A method for structure hysteretic curve regeneration based on controlled latent variable dynamics and physical constraints
By using a method based on controlled latent variable dynamics and physical constraints, processing non-uniform sampling data and introducing energy dissipation and stiffness constraints, the physical consistency and accuracy problems of structural hysteresis curve regeneration in existing technologies are solved, and high-precision hysteresis curve regeneration is achieved.
Patent Information
- Application Number
- CN202610339619.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-19
- Publication Date
- 2026-07-03
AI Technical Summary
Existing technologies struggle to achieve both physical consistency and high accuracy in regenerating structural hysteresis curves under non-uniform sampling and limited data conditions. Data-driven models are prone to results that do not conform to physical laws, such as negative stiffness and energy non-conservation. Numerical simulation methods are insufficient for characterizing complex loading paths.
A controlled latent variable dynamics and physical constraint-based approach is adopted. Non-uniform sampled data is processed by adaptive smoothing and arc length resampling to construct a controlled latent variable dynamics model. A composite loss function with energy dissipation consistency and stiffness evolution consistency terms is introduced to optimize the model parameters. The structural hysteresis curve is generated by combining the initial state predictor.
It achieves the generation of high-precision structural hysteresis curves that conform to physical laws under non-uniform sampling and limited data conditions, enhances the generalization ability of the model, avoids problems that do not conform to engineering physical laws, and reduces model error.
Smart Images
Figure CN122332772A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of structural performance analysis and intelligent modeling technology, specifically relating to a method for regenerating structural hysteresis curves based on controlled latent variable dynamics and physical constraints. Background Technology
[0002] Structural hysteresis curves are the core basis for evaluating the seismic performance of structures, reflecting the force-displacement relationship, stiffness degradation, and energy dissipation characteristics of structures under cyclic loading. Currently, the main methods for obtaining structural hysteresis curves include physical experiments, numerical simulation, and data-driven modeling. Physical experimental methods (such as full-scale tests and quasi-static tests) provide reliable results, but they are limited by high cost, long cycle time, and difficulty in covering multiple loading conditions, restricting their application in parameter sensitivity analysis and batch evaluation. Numerical simulation methods (such as those based on the Bouc-Wen model and the JS model) describe hysteresis behavior by establishing differential equations, possessing a certain degree of physical interpretability. However, these methods usually rely on simplifying assumptions, are insufficient in characterizing nonlinear features such as stiffness degradation and pinching effects under complex loading paths, and face difficulties in model parameter calibration, making them unsuitable for different structural types and material properties.
[0003] In recent years, data-driven methods (such as recurrent neural networks and long short-term memory networks) have been used for hysteresis curve modeling, demonstrating strong nonlinear fitting capabilities. However, purely data-driven models have inherent limitations: First, the models only learn statistical patterns from the data without introducing mechanical constraints, easily leading to results that violate physical laws, such as negative stiffness and energy non-conservation, outside the training data coverage. Second, actual experimental data often exhibits non-uniform sampling characteristics due to variations in loading rates or limitations of acquisition equipment, while existing discrete-time models, assuming a fixed time step, struggle to effectively handle such data. Furthermore, under limited training data, the model's generalization ability is limited, making it difficult to accurately predict hysteresis responses under different loading regimes. To address these issues, some studies have attempted to incorporate physical information into neural networks (such as the Physical Information Neural Network PINN), but these primarily focus on continuum mechanics problems and have not yet effectively solved the path dependence and non-uniform sampling challenges in hysteresis curve regeneration.
[0004] Therefore, how to achieve the regeneration of structural hysteresis curves with both physical consistency and high accuracy under conditions of non-uniform sampling and limited data is a technical problem that urgently needs to be solved in this field. Summary of the Invention
[0005] The purpose of this invention is to provide a method for regenerating structural hysteresis curves based on controlled latent variable dynamics and physical constraints, so as to solve the problems mentioned in the background art.
