Seismic Fragility Estimation Based on Machine Learning and Particle Swarm Optimization

Abstract

In seismic performance assessment, the development of building fragility curves is critical for performance-based engineering. Traditional methods for time history analysis, reliant on detailed ground motion (GM) inputs, often suffer from inefficiency and a lack of automation. This study proposes an accurate fragility assessment methodology, which is assisted by machine learning (ML) and particle swarm optimization (PSO), adept at handling scenarios with both scarce and sufficient fragility data. Under scenarios of scarce data, the integrated algorithms of PSO and ML are utilized, focusing on selecting GMs that may induce maximum inter-story drifts. When the dataset is sufficient, an ML fusion model is utilized to predict engineering demand parameters (EDPs), facilitating the generation of more accurate fragility curves. The effectiveness of this method is demonstrated through a case study on a high-rise reinforced concrete (RC) building, revealing a marked improvement in the precision of GM selection and the estimated range of fragility curves over traditional approaches. The proposed methodology aids in advancing structural optimization and the development of early-warning systems for seismic events, thus holding the potential to enhance current seismic risk mitigation strategies.

1. Introduction

Mitigating the impact of earthquakes on infrastructure remains a critical concern within the discipline of civil engineering disaster prevention. In light of this, the performance-based seismic design has been proposed, which seeks to regulate the extent of damage to buildings under different levels of seismic intensity, to accomplish various functions for different buildings. Consequently, seismic performance evaluation from the perspective of probability, improving buildings’ resilience, and operational efficiency are the emphasis of the performance-based seismic [1,2,3,4].

Seismic fragility analysis mainly predicts the probability of varying damage degrees of structural damage at different ground motion (GM) intensities using fragility curves. It quantitatively describes the seismic performance of engineering structures in the sense of probability and describes the relationship between the intensities of GM and the degree of structural damage from a macro perspective. The first attempt to determine fragility curves can be dated back to 1975, when the Seismic Design Decision Analysis procedure was proposed in the US, after that, different researchers used fragility curves to evaluate the seismic performance of the structure and estimate the performance of constructed buildings for retrofitting purposes [5]. The seismic performance of the Surakarta minaret was evaluated using the fragility function and presuming the fragility curves, enabling building owners to predict the probability of structural damage due to other earthquake intensity scenarios [6]. The efficacy of a novel buckling-restrained frame in enhancing the seismic resilience of reinforced concrete (RC) frames was evaluated by fragility curves, demonstrating significant efficiency gains [7]. Within the framework of structural seismic performance evaluation, the application of incremental dynamic analysis (IDA) emerges as a pivotal methodology. IDA relies on dynamic elastic–plastic time history analysis to facilitate a comprehensive assessment of structural behavior across a spectrum of seismic intensities. IDA was first proposed by Bertero [5] in 1977 and further promoted by Vamvatsikos and Cornell [8] as a rigorous method for obtaining structural capacity. IDA was utilized to evaluate the seismic fragility of typical existing RC structures subjected to earthquake sequences [9]. Considering the nonlinear soil–structure interaction, IDA was also applied to analyze the efficient and appropriate seismic intensity measures (IM) for shallowly buried multistory underground structures, resulting in obtaining the associated fragility [10]. Nevertheless, the utilization of IDA is constrained by its considerable computational requirements and repetitive workload, as evidenced by several studies [11,12,13,14,15].

