Seismic Demand Prediction Method Based on Vectorization and Sequence-to-Sequence Surrogate Model

Abstract

A seismic demand prediction method based on vectorization and sequence-to-sequence surrogate models belongs to the technical field of structural damage assessment caused by earthquakes, and includes the following steps: (1) generating multi-dimensional input parameters including geometry, materials, and seismic boundary conditions based on Latin hypercube sampling; (2) generating a dynamic response database of reinforced concrete frame structures based on the multi-dimensional input parameters by using finite element stochastic time history analysis; (3) adopting deep learning algorithms to train a point model, a vectorization model, and a sequence-to-sequence model based on the dynamic response database, which are respectively used for structural response prediction and multi-objective reliability analysis. The present invention realizes the efficient prediction of multi-objective dynamic responses and the assessment of multi-variable seismic vulnerability by integrating deep learning technologies (including deep neural network DNN, long short-term memory network LSTM, and Transformer architecture), and overcomes the deficiencies of existing methods in terms of computational efficiency, model adaptability, and multi-objective prediction accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural damage assessment caused by earthquakes, and particularly relates to a seismic demand prediction method based on vectorization and sequence-to-sequence surrogate models. Background Art

[0002] With the acceleration of the global urbanization process and the continuous improvement of building height and structural complexity, higher requirements are put forward for the seismic performance of building structures, especially reinforced concrete frame structures. However, traditional seismic analysis methods, such as finite element analysis, although able to provide high-precision results, show problems of high computational cost and long time consumption when facing multiple uncertain factors (such as the randomness of seismic input, the volatility of material and geometric parameters) and the reliability assessment of large-scale group structures. This severely restricts the practical application of seismic analysis based on the finite element method in disaster emergency response, rapid assessment, and multi-scenario prediction.

[0003] In recent years, with the rapid development of machine learning and deep learning technologies, surrogate models, as a technical means capable of quickly approximating the response of complex nonlinear systems, have gradually received attention and application in the field of structural engineering. Surrogate models can significantly reduce the computational cost and achieve real-time prediction of complex models while ensuring the result accuracy. Currently, common surrogate model technologies include polynomial regression, support vector machines, Gaussian process regression, decision trees, and deep learning methods based on neural networks. Among them, the deep learning-based surrogate models have particularly broad application prospects in structural dynamic analysis due to their powerful modeling ability for high-dimensional complex nonlinear problems.

[0004] Existing research shows that certain progress has been made in the application of machine learning technologies in seismic analysis. For example, hydrodynamic simulations of shallow water wave equations are realized through physics-driven neural networks; cable forces in structural optimization are predicted using various regression methods (such as Gaussian process regression and support vector regression). These studies demonstrate the potential of machine learning technologies in seismic modeling, but mostly focus on single-objective or simple multi-objective tasks, such as frequency analysis or single-point seismic vulnerability assessment.

[0005] In addition, although the research on multi-objective surrogate models has begun to receive attention, existing models still have certain limitations. Taking the adaptive vectorization surrogate modeling framework as an example, although this method realizes vectorized output, it still relies on multiple independent machine learning models, resulting in increased computational complexity and difficulty in expanding to more complex application scenarios. More importantly, most existing surrogate models are limited to fixed geometric and material properties and cannot adapt to the diversity of reinforced concrete frame structures in actual engineering. This limitation makes it difficult for existing models to meet the wide range of needs of urban building groups in seismic analysis.

[0006] Meanwhile, most traditional surrogate models adopt a single-point output modeling approach, ignoring the correlation between multiple target outputs. This method leads to inaccuracies in multi-objective reliability assessment and limits its application in actual complex tasks. Especially in seismic response analysis, there are significant coupling relationships among the inter-story drift, roof displacement, base shear, and acceleration of a structure. The single-point output model cannot effectively capture these internal connections, resulting in incomplete prediction results. In addition, existing research has focused more on point models rather than time series models, which further limits the comprehensive modeling ability of seismic input characteristics.

