Sampling weights enable adaptive dense sampling, addressing the blindness of traditional uniform sampling and improving fitting accuracy in high-gradient feature regions; S44: Embedding a hard physical constraint module for the BWBN hysteresis differential equation, directly integrating the control differential equation of the BWBN hysteresis model into the network's forward propagation process. The network's output displacement response must simultaneously satisfy the hysteresis differential equation and internal force equilibrium conditions, replacing traditional soft loss constraints and forcing the network output to strictly follow mechanical laws, fundamentally avoiding non-physical prediction results; S55: Constructing a fully connected output layer, with two fully connected layers following the LSTM network. The first hidden layer has 128 neurons, using ReLU activation; the second hidden layer has 64 neurons, also using ReLU activation; the output layer has 1 neuron, using a linear activation function to output a one-dimensional displacement prediction value; S66: Network parameters are initialized using a He normal distribution to ensure consistent output variance across layers; controlling the total number of network parameters balances training efficiency and feature extraction capability, ultimately forming a complete meta-learning enhanced PINN network architecture.

[0027] S4, Construction of the Total Loss Function for Collaborative Optimization: This step constructs the total loss function for multi-objective collaborative optimization, providing a clear optimization objective for the dual-loop optimization. The specific implementation process is as follows... Figure 5 As shown; S41, calculate data fidelity loss. The mean square error between the predicted displacement and the simulated true value is used for calculation, and the expression is as follows: ,in, For the number of data points, To predict displacement for the network, To numerically simulate real displacement, this loss term measures the accuracy of the network's fit to the data; S42, calculate the PINN physical conservation loss. The root mean square error of the residuals and internal force equilibrium deviations from the BWBN hysteresis differential equation is used for calculation, and the expression is as follows: ,in, For the residuals of the hysteretic differential equation, For the system internal forces calculated by the model, For external input loads, For the hysteresis model parameter set, this loss term measures the consistency between the prediction results and physical laws; S43, calculate the metaheuristic parameter regularization loss. Based on parametric physical boundary constraints and distribution stability calculation, the expression is as follows: ,in, For the number of parameters, This is a penalty term for parameters exceeding physical boundaries. S44, calculate the training stability loss, which represents the standard deviation of the parameter distribution and constrains the physical rationality and stability of the parameters. : Based on the gradient norm of the loss function, the expression is as follows ,in, This is the gradient vector of the total loss function with respect to the network parameters. Using the L2 norm, this loss term suppresses gradient explosion and ensures the stability of the training process; S45, construct the total loss function and set adaptive weight coefficients: data loss weight 1.0, physical loss weight... Parameter regularization loss weights Training stable loss weights The final total loss function is Each loss term is normalized so that its value ranges from 0 to 1, thus avoiding imbalance of loss terms caused by differences in dimensions.

[0028] S5, Dual-loop Collaborative Optimization Model Training: This step achieves bidirectional collaboration between metaheuristic parameter optimization and network training. The specific implementation process is as follows... Figure 6 As shown; S51, using the 42 sets of working condition data from the meta-training set as the source domain, the MAML algorithm is used for pre-training. The inner loop step count is set to 5, and the learning rate is set to 0.001. The network parameters are updated for single working condition data. The outer loop step count is set to 20, and the learning rate is set to 0.0001. The initial weights of the network are updated so that the model learns the general feature priors of hysteresis behavior, and the pre-training weight initialization is completed. S52, the outer loop meta-heuristic optimization population is initialized. The inner loop training hyperparameters are: batch size is set to 32, maximum number of training epochs is set to 100, early stopping threshold is set to no decrease in loss on the validation set for 15 consecutive epochs, optimizer weight decay coefficient is set to 0.001, first-order momentum coefficient is 0.9, second-order momentum coefficient is 0.999, and initial learning rate is 0.001. S53, based on the hysteresis model parameter set output by the current outer loop. Update the PINN physical constraint module; train the network with the total loss function as the optimization objective, and iteratively update the network parameters through backpropagation. After each epoch, the total loss value of the validation set is output; in S54, the total loss value of the validation set output by the inner loop is used as fitness feedback, and the population is iterated through an adaptive hybrid metaheuristic algorithm to complete selection, crossover, mutation, and escape operations, and update the hysteresis model parameter set. Enter the next round of inner loop training; S55, repeat steps S51~S54 until the total loss function is lower than the convergence threshold of 1e-5, or the maximum number of iterations is reached, or the early stopping mechanism is triggered, stop training, save the model parameters with the minimum total loss, and complete the dual-loop collaborative optimization training.