Advancements in computational technology and enhanced computing capabilities have facilitated the employment of machine learning (ML) methods for mitigating the time expenditure associated with extensive nonlinear time history analysis (NLTHA) inherent in traditional finite element models. Through the classification of structural types and the manual selection of pivotal parameters, trained on sufficient datasets, ML algorithms are capable of predicting engineering demand parameters (EDPs) effectively circumventing the need for traditional NLTHA. Notably, datasets comprising NLTHA results for buckling restrained brace frames, spanning 2 to 12 stories, have been utilized to train ML algorithms, achieving prediction accuracies exceeding 90% [16]. Furthermore, in addressing the seismic analysis of high-pier bridges, deep learning algorithms were applied to estimate seismic demand parameters rapidly by employing GM time history parameters. This approach resulted in a significant time efficiency improvement, with a reported enhancement of 97% over conventional NLTHA methods [14]. In another innovative application, a one-dimensional convolutional neural network was leveraged as an alternative predictive model for structural seismic responses, offering a data-driven solution to traditional analysis methods [17]. ML algorithms were also used to select the important factors affecting the fragility of buildings and calculate them with high prediction accuracy [18,19]. In terms of building groups fragility, regarding the fragility of building groups, ML was utilized to estimate the fragility of buildings in Pozzuoli, Italy, and the California bridge network [20,21]. However, despite these notable achievements, the application of ML in structural engineering is not without its limitations. The success of ML algorithms heavily relies on the availability of extensive, high-quality datasets and the precise pre-processing of these datasets, including the classification of structural types and the selection of pivotal parameters. This dependency may inadvertently overlook other significant variables, and the assurance of accuracy by ML is contingent upon their training on ample and valid datasets.

Considering these factors, the present study investigates the application of ML in fragility analysis, introducing an innovative methodology that leverages ML and PSO in both data-scarce and data sufficient scenarios. In the face of scarce data availability, the methodology synergizes PSO with ML algorithms to pinpoint GMs that are likely to induce maximum inter-story drifts. The efficacy of this integrative approach is further evaluated by comparing its selection accuracy for GMs against that of a standalone ML model in a high-rise RC structure. When sufficient data are available, the methodological framework sidesteps the manual pinpointing of critical parameters contingent upon structural typologies. The approach favorably utilizes the characteristic values of GMs to employ a comprehensive suite of machine learning (ML) models. This suite includes the Light Gradient Boosting Machine (LightGBM), developed by Microsoft’s DMTK project team and hosted on GitHub (Microsoft Corporation, Redmond, WA, USA); Gradient Boosting Regression (GBR), which is part of the open-source project Scikit-learn (Paris, France); as well as Long Short-Term Memory networks (LSTM) and Bidirectional LSTM (BiLSTM), which are open-source projects supported by a global community of developers (Google LLC, Mountain View, CA, USA). The suite is further expanded by the integration of fusion models. These models are meticulously trained with exacting responses from NLTHA as the training dataset, thereby guaranteeing enhanced precision in the prediction of the structure’s EDPs. The optimal fusion model is achieved through hyperparameter tuning and the adjustment of fusion model weight ratios using grid search, which reduces the variability range of the fragility curve and, in turn, enhances the accuracy of the predictions.

2. Methodology

2.1. Comprehensive Workflow Overview

Figure 1 presents the structured workflow adopted in this study. The initial phase, depicted in the grey column, encompasses the deployment of programmatic IDA, which is facilitated by the integration of the ANSYS Parametric Design Language (APDL) version 2020 R2 and Python scripting version 3.6 for batch processing. The associated methodologies are elaborated in Section 2.2, Section 2.3 and Section 2.4. Subsequent to the definition of characteristic values delineated in Section 2.5, two distinct approaches are formulated contingent upon the availability of fragility data. Under fragility data-scarce scenario, delineated in the yellow column, the integrated algorithms of PSO and ML are essential for the selection of GMs that are likely to induce maximum inter-story drifts. In contrast, when fragility data are sufficient, as shown in the green column, a comparative analysis of different ML models is conducted, leading to the adoption of a fusion model for predicting EDPs, thereby enhancing the accuracy of the resultant fragility curves.

2.2. Selection of GMs Input

To accurately simulate the dynamic response of the structure under earthquakes, GMs input in this structure are carefully curated, comprising both natural and artificial waves. These waves are closely matched with the seismic response spectrum of Shanghai, the geographic locus of the building, considering the region’s unique soil conditions. To meet the data-intensive demands necessary for achieving high accuracy with ML models, our dataset integrates specified earthquakes from the Shanghai building code with additional selections from the Pacific Earthquake Engineering Research Center (PEER) database. This strategic combination yields a robust dataset of 42 GMs, ensuring the representation of seismic activity relevant to Shanghai’s context.