[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for regenerating structural hysteresis curves based on controlled latent variable dynamics and physical constraints includes the following steps: S1: Obtain non-uniform sampling time-series data of the target structure during the loading process. The time-series data includes a displacement sequence and a corresponding force sequence. The displacement values in the displacement sequence constitute the loading displacement signal. At the same time, obtain static parameters describing the loading condition. S2: The non-uniformly sampled time-series data is preprocessed by removing noise through adaptive smoothing and constructing a standardized input sequence through parameterized path resampling based on arc length; S3: The standardized input sequence is mapped to low-dimensional latent variables using an encoding network, and the static parameters are fused with the low-dimensional latent variables to obtain an initial state vector; S4: Construct a controlled latent variable dynamic model, which is defined as a continuous differential equation with respect to time. Its inputs include the current state of the latent variable, the real-time displacement input, and the static parameters. The output is the rate of change of the latent variable with time. S5: Construct a composite loss function, which includes at least a data fitting error term, an energy dissipation consistency term, and a stiffness evolution consistency term; S6: Based on the composite loss function, jointly train the controlled latent variable dynamics model and the encoding network to optimize the model parameters; S7: Using the trained model, receive a new displacement input sequence, solve the continuous differential equation numerically, generate a structural force response sequence that conforms to physical laws, and then regenerate the structural hysteresis curve.
[0007] The preprocessing in S2 also includes: S101. Automatically identify displacement data columns and force data columns from the data file; S102. Abnormal sampling points are identified and marked as missing data by combining coarse screening anomaly detection and fine screening anomaly detection; S103. Spline interpolation is used to repair intervals with consecutive missing lengths less than a preset threshold, and intervals with consecutive missing lengths exceeding the threshold are retained as missing. S104. Perform uniform scaling based on displacement amplitude; S105. Extract characteristic parameters, including maximum displacement, energy dissipation, and initial stiffness, from the processed hysteresis curve as the static parameters.
[0008] In step S3, the encoding network uses a recurrent neural network, a gated recurrent unit, or a variational autoencoder to encode the historical displacement-force sequence and obtain the probability distribution or deterministic representation of the latent variables.
[0009] In S4, the continuous differential equation satisfies the following relationship: in, This represents the latent variable state at time t. The initial state of the latent variables, For loading displacement control input, These are static operating parameters. and These represent the intrinsic dynamics term and the controlled driving term of the latent variable, respectively. The loading displacement is introduced in the form of a continuous control path or a discrete sampling path to drive the evolution of the latent variable in the latent state space.
[0010] In step S5, the energy dissipation consistency term is constructed as follows: S501: Based on the displacement extreme points, the loading process is divided into several complete hysteresis loops. The area enclosed by the force sequence predicted by the model and the corresponding displacement sequence within each complete hysteresis loop is calculated as the predicted energy dissipation value of that hysteresis loop, satisfying the expression: In the formula, The total number of sampling points. and These represent the structural force response and displacement value at the i-th sampling point, respectively. S502: During the model training phase, obtain reference values for energy dissipation based on measured data; during the generalization prediction phase, if energy constraints need to be applied, the theoretical dissipation upper limit can be estimated using empirical formulas based on static operating parameters as a reference value. S503: Calculate the difference between the predicted energy dissipation value and the energy dissipation reference value, and add the difference as a penalty term to the composite loss function; for local paths that are not closed at the beginning and end, energy dissipation constraints are not included, and constraints are only imposed through the data fitting error term.
[0011] In step S5, the construction of the stiffness evolution consistency term includes the following steps: Step S511: Calculate the equivalent stiffness or tangential stiffness of the force sequence and corresponding displacement sequence predicted by the model during the loading, unloading, and reverse loading stages, satisfying the following relationship: Step S512: Monitor the numerical sign and trend of the tangential stiffness. If an abnormal stiffness mutation that violates the material constitutive relation is detected, a corresponding penalty term is generated and added to the composite loss function. The physical allowable range is preset with a threshold based on the structural material type.
[0012] In step S5, the composite loss function is a model optimization objective formed by jointly weighting the data fitting error term, the energy dissipation consistency term, and the stiffness evolution consistency term.