[0007] To address the above problems, in recent years, the introduction of deep learning methods such as long short-term memory networks (LSTMs) and Transformers has provided new solutions for surrogate models. The LSTM network can effectively capture the dependencies of long time series data through its unique memory cell design and has been widely used in language modeling, time series prediction, and structural response analysis. The Transformer architecture, on the other hand, achieves efficient parallel computing and the ability to model long-range dependencies through self-attention mechanisms, making it particularly suitable for sequence-to-sequence tasks with complex input characteristics. However, the application of LSTMs and Transformers in structural engineering is still in the exploratory stage, especially in complex multi-objective and time series modeling, and their potential has not been fully exploited.

[0008] Generally speaking, the current research gaps include:

[0009] Adaptive modeling of diverse structural characteristics: Existing models are difficult to adapt to the diverse geometric, material, and boundary condition characteristics of reinforced concrete frame structures.

[0010] Effective capture of time series characteristics: The time characteristics of seismic input are not fully utilized, resulting in deficiencies in the dynamic response prediction of surrogate models.

[0011] Accurate modeling of multi-objective outputs: There is a lack of a surrogate model framework that can synchronously output multiple target responses.

[0012] Computational efficiency and scalability: Existing methods have high computational complexity and are difficult to meet the needs of group structure analysis and rapid disaster emergency response.

[0013] Therefore, developing an efficient surrogate model framework that can adapt to diverse structural characteristics, capture the time series characteristics of seismic input, and support multi-objective synchronous output has become the key to solving the seismic analysis problems of reinforced concrete frame structures. Based on this research background, the present invention proposes a vectorized and sequence-to-sequence surrogate model framework, providing a new solution for the rapid seismic demand prediction and vulnerability analysis of reinforced concrete frame structures. Summary of the Invention

[0014] The present invention discloses a seismic demand prediction method based on vectorization and sequence-to-sequence surrogate models. By integrating deep learning techniques (including deep neural network DNN, long short-term memory network LSTM, and Transformer architecture), the present invention realizes efficient prediction of multi-objective dynamic responses and multi-variable seismic vulnerability assessment, overcoming the deficiencies of existing methods in terms of computational efficiency, model adaptability, and multi-objective prediction accuracy.

[0015] To achieve the above object, the technical solution of the present invention is as follows:

[0016] A seismic demand prediction method based on vectorization and sequence-to-sequence surrogate models includes the following steps:

[0017] (1) Generate multi-dimensional input parameters including geometric, material, and seismic boundary conditions based on Latin hypercube sampling;

[0018] (2) Based on the multi-dimensional input parameters, use finite element stochastic time history analysis to generate a dynamic response database of reinforced concrete frame structures;

[0019] (3) Adopt deep learning algorithms to train a point model, a vectorization model, and a sequence-to-sequence model based on the dynamic response database, which are respectively used for structural response prediction and multi-objective reliability analysis.

[0020] Preferably, in the step (1), the multi-dimensional input parameters include parameter one based on geometric attributes, parameter two based on material attributes, and parameter three based on seismic boundary condition attributes.

[0021] Preferably, in the step (1), the parameter one includes floor height, single-span length, single-span width, column width, beam depth, column cross-sectional area, beam cross-sectional area, concrete cover thickness, and floor slab thickness; the parameter two includes concrete strength grade, steel yield strength, stiffness ratio before and after steel yield, elastic modulus, and Poisson's ratio; the parameter three includes earthquake magnitude, fault zone length, earthquake duration, peak ground acceleration, spectral acceleration, and cumulative absolute acceleration.

[0022] Preferably, in the step (3), the point model refers to: realizing fast prediction of single-objective output response through DNN, which is applicable to single-variable analysis tasks of structural dynamic responses; the vectorization model refers to: designing a network model with a vectorized output structure based on DNN, simple LSTM, and Transformer to achieve synchronous prediction of multi-objective responses; the sequence-to-sequence model refers to: using complex LSTM and Transformer architectures to construct a network model to capture the time series characteristics of seismic inputs and generate the time history of structural dynamic responses.

[0023] Preferably, in the step (3), the vectorization model is used to achieve multi-objective synchronous output, and the outputs of multi-objective responses include the maximum top displacement, maximum inter-story drift ratio, maximum acceleration, and maximum base shear force of the reinforced concrete frame structure.