Figure 2 depicts the comparison between the code-prescribed design acceleration spectrum and the mean acceleration spectrum derived from the selected GMs employed in this study.

Table 1. Characteristics of some GMs in earthquake dataset.

ID	Year	Event	Station	Magnitude	D5-75(s)	D5-95(s)
1	1937	Humbolt Bay	Ferndale City Hall	5.8	9.5	23.2
2	1938	Imperial Valley-01	El Centro Array #9	5.0	7.6	15.8
3	1938	Northwest Calif-01	Ferndale City Hall	5.5	4.1	11.6
4	1940	Imperial Valley-02	El Centro Array #9	6.95	17.7	24.2
5	1941	Northwest Calif-02	Ferndale City Hall	6.6	9.0	22.2

delineates the attributes of some selected GMs within the earthquake dataset, providing a detailed overview of their characteristics.

2.3. Programmatic Batch-Processing Calculation Approach

Figure 3 delineates the workflow of programmatic batch variable parameter calculation and the corresponding response output process orchestrated through the integration of APDL and Python. APDL is a function provided by ANSYS software version 2020 R2 to analyze in the form of command flow, which is a scripting language similar to FORTRAN for automatically analyzing common structures or changing parameters for rapid modeling [22]. The workflow is visually represented with the orange column illustrating the primary calculation procedure, while the blue and green columns distinctly highlight the processes executed via APDL and Python, respectively. This automated procedure enhances the efficiency and speed of the calculations and the generation of fragility curves, representing a significant improvement over the conventional approach of manual inputs through the ANSYS GUI and manual PGA adjustments.

2.4. Seismic Fragility Calculation Based on IDA

The process of seismic fragility based on IDA employed in this research is outlined below:

(1)

Selection of seismic intensity indicator intensity measure (IM) and EDP. In this study, PGA has been selected as the IM due to its demonstrated strong correlation with the potential for structural damage across a diverse array of architectural forms, as evidenced by empirical observations and scholarly research [23,24,25]. Specified PGA levels are set at 0.035 g, 0.1 g, 0.22 g, 0.4 g, and 0.6 g to encompass the entire range of the structural response, from elastic to plastic behavior. Furthermore, maximum inter-story drift ${\theta }_{max}$ is chosen as EDP.

(2)

Characterizing limit states (LS) and quantifying associations with EDP. Referring to the guidelines for performance-based seismic design of tall buildings in the United States [26] and the code for seismic design of buildings in Shanghai [27], the definition of LS and its correlation with maximum inter-story drift ${\theta }_{max}$ for the quantification in RC frame structures are shown in Table 2.

(3)

Calculating the probability that the structural response exceeds a certain limit state ${LS}_i$ under different GM intensities. If ${LS}_i$ is quantified by EDP as ${edp}_i$, then when IM = im, the probability that EDP exceeds ${edp}_i$ can be expressed as:

$$P\left({LS}_i|\mathrm{I}\mathrm{M}=im\right)=P\left(\mathrm{E}\mathrm{D}\mathrm{P}\ge ed{p}_i|\mathrm{I}\mathrm{M}=im\right)$$

(1)

Based on existing research [28], it is considered that the maximum inter-story drift ${\theta }_{max}$ is in accordance with the logarithmic normal distribution to the PGA, that is,

$$P\left({\theta }_{max}\ge ed{p}_i|\mathrm{P}\mathrm{G}\mathrm{A}\right)=1-P\left({\theta }_{max}<ed{p}_i|\mathrm{P}\mathrm{G}\mathrm{A}\right)=1-\Phi \left[\frac{lned{p}_i-{\mu }_{ln{\theta }_{max}|\mathrm{P}\mathrm{G}\mathrm{A}}}{{\sigma }_{ln{\theta }_{max}|\mathrm{P}\mathrm{G}\mathrm{A}}}\right]$$

(2)

Here, ${\mu }_{ln{\theta }_{max}|PGA}$ and ${\sigma }_{ln{\theta }_{max}|PGA}$ are the log mean and log standard deviation of ${\theta }_{max}$ under the corresponding PGA, respectively; Φ(.) is the standard normal cumulative distribution function.