[0013] In step S7, the numerical solution of the continuous differential equation is discretized using a numerical integrator. The integration step size is dynamically adjusted according to the time interval of the input displacement sequence to adapt to input data with different sampling frequencies. During the training process, the adjoint sensitivity method or backpropagation of the numerical integral calculation graph is used to ensure the numerical stability of the gradient calculation.
[0014] The method also includes a generalization prediction step: S8: When complete historical time series data is lacking and only the static parameters are available, the initial state of the latent variables is predicted based on the static operating condition parameters by the initial state predictor. S9: Using the predicted initial state of the latent variables as the initial condition of the latent variable dynamics model, and combining it with the new displacement input sequence, the latent variable dynamics model generates the structural hysteresis curve under the corresponding loading condition.
[0015] The initial state predictor is constructed using a neural network model to establish a mapping relationship between static operating parameters and latent variable initial states.
[0016] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1) This invention constructs a controlled latent variable dynamic model to explicitly describe the continuous evolution of hysteresis behavior over time in the latent state space, and uses the loading displacement as a control input to directly act on the latent variable state change rate, which can naturally adapt to non-uniform sampling, variable loading rate and different loading path conditions.
[0017] 2) This invention introduces physical constraints that reflect the characteristics of hysteresis energy dissipation and stiffness change during model training, organically integrating structural mechanical properties with the data-driven model, thus avoiding the problems that easily occur in pure data-driven methods that do not conform to the laws of engineering physics.
[0018] 3) By introducing an initial state predictor, this invention can predict the initial state of latent variables based solely on static working condition parameters in the absence of complete historical displacement-force observation data. Combined with the loading regime, it can regenerate the structural hysteresis curve, thereby enhancing the model's generalization ability under limited data conditions. Attached Figure Description
[0019] Figure 1 This is a flowchart of the structural hysteresis curve regeneration method based on controlled latent variable dynamics and physical constraints in this invention.
[0020] Figure 2This is a network structure framework diagram corresponding to the structural hysteresis curve regeneration method of the present invention.
[0021] Figure 3 This is a flowchart of the data preprocessing process.
[0022] Figure 4 The evolution of latent variables in the continuous time domain when the displacement is used as the control input.
[0023] Figure 5 This is a diagram showing the energy dissipation characteristics and stiffness variation constraints of the hysteresis curve.
[0024] Figure 6 This is a flowchart for regenerating structural hysteresis curves based on an initial state predictor. Detailed Implementation
[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.
[0026] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.
[0027] Example 1 This embodiment uses a buckling-resistance brace structure as an example to illustrate the structural hysteresis curve regeneration method based on controlled latent variable dynamics and physical constraints proposed in this invention. Figure 1 As shown, in order to quantify the hysteresis curve of the regenerated buckling-restrained brace structure, the present invention mainly includes the following steps: Step 1: Data Preprocessing In terms of specific implementation, such as Figure 2 As shown, displacement-force time series data of structures or materials under cyclic loading conditions are obtained, preprocessed and normalized, and a regenerated dataset of structural hysteresis curves containing static load parameters is constructed.
[0028] First, displacement-force time-series data of the structure or material under cyclic loading conditions are acquired. This data can be derived from full-scale tests, quasi-static tests, or numerical simulation results. The displacement-force time-series data is automatically read from a preset data file type, and the corresponding displacement and force data columns are automatically identified based on preset column name matching rules. In actual experiments, due to variations in loading rate or limitations of the acquisition equipment, the acquired displacement-force time-series data often exhibits non-uniform sampling characteristics, meaning that the time intervals or displacement increments between adjacent sampling points are inconsistent.
[0029] Subsequently, a combination of coarse screening anomaly detection and fine screening anomaly detection was used to identify abnormal sampling points in the displacement-force time series data. These abnormal sampling points were marked as missing data, and the missing data were classified according to the continuous length of the missing interval to avoid introducing errors that do not conform to physical laws through cross-interval interpolation.
[0030] Then, by searching for different combinations of smoothing parameters and using the change in the energy dissipation characteristics of the hysteresis curve as a constraint, the smoothing parameters are adaptively determined to suppress noise while maintaining the overall physical properties of the hysteresis curve.