[0024] Preferably, in the step (3), the sequence-to-sequence model captures the time series characteristics of seismic input through LSTM and Transformer networks.

[0025] Preferably, in the step (3), based on the constructed point model, vectorization model, and sequence-to-sequence model, the Monte Carlo method is used for univariate and multivariate vulnerability analysis, and the relationship curve between seismic intensity index and failure probability is output.

[0026] Preferably, in the step (3), the seismic intensity indexes include spectral acceleration, peak ground acceleration, and cumulative absolute acceleration.

[0027] The beneficial effects of the seismic demand prediction method based on the vectorization and sequence-to-sequence surrogate models of the present invention are as follows:

[0028] 1. The present invention realizes the synchronous prediction of multi-objective responses through the vectorization model framework, significantly improving the calculation efficiency and prediction accuracy of multi-objective reliability analysis.

[0029] 2. The sequence-to-sequence model of the present invention introduces the LSTM and Transformer architectures, enabling the surrogate model to capture the time series characteristics of seismic input and adapt to complex dynamic response prediction tasks.

[0030] 3. Through the sensitivity analysis of input features, the present invention screens out the most important seismic features for the response of reinforced concrete frames, optimizing the input parameter combination of the model.

[0031] 4. The present invention uses the Monte Carlo method combined with the surrogate model to quickly generate univariate and multivariate seismic vulnerability curves, which are applicable to disaster emergency management and reliability assessment.

[0032] 5. The present invention has a wide range of application scenarios, specifically as follows:

[0033] A. Individual structure reliability analysis: It is applicable to the rapid seismic demand prediction and reliability assessment of reinforced concrete frame structures, providing technical support for seismic design and performance evaluation.

[0034] B. Group structure disaster assessment: The method of the present invention has good scalability and can be further applied to the analysis of structural groups at the community level, supporting urban disaster prevention and control planning and emergency response.

[0035] C. Engineering Decision Support: By quickly generating multi-objective seismic response and vulnerability analysis results, the present invention provides data support for engineering decision-making, resource allocation, and post-disaster recovery. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Shows the process of generating surrogate model training data;

[0037] Figure 2 Is a schematic diagram of the architecture of the point model;

[0038] Figure 3 Is a schematic diagram of the architecture of the vectorization model;

[0039] Figure 4 Is a schematic diagram of the LSTM architecture of the sequence-to-sequence model;

[0040] Figure 5 Is a schematic diagram of the Transformer architecture of the sequence-to-sequence model;

[0041] Figure 6 Is a correlation analysis diagram of seismic input and structural response;

[0042] Figure 7 Is the result of single-variable seismic vulnerability analysis;

[0043] Figure 8 Is the result of multi-variable seismic vulnerability analysis;

[0044] Figure 9 Is a comparison chart of the prediction accuracy of different surrogate models;

[0045] Figure 10 Is a schematic diagram of the seismic response time history;

[0046] Figure 11 Is a schematic diagram of the application of the surrogate model in community structure group analysis. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] The following description is only for the preferred embodiments of the present invention and is not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0048] The following embodiments can be understood as separately expressing a part of the local structure or method of the present invention, or can also be understood as the embodiments combined with each other to explain the connotation of the structure or method in a larger scope of the present invention.

[0049] Embodiment 1

[0050] The seismic demand prediction method of the present invention based on the vectorization and sequence-to-sequence surrogate models, as Figure 1-11As shown, it includes the following steps:

[0051] (1) Generate multi-dimensional input parameters including geometry, material, and seismic boundary conditions based on Latin hypercube sampling; the input parameters cover a wide range of structural and seismic characteristics to ensure the generality and adaptability of the model;

[0052] (2) Based on the multi-dimensional input parameters, use finite element random time history analysis to generate a dynamic response database of reinforced concrete frame structures; perform random time history analysis through the finite element method to construct a dynamic response database covering various structural configurations and seismic input conditions, which is used to train the surrogate model to enable it to efficiently predict structural dynamic responses in complex non-linear systems;

[0053] (3) Adopt deep learning algorithms to train point models, vectorization models, and sequence-to-sequence models (i.e., the surrogate model includes the above three models) based on the dynamic response database, which are respectively used for structural response prediction and multi-objective reliability analysis.