[0029] S6, Structural Hysteresis Behavior Prediction and Performance Verification, Specific Implementation Process as follows: Figure 7 As shown; S61, input the untrained load sequences from the test set into the trained meta-learning-PINN model, quickly output the corresponding displacement response time history and hysteresis curve, and simultaneously quantify the uncertainty of the prediction results based on Monte Carlo Dropout, outputting the 95% confidence interval; S62, performance verification: using mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²) as the benchmarks. 2 Using the metric , the model performance was verified; for small sample working conditions with new cross-sectional parameters, the same prediction accuracy could be achieved with only 10% of the training data, proving that the model has a very strong small sample generalization ability; S63, the predicted pinching effect, stiffness degradation, and energy dissipation characteristics of the hysteresis curve are highly consistent with the numerical simulation results, and strictly meet the internal force equilibrium conditions, with no non-physical prediction results, proving that the model has excellent physical consistency.

[0030] like Figure 8 As shown, the method in this embodiment is implemented through cascaded functional units, including: a multi-condition hysteresis data generation unit, a meta-heuristic parameter global identification unit, a meta-learning-PINN network construction unit, a collaborative optimization loss function construction unit, a dual-loop collaborative training unit, and a hysteresis behavior prediction and verification unit. Each unit is connected in sequence to form a complete technical link from data generation to prediction output.

[0031] The above embodiments are merely preferred embodiments of the present invention, and the scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principle of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for structural hysteretic behavior prediction by fusion of meta-learning-PINN-meta-heuristic optimization, characterized in that, Includes the following steps: S1. Based on the vector finite element method, a multi-scale structural numerical model is constructed, low-cycle repeated loads are applied, and a multi-condition hysteresis curve dataset covering the entire stress stage is generated. Preprocessing and dataset partitioning are then completed. S2 constructs an adaptive hybrid meta-heuristic optimization framework that integrates parallel genetic algorithm, adaptive particle swarm optimization and simulated annealing escape mechanism. Based on the multi-condition hysteresis curve, it performs global parallel optimization of the high-dimensional parameters of the BWBN hysteresis model and outputs the multi-condition hysteresis model parameter set. S3, construct the meta-learning enhanced PINN network architecture, with RNN-LSTM hybrid network as the backbone for temporal feature extraction, embedding meta-learning adaptive sampling module and BWBN hysteresis differential equation hard physical constraint module, and connecting fully connected layer at the tail to output displacement prediction value; S4. Construct the total loss function, which integrates data fidelity loss, PINN physical conservation loss, metaheuristic parameter regularization loss, and training stability loss to provide multi-objective constraints for model optimization. S5. Construct a dual-loop collaborative optimization mechanism with an outer loop and an inner loop. The outer loop iteratively updates the hysteresis model parameters through an adaptive hybrid meta-heuristic algorithm, while the inner loop iteratively updates the network parameters through meta-learning, the AdamW optimizer, and an improved StepLR learning rate scheduler. The dual loops provide bidirectional feedback and synchronous iteration until convergence, thus completing model training. S6, based on the trained model, takes an external load sequence as input and outputs the structural hysteretic displacement response, thus completing the uncertainty quantification and performance verification of the prediction results.

2. The structural hysteresis behavior prediction method integrating meta-learning-PINN-meta-heuristic optimization according to claim 1, characterized in that, In S2, the fitness function of the adaptive hybrid metaheuristic optimization framework is: ,in, For the number of data points, For numerical simulation of load values, Identify load values ​​for the hysteresis model. These are the error weighting coefficients. The stability coefficient, The standard deviation of the parameter distribution. The boundary penalty coefficient, This is a penalty term for parameters that exceed physically reasonable boundaries.

3. The structural hysteresis behavior prediction method integrating meta-learning-PINN-meta-heuristic optimization according to claim 1, characterized in that, In S2, the optimization framework adopts an MPI parallel computing architecture with ≥8 parallel nodes, a population size of 200~500, 300~500 iterations, an adaptive adjustment range of 0.5~0.9 for crossover probability, an adaptive adjustment range of 0.01~0.1 for mutation probability, and adaptive switching of optimization strategies during the iteration process: in the early stage, particle swarm optimization is the main approach; in the middle stage, parallel genetic algorithm is the main approach; and in the later stage, simulated annealing escape mechanism is introduced.