[0031] Next, for hysteresis curves where displacement exhibits non-monotonic variation, to avoid parameterization singularities at displacement inflection points, a parameterized path resampling method based on arc length is adopted: the cumulative arc length is constructed based on the displacement change and force change. Furthermore, equidistant sampling is performed in the arc length parameter domain to obtain standardized time-series data of uniform length. This method can map non-uniform time steps to a uniform parameter domain, effectively solving the modeling difficulties caused by non-uniform sampling, while ensuring sampling stability at turning points.
[0032] Finally, the displacement time series data is normalized simultaneously using the maximum absolute value as the normalization factor, and the displacement data and force data are normalized simultaneously. The maximum displacement, energy dissipation, initial stiffness, stiffness degradation coefficient and pinching characteristic parameters are automatically extracted and used as static condition parameters for subsequent structural hysteresis curve regeneration model.
[0033] Step 2: Initial state encoding of latent variables In terms of specific implementation, such as Figure 3 As shown, the normalized displacement-force time series data is input into the encoding module to extract and compress features from the historical hysteresis response of the structure. The encoding module can employ a recurrent neural network, a gated recurrent unit, a variational autoencoder, or a combination thereof to encode the historical displacement-force sequence to obtain initial values of latent variables that characterize the initial state of the structure's hysteresis behavior.
[0034] Specifically, in one implementation, the initial values of the latent variables can be deterministic vectors; in another implementation, the initial values of the latent variables can be represented in the form of a probability distribution to enhance the model's ability to represent uncertainty.
[0035] Step 3: Dynamic modeling of controlled latent variables In specific implementation, in step 3, such as Figure 4 As shown, a latent variable dynamic model is constructed that includes the displacement as the control input, and the continuous evolution process of the latent variable in the time dimension is solved by numerical integration.
[0036] First, after obtaining the initial state of the latent variables, the loading displacement signal is introduced as the control input, and it is jointly characterized with the current state of the latent variables and the static working condition parameters.
[0037] Then, a nonlinear mapping function is constructed to describe the rate of change of the latent variable state.
[0038] Finally, based on the aforementioned nonlinear mapping function, a controlled continuous dynamical model of the latent variables with respect to time is established to characterize the continuous evolution of the structural hysteresis behavior in the latent state space. The evolution of the latent variables with respect to time satisfies the following relationship: (1) in, This represents the latent variable state at time t. The initial state of the latent variables, For loading displacement control input, These are static operating parameters. and These represent the latent variable intrinsic dynamics term and the controlled driving term, respectively. The loading displacement control input... In the numerical solution process, a continuous-time function is constructed using linear interpolation or cubic spline interpolation to accommodate the arbitrary step size requirements of the numerical integrator. By solving the above-mentioned controlled dynamic model through numerical integration, the continuous evolution trajectory of the latent variables over time can be obtained.
[0039] Step 4: Force Response Decoding and Generation In practical implementation, the latent variable evolution trajectory obtained through numerical integration is input into the decoding module to establish the latent variable state. The mapping relationship between structural force response and the data is established to generate corresponding normalized structural force response time-series data. The decoding module is implemented using a neural network, with latent variable states as input. The output is the normalized force response. To ensure the effective transmission of physical constraints, all physical constraint loss functions are directly based on the decoded force sequence. The calculations are performed and jointly optimized with the data fitting error. During training, the decoder parameters are updated synchronously with the dynamic model parameters to ensure that the decoding process does not negate the effects of physical constraints.
[0040] Step 5: Introduction of Physical Constraints and Model Optimization In practical implementation, during model training, such as Figure 5 As shown, a constraint loss function reflecting the physical characteristics of structural hysteresis behavior is introduced to jointly optimize the model parameters.