(4)

Using PGA as the horizontal axis and $P\left({LS}_i|\mathrm{P}\mathrm{G}\mathrm{A}\right)$ as the vertical axis to draw the seismic fragility curve.

Table 2. The definition of LS of RC frame structures.

	Fully Operational LS1	Essentially Operational LS2	Repairable LS3	Life Safety LS4
Maximum inter-story drift ${\theta }_{max}$	1/550	1/250	1/120	1/50

Table 2. The definition of LS of RC frame structures.

	Fully Operational LS1	Essentially Operational LS2	Repairable LS3	Life Safety LS4
Maximum inter-story drift ${\theta }_{max}$	1/550	1/250	1/120	1/50

2.5. Definition of Characteristic Values

Data and features determine the upper bound of ML, while models and algorithms only approach this upper bound.

Table 3. Characteristic values of GMs.

Characteristic Value	Name	Definition
Tg	Design characteristic period of GMs
t	Duration
EPV	Effective peak velocity	$\frac{1}{2.5}{S}_V\left(T=1.0 \mathrm{s}\right)$
EPA	Effective peak acceleration	$\frac{1}{2.5}\overline{S_a}\left(0.1\le T\le 0.5 \mathrm{s}\right)$
Ia	Arias intensity	$(\frac{\pi }{2g}){\int }_0^t{a}^2\left(t\right)dt$
SED	Specific energy density	${\int }_0^t{v}^2\left(t\right)dt$
CAV	Cumulative absolute velocity	${\int }_0^t\left|a\left(t\right)\right|dt$
PGA	Peak ground acceleration	$Max\left|a\left(t\right)\right|$
PGV	Peak ground velocity	$Max\left|v\left(t\right)\right|$

enumerates the characteristic values of GMs, which are widely regarded as representative of the input GM features, after employing the backward elimination method in the research [29]. As the maximum inter-story drift is reckoned as EDP in this study, it is selected as the predicted value. Through ML, the maximum inter-story drift is predicted according to the characteristic values of GMs.

2.6. Integrated Algorithms of PSO and ML under Fragility Data-Scarce Scenario

In the domain of ML, the accuracy of predictive models is fundamentally tied to the volume of training data. This relationship holds particular significance in fields such as civil engineering, where EDPs are critical quantitative indicators of structural safety and demand precise prediction to ensure redundancy. However, in scenarios characterized by scarce data, the reliability of ML-based predictions can be markedly compromised and affected by compromised representativeness, overfitting, reduced statistical power, and constraints on modeling complexity. Compromised representativeness due to small sample sizes can lead to models that do not generalize well beyond their training data, affecting the validity of their predictions. Overfitting becomes a significant risk when complex ML models capture noise instead of the underlying data structure, resulting in poor predictive performance on new datasets. Additionally, the lack of data restricts the statistical power of the models and limits the complexity of the algorithms that can be effectively employed.

To address the issue of unconservative estimations that might jeopardize structural integrity, as characterized by predicted values falling short of actual values, this study tackles the challenges by adopting integrated algorithms of PSO and ML. Specifically, LightGBM was chosen as the ML algorithm due to its swift calculation speed, minimal memory requirement, and superior calculation accuracy [30].

Figure 4 delineates the integrated algorithm of PSO and ML, illustrating the cohesive workflow of this integrated algorithm. This integration harnesses the strengths of both methodologies, thereby enhancing the model’s performance and generalization capability. The PSO algorithm is renowned for its robust global search capability, which significantly aids ML models in circumventing local optima, thereby increasing the likelihood of identifying the global optimal solution. Moreover, PSO’s inherent ability to autonomously search and select features plays a pivotal role in extracting more informative and relevant features. This, in turn, substantially boosts the performance of ML models.