4. The structural hysteresis behavior prediction method integrating meta-learning-PINN-meta-heuristic optimization according to claim 1, characterized in that, In S3, the sampling weight update formula of the meta-learning adaptive sampling module is as follows: ,in, For the first Sampling weights at each time step, Let the gradient magnitude of the physical loss be at that time step. For smoothing coefficients, The total time step is denoted as ; the sampling weight is positively correlated with the gradient magnitude, enabling adaptive dense sampling of the high gradient region of the hysteresis curve.

5. The structural hysteresis behavior prediction method integrating meta-learning-PINN-meta-heuristic optimization according to claim 1, characterized in that, In S3, the BWBN hysteresis differential equation hard physics constraint module directly integrates the hysteresis constitutive control equation into the network forward propagation process. The displacement response output by the network must simultaneously satisfy the hysteresis differential equation and the internal force equilibrium condition, forcing the prediction results to follow the laws of mechanics.

6. The structural hysteresis behavior prediction method integrating meta-learning-PINN-meta-heuristic optimization according to claim 1, characterized in that, In S4, the expression for the total loss function is: ,in, The set of network weights and bias parameters. For the hysteresis model parameter set, To preserve data integrity, For PINN physical conservation loss, For metaheuristic parameter regularization loss, To train stable loss, , , These are the adaptive weighting coefficients for the corresponding loss term.

7. The structural hysteresis behavior prediction method integrating meta-learning-PINN-meta-heuristic optimization according to claim 1, characterized in that, In S5, the inner loop of the dual-loop collaborative optimization mechanism adopts the MAML algorithm. First, pre-training is completed in the source domain to learn the hysteresis general feature prior, and then fine-tuning is completed in the target domain. The inner loop iteration steps are 3 to 10 steps, and the outer loop iteration steps are 10 to 30 steps.

8. The structural hysteresis behavior prediction method integrating meta-learning-PINN-meta-heuristic optimization according to claim 1, characterized in that, In S5, the StepLR dynamic learning rate scheduler is used, and the learning rate update formula is as follows: ,in, The initial learning rate, Scaling factor To adjust the cycle length, The logarithmic adjustment coefficient is... For the number of iterations, The meta-learning decay coefficient, This represents the number of iterations in the inner loop of the MAML.

9. The structural hysteresis behavior prediction method integrating meta-learning-PINN-meta-heuristic optimization according to claim 1, characterized in that, S3 includes: S31, constructing a 4-layer RNN temporal feature extraction network, with the first layer having an input dimension of 1 and an output dimension of 256, and the other three layers having input and output dimensions of 256, with dropout layers between layers and a neuron dropout rate of 0.3; S32, cascading a 3-layer LSTM network, with input and output dimensions of 256, and dropout layers with the same dropout rate between layers, capturing long-term temporal dependencies of hysteresis behavior through gating units; S33, embedding a meta-learning adaptive sampling module, dynamically updating the sampling weights at each time step based on the gradient magnitude of the physical loss, focusing on high-gradient feature regions; S34, embedding a BWBN hysteresis differential equation hard physical constraint module, directly integrating the hysteresis constitutive control equation into the network forward propagation; S35, connecting a fully connected layer, mapping high-dimensional temporal features to one-dimensional displacement prediction values, completing the network architecture construction.

10. A structural hysteresis behavior prediction method integrating meta-learning-PINN-meta-heuristic optimization according to any one of claims 1 to 9, characterized in that, Including cascaded multi-condition hysteresis data generation units, used to construct multi-scale numerical models based on vector finite element method and generate standardized multi-condition hysteresis datasets; The system comprises the following components: a global metaheuristic parameter identification unit with a built-in adaptive hybrid metaheuristic optimization framework for global parallel optimization of high-dimensional parameters of hysteresis models, outputting a set of physical parameters; a meta-learning-PINN network construction unit for building a prediction network architecture that integrates temporal feature extraction, adaptive sampling, and hard physical constraints; a collaborative optimization loss function construction unit for constructing a multi-objective collaborative total loss function; a dual-loop collaborative training unit for achieving bidirectional collaborative iteration of metaheuristic parameter optimization and network training to complete model training; and a hysteresis behavior prediction and verification unit for outputting hysteresis displacement response, uncertainty quantification, and performance verification results.

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