[0041] First, based on the generated normalized force response sequence and corresponding loading displacement data, the energy dissipation characteristics of the hysteresis curve within one or more loading cycles are calculated. To avoid confusion between accumulated work and hysteresis loop area, a segmentation calculation method based on complete hysteresis loops is adopted: the loading process is divided into several complete hysteresis loops according to the displacement extreme points, and the enclosed area of each hysteresis loop is calculated separately. In this embodiment, the sliding window comparison method is used to identify displacement extreme points: for the displacement sequence... A point is considered a local maximum when its displacement is greater than that of the k points before and after it (k=5), and a point is considered a local minimum when its displacement is less than that of the k points before and after it. Adjacent maxima and minima constitute a partial loading cycle, and two adjacent partial cycles form a complete hysteresis loop. For paths that are not closed at the beginning and end, if the displacement difference between the endpoint and the starting point is less than a preset threshold, the path is forcibly closed and included in the calculation; otherwise, it is not included in the energy dissipation constraint.
[0042] Subsequently, the equivalent stiffness or tangential stiffness variation characteristics of the hysteresis curve during the loading, unloading, and reverse loading stages are calculated.
[0043] Then, a physical constraint loss function is constructed based on the energy dissipation characteristics and stiffness change characteristics. The energy dissipation characteristics are calculated by numerical integration over the area enclosed by the force-displacement curves, and formula (1) is used independently for each hysteresis loop. For local paths that are not closed at the beginning and end, energy dissipation constraints are not included, and constraints are only imposed through the data fitting error term, satisfying the expression: (2) Meanwhile, the equivalent stiffness or tangential stiffness variation characteristics satisfy the following relationship: (3) In the formula, The total number of sampling points. and These represent the structural force response and displacement value at the i-th sampling point, respectively. In this embodiment, the stiffness constraint only applies to two non-physical situations: ① negative stiffness occurring in the initial stage of loading; ② the stiffness degradation rate of two adjacent cycles exceeding the upper limit of material test statistics. No penalty is imposed for normal softening behavior after yielding. It should be noted that the energy dissipation consistency constraint is only used during the training phase and relies on measured data to calculate reference values; when inferring and generating new hysteresis curves, this constraint term does not participate in the calculation, and the physical rationality of the generated results is only ensured by the already trained model parameters.
[0044] Next, based on the aforementioned energy dissipation and stiffness variation characteristics, a physical constraint loss function is constructed. This function, along with the data fitting error, is used as the model optimization objective to jointly optimize the parameters of the latent variable dynamics model and the decoding module. In this embodiment, the composite loss function is expressed as: (4) in, This is the data fitting error term. For energy dissipation consistency term, This is a term representing the consistency of stiffness evolution; and The weighting coefficients are configured to be adjusted based on the performance of the validation set. In this embodiment, a grid search is used, with values ranging from [0.1, 10] and a step size of 0.1.
[0045] Finally, a comparative model without introducing a physical constraint loss function is constructed, while the remaining network structure and training parameters remain consistent with the method of this invention. Without introducing physical constraints, 30% of the samples in the generated hysteresis curves show a negative equivalent stiffness during the unloading or reverse loading phase. After introducing physical constraints, the average relative error of the model in peak force and energy consumption indicators is reduced from 28% to 4%.
[0046] Step 6: Hysteresis Curve Output In practice, after the model training is completed, the corresponding force scale parameters are obtained based on the static load condition parameters. The generated normalized force response sequence is then denormalized, and the final output is the structural hysteresis curve under the corresponding loading condition. For example... Figure 6 As shown, the decoding module can restore the evolution results in the latent variable space to the force-displacement response curve of the structure during the loading process.
[0047] It should be noted that the inverse normalization process depends on the acquisition of force scale parameters. When the static operating condition parameters include known force scale parameters, they are directly used for inverse normalization; when the force scale parameters are unknown in the generalization prediction stage, the decoding module, after training, already has the ability to directly output physical dimension forces, or the force scaling coefficient can be predicted through auxiliary branches, in which case an explicit inverse normalization step is not required.