[0054] Example 2

[0055] As Figure 1-11 shown, in the step (1), the multi-dimensional input parameters include parameter one based on geometric attributes, parameter two based on material attributes, and parameter three based on seismic boundary condition attributes;

[0056] In the step (1), the parameter one includes floor height, single-span length, single-span width, column width, beam depth, column cross-sectional area, beam cross-sectional area, concrete cover thickness, and floor slab thickness; the parameter two includes concrete strength grade, steel yield strength, stiffness ratio before and after steel yield, elastic modulus, and Poisson's ratio; the parameter three includes earthquake magnitude, fault zone length, earthquake duration, peak ground acceleration, spectral acceleration, and cumulative absolute acceleration. The input parameters are normalized to eliminate dimension differences and improve the stability and accuracy of model training.

[0057] Example 3

[0058] As Figure 1-11As shown in the figure, in step (3), the point model refers to: a fast prediction of single-object output response implemented by DNN, which is applicable to the univariate analysis task of structural dynamic response; the vectorization model refers to: a network model designed with a vectorized output structure based on DNN, simple LSTM, and Transformer to achieve synchronous prediction of multi-object responses and improve the accuracy and efficiency of multi-object reliability assessment; the sequence-to-sequence model refers to: a network model constructed using complex LSTM and Transformer architectures to capture the time series characteristics of seismic inputs and generate the time history of structural dynamic responses, which is applicable to complex dynamic response prediction and higher-dimensional data modeling tasks.

[0059] Example 4

[0060] As Figure 1-11 shown: In step (3), the vectorization model is used to achieve multi-object synchronous output. The outputs of multi-object responses include the maximum top displacement, maximum inter-story drift ratio, maximum acceleration, and maximum base shear force of the reinforced concrete frame structure.

[0061] As Figure 1-11 shown: In step (3), the sequence-to-sequence model captures the time series characteristics of seismic inputs through LSTM and Transformer networks.

[0062] As Figure 1-11 shown: In step (3), based on the constructed point model, vectorization model, and sequence-to-sequence model, the Monte Carlo method is used for univariate and multivariate vulnerability analysis, and the relationship curve between seismic intensity indicators and failure probability is output.

[0063] As Figure 1-11 shown: In step (3), the seismic intensity indicators include spectral acceleration, peak ground acceleration, and cumulative absolute acceleration.

[0064] Example 5

[0065] As Figure 1-11 shown: This example discloses the implementation methods of each surrogate model, specifically:

[0066] (1) The implementation method of the point model is as follows:

[0067] The point model is based on a deep neural network (DNN) and is used to predict single-object responses. The structure of the point model includes: Input layer: including normalized geometric, material, and seismic input parameters; Hidden layer: setting multiple fully connected layers, each layer including a certain number of neurons, and the activation function is ReLU; Output layer: single-object output (such as the maximum inter-story drift ratio). The model weights are optimized by the stochastic gradient descent method, and an early stopping strategy is used to prevent overfitting.

[0068] (2) The implementation method of the vectorization model is as follows:

[0069] The vectorization model is an extension of the point model to multi-objective output, realizing the synchronous prediction of the maximum vertex displacement, the maximum inter-story displacement angle, the maximum base shear force, and the maximum acceleration. The vectorization model includes: Input layer: the same as the point model; Output layer: a vector including multi-objective responses (including the maximum top displacement, the maximum inter-story displacement angle, the maximum base shear force, and the maximum acceleration at the same time). This multi-objective output structure can capture the correlation between objectives and significantly improve the efficiency of multi-objective reliability analysis.

[0070] (3) The implementation method of the sequence-to-sequence model is as follows:

[0071] The sequence-to-sequence model uses the long short-term memory network (LSTM) and the Transformer architecture to realize the modeling of the earthquake input time series and the prediction of the time history of the dynamic response. Among them, the LSTM model: captures the time dependence of the earthquake input through memory units; the Transformer model: processes the earthquake input in parallel through the self-attention mechanism and is suitable for long-sequence modeling tasks. The output result is the time series of the dynamic response (such as the time history of the top displacement).