The integrated algorithm of PSO and ML paradigm notably augments the global search functionality, mitigating the risk of entrapment in local optima. However, the stochastic nature of PSO introduces a degree of variability in outcomes, necessitating rigorous hyperparameter optimization to ensure consistent results across various iterations. Despite these challenges, the integration of PSO and ML algorithms, especially when demonstrating superior efficacy compared to standalone ML approaches, affirms the viability and relevance of the combined strategy. This is particularly pertinent in scenarios characterized by data scarcity, thereby delineating a promising avenue for future research aimed at enhancing the synergy between PSO and ML for increased operational efficiency and resilience in data-constrained environments.

2.7. ML Models under Fragility Data Sufficient Scenario

2.7.1. Principles of ML Algorithms

In this study, we have selected four ML algorithms, namely LightGBM, GBR, LSTM, and BiLSTM to predict EDP under data sufficient scenarios. These algorithms are categorized into two major groups: ensemble learning and deep learning algorithms, each selected for their distinct strengths in handling complex data patterns and improving prediction performance.

On the ensemble learning front, the LightGBM and GBR algorithms are incorporated due to their distinct merits in handling large-scale data and achieving high prediction accuracy. LightGBM stands out as a lightweight, yet powerful, optimization algorithm within the gradient boosting decision tree framework, celebrated for its swift calculation speed, minimal memory requirement, and superior calculation accuracy [30]. Concurrently, the GBR algorithm is recognized for its excellent regression capacity and outstanding generalization capability, attributed to the applied boosting strategy [31]. These ensemble methods complement the deep learning models by enriching the model’s ability to interpret and predict complex patterns through a combination of multiple predictive signals. Within the deep learning category, the LSTM and BiLSTM neural network models are highlighted for their exceptional accuracy and proficiency in processing sequential or time series data. The LSTM model, with its capacity to remember long-term dependencies, and the BiLSTM, which extends this ability by incorporating information from both past and future states, are particularly advantageous for their deep structural insights into data. Figure 5 illustrates the algorithm frame diagram utilized in this study, providing a visual representation of the methodology.

2.7.2. Model Preprocessing

Data preprocessing is the process of cleaning, transforming, and integrating. Data analysis refers to the process of extracting useful information and forming conclusions by using appropriate statistical analysis methods to study and summarize the data in detail.

In this study, following the preprocessing protocol referenced from existing research [29], the post-preprocessing phase involves a thorough examination of the data’s characteristics, including its discreteness, adherence to a normal distribution, and inter-variable correlations. This analysis is primarily conducted using three graphical methods: box plots, quantile–quantile (QQ) plots, and heat maps calculated by Pearson correlation coefficient.

2.7.3. Grid Search and Model Fusion

In the domain of ML and predictive modeling, the construction of robust and efficient models is paramount for achieving high precision and reliability. This endeavor is underpinned by the intricate process of hyperparameter tuning—a critical step that significantly influences the performance of algorithms including LightGBM, GBR, LSTM, and BiLSTM.

In this study, the optimal hyperparameter configurations for four ML algorithms were ascertained through the application of a grid search strategy.

The grid search strategy operates on the premise of executing an exhaustive exploration within a delineated spectrum of parameter values to identify the hyperparameter set that confers the maximal algorithmic efficacy. This process entails an iterative assessment of all feasible permutations of parameters, culminating in the selection of the combination that delivers superior performance metrics.