[0048] Step 7: Regeneration of hysteresis curves based on the initial state predictor In practical implementation, without complete displacement-force historical observation data, the initial state of latent variables can be predicted solely based on static load parameters by the initial state predictor. This prediction serves as the initial condition for the controlled latent variable dynamics model, enabling the regeneration of the structural hysteresis curve. In generalized prediction scenarios, if the static parameters do not contain force scale information, the controlled latent variable dynamics model and decoding module, after joint training, can directly map force responses with physical dimensions from the latent variable space without additional inverse normalization processing. Statistical analysis of the correlation between static load parameters and the initial state of latent variables shows a significant correlation, with a Pearson correlation coefficient greater than 0.85.
[0049] Specifically, the initial state predictor is constructed using a neural network model to establish the mapping relationship between static operating parameters and latent initial states. This predictor is optimized together with the main model, updating parameters during training through the overall model loss function. The predictor, constructed using a neural network, outputs... As the initial condition of differential equation (1). During training, the gradient of the composite loss function (4) is backpropagated through the adjoint sensitivity method, updating the decoder and dynamic model parameters in sequence, and finally propagating to the initial state predictor to achieve end-to-end joint optimization. Combined with the loading displacement sequence provided by the loading regime generator, the structural hysteresis curve under the corresponding loading condition is generated through the controlled latent variable dynamic model, thereby realizing the conditional regeneration of the structural hysteresis curve.
[0050] Example 2: Further Explanation of Numerical Solution In step 7, the numerical solution of the continuous differential equation employs a numerical integrator for discretization. Specifically, an adaptive step-size numerical integrator (such as the Runge-Kutta45 method) can be used to dynamically adjust the integration step size based on the time intervals of the input displacement sequence to adapt to input data with different sampling frequencies. The step size is increased when the local error estimate is less than a threshold to improve computational efficiency; the step size is automatically decreased when the error exceeds the threshold or divergence of the state variable is detected to maintain numerical stability. During training, the adjoint sensitivity method or direct backpropagation of the numerical integration graph is used to ensure the numerical stability of gradient calculation.
[0051] Example 3: Multiple methods for fusing static parameters and latent variables In step 3, the fusion method of the static parameters and the low-dimensional latent variables is not limited to concatenation. It can also be achieved through weighted fusion using an attention mechanism, or by mapping the static parameters to feature vectors via an embedding layer and combining them with the latent variables to serve as the initial conditions or control inputs of the controlled latent variable dynamics model. The attention mechanism can dynamically adjust the influence weights of the static parameters according to different parts of the input sequence, improving the model's adaptability to changes in operating conditions. The static parameter c has a dual role in the model: on the one hand, it serves as a component of the initial state vector, determining the starting point of evolution; on the other hand, it serves as a conditional input, continuously influencing the dynamic function through modulation network parameters (such as a feature linear modulation layer). and This allows them to adapt to the evolutionary patterns of different structural types.
Claims
1. A method for structural hysteretic curve regeneration based on controlled latent variable dynamics and physical constraints, characterized by, Includes the following steps: S1: Obtain non-uniform sampling time-series data of the target structure during the loading process. The time-series data includes a displacement sequence and a corresponding force sequence. The displacement values in the displacement sequence constitute the loading displacement signal. At the same time, obtain static parameters describing the loading condition. S2: The non-uniformly sampled time-series data is preprocessed by removing noise through adaptive smoothing and constructing a standardized input sequence through parameterized path resampling based on arc length; S3: The standardized input sequence is mapped to low-dimensional latent variables using an encoding network, and the static parameters are fused with the low-dimensional latent variables to obtain an initial state vector; S4: Construct a controlled latent variable dynamic model, which is defined as a continuous differential equation with respect to time. Its inputs include the current state of the latent variable, the real-time displacement input, and the static parameters. The output is the rate of change of the latent variable with time. S5: Construct a composite loss function, which includes at least a data fitting error term, an energy dissipation consistency term, and a stiffness evolution consistency term; S6: Based on the composite loss function, jointly train the controlled latent variable dynamics model and the encoding network to optimize the model parameters; S7: Using the trained model, receive a new displacement input sequence, solve the continuous differential equation numerically, generate a structural force response sequence that conforms to physical laws, and then regenerate the structural hysteresis curve.