[0072] Example 6

[0073] As Figure 1-11 shown, this example discloses that the vulnerability analysis includes the following methods:

[0074] (1) Univariate vulnerability analysis: Combining the point model or the vectorization model, calculate the univariate vulnerability curve: fix the geometric and material parameters, and perform simulations with gradually increasing amplitudes for one earthquake input variable (such as PGA); use the Monte Carlo method to sample the model multiple times to estimate the failure probability; plot the relationship curve between the failure probability and the earthquake intensity.

[0075] (2) Multivariate vulnerability analysis: Combining the vectorization model or the sequence-to-sequence model, and considering the combined action of multiple earthquake input variables at the same time: taking the spectral acceleration, the peak ground acceleration, and the cumulative absolute acceleration as the combined input variables; ensuring the actual correlation between the input variables (for example, positive correlation between the peak ground acceleration and the spectral acceleration); using the Monte Carlo method to generate the joint failure probability surface and plot the vulnerability curve.

[0076] Example 7

[0077] As Figure 1-11 shown, this example discloses an example of the specific application of the present invention:

[0078] For a reinforced concrete frame structure, with fixed geometric and material parameters and earthquake motion characteristics as input parameters, predict its top displacement under earthquake action. The results show that the point model can quickly provide high-precision single-object prediction.

[0079] For the same reinforced concrete frame structure, with the same parameters input, output the synchronous prediction values of top displacement, inter-story drift ratio, base shear force and acceleration. The experimental results show that the vectorized model effectively captures the correlation between each target and improves the overall accuracy of multi-object prediction.

[0080] Input a set of earthquake records containing time series, and use LSTM and Transformer respectively to predict the time history of the top displacement of the reinforced concrete frame structure. The results show that the LSTM model performs better in capturing the characteristics of long sequences, and the prediction accuracy of the time history is higher than that of the Transformer model.

[0081] Use the vectorized model to conduct peak ground acceleration univariate vulnerability analysis on the reinforced concrete frame structure, and calculate its failure probability under different earthquake intensities. The vulnerability curve shows that the failure probability increases with the increase of peak ground acceleration.

[0082] Under the joint input of spectral acceleration, peak ground acceleration and cumulative absolute acceleration, use the sequence-to-sequence model to calculate the multi-variable vulnerability curve. The results show that considering the correlation between variables, the vulnerability curve is closer to the actual engineering conditions.

[0083] The working principle of the present invention:

[0084] 1. Data generation and preprocessing: Generate a multi-dimensional sample set covering geometry, materials and earthquake inputs through Latin hypercube sampling, and conduct random time history analysis on the reinforced concrete frame structure by the finite element method to generate the dynamic response data set required for training the surrogate model. Conduct sensitivity analysis on the input features and find that spectral acceleration, cumulative absolute acceleration and peak ground acceleration are the key parameters affecting the response of the reinforced concrete frame.

[0085] 2. Surrogate model construction and training: According to the task requirements, construct a point model, a vectorized model and a sequence-to-sequence model respectively, and use the random time history analysis data for training.

[0086] 3. Vulnerability analysis: Combine the constructed surrogate model and use the Monte Carlo simulation method to conduct univariate and multi-variable seismic vulnerability analysis:

[0087] Calculation method: Based on the Gardoni model (predictive vulnerability) and the Wen model (median vulnerability), estimate the vulnerability of the reinforced concrete frame structure under different earthquake intensities.

[0088] Parameter adjustment: Perform distribution fitting on the seismic input parameters to maintain reasonable correlations (such as the positive correlation between spectral acceleration and peak ground acceleration).

[0089] 4. Multi-objective output and multi-variable vulnerability analysis:

[0090] The present invention proposes a multi-objective surrogate model framework based on vectorization and sequential output, which can synchronously output multi-objective responses for single-variable and multi-variable seismic vulnerability assessments.

[0091] Single-variable vulnerability analysis: Based on a single seismic feature (such as peak ground acceleration or spectral acceleration), calculate the vulnerability curve of a reinforced concrete frame structure.