Model fusion, also known as ensemble learning, is a technique that has consistently delivered superior predictive performance in various complex tasks across numerous scientific fields. The essence of model fusion lies in its ability to integrate diverse models, each with unique strengths and compensatory attributes, to forge a more robust and accurate meta-model. In this study, we leverage the complementary properties of four distinct algorithms—LightGBM, GBR, LSTM, and BiLSTM—to enhance the predictive fidelity of our ensemble. By fusing these models, we capitalize on LightGBM’s and GBR’s powerful feature handling and iterative refinement, alongside LSTM’s and BiLSTM’s temporal pattern recognition capabilities. The choice of appropriate weights is paramount, as it directly influences the combined model’s capacity to leverage the distinct strengths of its constituent algorithms. To optimize these weights, our study also uses the grid search strategy, a comprehensive exploratory technique that iteratively evaluates a predefined grid of weight combinations to identify the configuration that minimizes predictive error.

3. Results

3.1. APDL Digital Model and Structural Details

This study employs the APDL for the simulation of a high-rise reinforced concrete (RC) building, characterized by a primary tower and secondary structures, designed to accommodate a high occupancy load, tailored for library use. Following its initial construction, the building has been subject to a series of retrofitting and reinforcement strategies to meet the increased structural demands. Figure 6 shows the finite element model constructed using APDL, whereas

Table 4. Design information of major structural components.

Component	Material	Dimension	Section Type	Element Type
Frame column	Concrete	600 mm × 600 mm	Rectangle	BEAM 188
Floor beam	Steel	300 mm × 300 mm × 15 mm × 10 mm	I-beam	BEAM 188
Floor plate	Concrete	150 mm	Thickness	SHELL 181

and

Table 5. Material properties and corresponding non-linear constitutive models.

Material	Property			Non-Linear Constitutive Model
	Elastic Modulus/E	Poisson’s Ratio/ν	Density/ρ
Concrete	3.0 × 1010 N/m2	0.2	2500 kg/m3	MISO
Steel	2.1 × 1011 N/m2	0.3	7800 kg/m3	BISO

delineate the salient structural elements and their corresponding material properties, respectively.

3.2. GMs Selected by Integrated Algorithms of PSO and ML under Fragility Data-Scarce Scenario

In order to quantitatively evaluate the benefits of an integrated algorithmic framework over a standalone ML algorithm, this investigation implements both methodologies to select GMs from five distinct groups of data characterized by varying PGAs. The criterion for selection is the elicitation of maximum inter-story drift. The GMs identified by each algorithm as inducing the greatest inter-story drift are then subjected to finite element analysis to compute their precise displacement values. Figure 7 provides a visual representation of these values to show the differences. It is observed that the integrated algorithms of PSO and ML significantly enhance the precision in selecting GMs that are likely to cause the maximum inter-story drifts. This improvement in accuracy is crucial for avoiding the underestimation of EDPs linked to GMs capable of inducing significant structural responses, thereby advancing the overall safety assessment.

3.3. ML Model Construction under Fragility Data Sufficient Scenario

3.3.1. Model Preprocessing

To elucidate the data preprocessing and analysis steps more comprehensively, Figure 8 presents the box plot, QQ plot, and heat map for selected characteristic values.

After data preprocessing and basic analysis, the data are segmented and the training set and test set are randomly divided by 4:1.

3.3.2. Four ML Models’ Construction

The hyperparameter values appertaining to each of the four algorithms are systematically enumerated in

Table 6. Four ML models’ hyperparameter values.

LightGBM Model
Hyperparameter	num_leaves	learning_rate	max_depth	feature_fraction
value	27	0.5	7	0.6
GBR Model
Hyperparameter	n_estimators	learning_rate	max_depth	min_samples_split
value	100	0.1	3	0.2
LSTM Model
Hyperparameter	learning_rate	num_units	batch_size	dropout_rate
value	0.01	1000	168	0.2
BiLSTM Model
Hyperparameter	learning_rate	num_units	batch_size	dropout_rate
value	0.01	500	168	0.2

. Additionally, to mitigate the risk of overfitting, the training process for each of the four models was monitored by plotting the mean absolute error (MAE) against the epochs shown in Figure 9. Early stopping was implemented to ensure that each model ceased training at the point of optimal generalization.