2. The method of claim 1, wherein, The preprocessing in S2 also includes: S101. Automatically identify displacement data columns and force data columns from the data file; S102. Abnormal sampling points are identified and marked as missing data by combining coarse screening anomaly detection and fine screening anomaly detection; S103. Spline interpolation is used to repair intervals with consecutive missing lengths less than a preset threshold, and intervals with consecutive missing lengths exceeding the threshold are retained as missing. S104. Perform uniform scaling based on displacement amplitude; S105. Extract characteristic parameters, including maximum displacement, energy dissipation, and initial stiffness, from the processed hysteresis curve as the static parameters.
3. The method of claim 1, wherein, In step S3, the encoding network uses a recurrent neural network, a gated recurrent unit, or a variational autoencoder to encode the historical displacement-force sequence and obtain the probability distribution or deterministic representation of the latent variables.
4. The method of claim 1, wherein, In S4, the continuous differential equation satisfies the following relationship: wherein, represents the latent variable state at time t, is the latent variable initial state, is the loading displacement control input, is the static operating condition parameter, and respectively represent the latent variable intrinsic dynamics term and the controlled driving term, the loading displacement being introduced in the form of a continuous control path or a discrete sampled path for driving the evolution of the latent variable in the latent state space.
5. The method of claim 1, wherein, In step S5, the energy dissipation consistency term is constructed as follows: S501: Based on the displacement extreme points, the loading process is divided into several complete hysteresis loops. The area enclosed by the force sequence predicted by the model and the corresponding displacement sequence within each complete hysteresis loop is calculated as the predicted energy dissipation value of that hysteresis loop, satisfying the expression: wherein is the total number of sampling points, and and represent the structural force response and displacement value at the i-th sampling point, respectively. S502: During the model training phase, obtain reference values for energy dissipation based on measured data; In the generalization prediction stage, if energy constraints need to be applied, the theoretical dissipation upper limit can be estimated based on static operating parameters using empirical formulas as a reference value. S503: Calculate the difference between the predicted energy dissipation value and the energy dissipation reference value, and add the difference as a penalty term to the composite loss function; for local paths that are not closed at the beginning and end, energy dissipation constraints are not included, and constraints are only imposed through the data fitting error term.
6. The method of claim 5, wherein, In step S5, the construction of the stiffness evolution consistency term includes the following steps: Step S511: Calculate the equivalent stiffness or tangential stiffness of the force sequence and corresponding displacement sequence predicted by the model during the loading, unloading, and reverse loading stages, satisfying the following relationship: Step S512: Monitor the numerical sign and trend of the tangential stiffness. If an abnormal stiffness mutation that violates the material constitutive relation is detected, a corresponding penalty term is generated and added to the composite loss function. The physical allowable range is preset with a threshold based on the structural material type.
7. The method of claim 6, wherein, In step S5, the composite loss function is a model optimization objective formed by jointly weighting the data fitting error term, the energy dissipation consistency term, and the stiffness evolution consistency term.
8. The method of claim 1, wherein, In step S7, the numerical solution of the continuous differential equation is discretized using a numerical integrator, and the integration step size is dynamically adjusted according to the time interval of the input displacement sequence to adapt to input data with different sampling frequencies. During training, the adjoint sensitivity method or backpropagation of the numerical integral computation graph is used to ensure the numerical stability of gradient calculation.
9. The method of claim 1, wherein, The method also includes a generalization prediction step: S8: When complete historical time series data is lacking and only the static parameters are available, the initial state of the latent variables is predicted based on the static operating condition parameters by the initial state predictor. S9: Using the predicted initial state of the latent variables as the initial condition of the latent variable dynamics model, and combining it with the new displacement input sequence, the latent variable dynamics model generates the structural hysteresis curve under the corresponding loading condition.
10. The method of claim 9, wherein, The initial state predictor is constructed using a neural network model to establish the mapping relationship between static operating parameters and the initial state of latent variables. The initial state predictor, the controlled latent variable dynamic model, and the decoding module are jointly trained in an end-to-end manner, and the gradient is backpropagated from the composite loss function through the decoding module and the dynamic model to the initial state predictor.