[0092] Multi-variable vulnerability analysis: Take multiple seismic features (such as spectral acceleration, peak ground acceleration, and cumulative absolute acceleration) as inputs, and predict the failure probability distribution of the structure under combined seismic inputs through a surrogate model.

[0093] Monte Carlo method: Combine the surrogate model and Monte Carlo simulation to calculate the failure probability of a reinforced concrete frame structure under different seismic intensities, providing a rapid assessment tool for earthquake disaster emergency management.

[0094] Application prospects of the present invention:

[0095] 1. Individual structure reliability analysis: Suitable for rapid seismic demand prediction and reliability assessment of reinforced concrete frame structures, providing technical support for seismic design and performance evaluation.

[0096] 2. Group structure disaster assessment: The method of the present invention has good scalability and can be further applied to the analysis of structural groups at the community level to support urban disaster prevention and control planning and emergency response.

[0097] 3. Engineering decision-making support: By rapidly generating multi-objective seismic response and vulnerability analysis results, the present invention provides data support for engineering decision-making, resource allocation, and post-disaster recovery.

Claims

1. A seismic demand prediction method based on a vectorization and sequence-to-sequence surrogate model, characterized by comprising the following steps: (1) Generating multi-dimensional input parameters including geometric, material, and seismic boundary conditions based on Latin hypercube sampling; (2) Generating a dynamic response database of a reinforced concrete frame structure by using finite element stochastic time history analysis based on the multi-dimensional input parameters; (3) Adopting a deep learning algorithm to train a point model, a vectorization model, and a sequence-to-sequence model based on the dynamic response database, which are respectively used for structural response prediction and multi-objective reliability analysis; In the step (3), the point model refers to: realizing fast prediction of single-objective output response through DNN, which is applicable to the single-variable analysis task of structural dynamic response; the vectorization model refers to: designing a network model with a vectorized output structure based on DNN, simple LSTM, and Transformer to realize synchronous prediction of multi-objective responses; the sequence-to-sequence model refers to: constructing a network model by using complex LSTM and Transformer architectures to capture the time series characteristics of seismic input and generate the time history of structural dynamic response.

2. The seismic demand prediction method based on vectorization and sequence-to-sequence surrogate model according to claim 1, characterized in that, In the step (1), the multi-dimensional input parameters include parameter one based on geometric attributes, parameter two based on material attributes, and parameter three based on seismic boundary condition attributes.

3. The seismic demand prediction method based on vectorization and sequence-to-sequence surrogate model according to claim 2, characterized in that, In the step (1), the parameter one includes floor height, single-span length, single-span width, column width, beam depth, column cross-sectional area, beam cross-sectional area, concrete cover thickness, and floor slab thickness; the parameter two includes concrete strength grade, steel yield strength, stiffness ratio before and after steel yield, elastic modulus, and Poisson's ratio; the parameter three includes earthquake magnitude, fault zone length, earthquake duration, peak ground acceleration, spectral acceleration, and cumulative absolute acceleration.

4. The seismic demand prediction method based on vectorization and sequence-to-sequence surrogate model according to claim 3, characterized in that, In the step (3), the vectorization model is used to realize multi-objective synchronous output, and the output of multi-objective responses includes the maximum top displacement, maximum inter-story drift angle, maximum acceleration, and maximum base shear force of the reinforced concrete frame structure.

5. The seismic demand prediction method based on vectorization and sequence-to-sequence surrogate model according to claim 4, characterized in that, In the step (3), the sequence-to-sequence model captures the time series characteristics of seismic input through LSTM and Transformer networks.

6. The seismic demand prediction method based on vectorization and sequence-to-sequence surrogate model according to claim 5, characterized in that, In the step (3), based on the constructed point model, vectorization model, and sequence-to-sequence model, the Monte Carlo method is used for single-variable and multi-variable vulnerability analysis, and the relationship curve between seismic intensity index and failure probability is output.

7. The seismic demand prediction method based on vectorization and sequence-to-sequence proxy model according to claim 6, characterized in that, In the step (3), the seismic intensity indexes include spectral acceleration, peak ground acceleration, and cumulative absolute acceleration.

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