Therefore, these four ML models are used to predict the maximum inter-story drift ${\theta }_{max}$, and the mean square error (MSE), root mean square error (RMSE), and mean absolute error (MAE) are used to evaluate the prediction results of the model. The specific values are shown in

Table 7. Model error values.

Model	MSE	RMSE	MAE
LightGBM regression model	1.0023 × 10−5	3.1660 × 10−3	2.0861 × 10−3
GBR model	1.1829 × 10−5	3.4394 × 10−3	2.2864 × 10−3
LSTM neural network model	3.6242 × 10−5	6.0201 × 10−3	3.5868 × 10−3
BiLSTM neural network model	3.2502 × 10−5	5.7010 × 10−3	3.8841 × 10−3

, while the images of the actual value and the predicted value are drawn in Figure 10.

It can be seen that the LightGBM model has the minimum value among these four models.

3.3.3. Model Fusion

Figure 11 illustrates the comparison of MSE values for a range of weight configurations within the ensemble fusion model, juxtaposed against the MSE values derived from the four individual ML models previously discussed. It shows that the fusion model’s accuracy is higher than the four ML models above and analysis reveals that the model with a weight distribution of 0.7 for LightGBM, 0.1 for GBR, 0.1 for LSTM, and 0.1 for BiLSTM demonstrates the highest accuracy.

3.4. Accurate Fragility Analysis Using Fusion Model under Fragility Data Sufficient Scenario

Following data preprocessing and the development of our fusion model, it became possible to estimate maximum inter-story drift in mere seconds. In an effort to substantiate the potential of ML in generating fragility curves with enhanced precision, a random selection of 10 datasets containing 168 GMs each was made. The randomness inherent in the selection process allowed for the depiction of fragility curves across varied combinations, graphically representing their range of variability. For each dataset, the maximum inter-story drift prompted by the remaining 42 GMs was predicted using the optimal fusion model, effectively capturing the extent of variability inherent in the fragility curves. This comparison provided an extensive assessment of the ML model’s capability to enhance the accuracy of fragility curve estimations.

Figure 12 illustrates the comparison of fragility variability ranges before and after the application of ML. It is evident from the figure that the application of ML leads to a reduction in the variability range, signifying a substantial improvement in the stability and reliability of the fragility curve outcomes.

4. Conclusions

This paper suggests a precise prediction methodology using ML and PSO under given scenarios, which could be used to predict structure fragility by analyzing input GM parameters. The accuracy of this prediction methodology is assessed by a large number of finite elements NLTHA results. Based on the analytical results, the following main conclusions could be obtained:

(1) Under the fragility data-scarce scenario, the integrated algorithms of PSO and ML significantly enhance the precision in selecting GMs that are likely to cause the maximum inter-story drifts, thus mitigating unconservative EDP estimates that could potentially compromise structural safety.

(2) Under a fragility data sufficient scenario, by model confusion, the accuracy of prediction could be improved. Here in this study, through grid search, it reveals that the model with a weight distribution of 0.1 for GBR, 0.7 for LightGBM, 0.1 for LSTM, and 0.1 for BiLSTM demonstrates the highest accuracy.

(3) The implementation of ML results in a diminished variability range when employing diverse datasets, thereby indicating a significant enhancement in the stability and dependability of the derived fragility curve results.

(4) By combining Python and APDL, programmatic modeling and batch calculation could be achieved which reduces the repetitive workload performing seismic fragility.

In conclusion, the methodology introduced in this study offers a transformative approach to the analysis of structural fragility and the estimation of EDPs, adept at handling both situations with scarce and abundant fragility data. This method greatly surpasses traditional approaches in selecting ground motions (GMs) and accurately establishing fragility curves, thereby assisting disaster managers in pinpointing critical seismic events for structural optimization. Our validated ML fusion model predicts EDPs rapidly and with high precision, enabling quantitative analysis of structural responses and enhancing the granularity of early warning systems. These advancements make a significant contribution to the optimization of structural design and modern seismic risk mitigation strategies, highlighting their practicality in urban disaster management.