Screening of critical intensity measures for rapid structural seismic response prediction based on machine learning

Abstract

The challenge in applying machine learning for rapid structural seismic response prediction lies in establishing a reliable mapping between seismic intensity measures (IMs) and damage indicators. Current IMs are often inadequate due to the complex, non-linear interaction of multiple seismic factors, including intensity, source mechanism, and pulse effects, making single-indicator quantification difficult. This study addresses this gap by considering three distinct seismic wave types (near-field, far-field, and pulse waves) and establishing six multiple degrees of freedom (MDOF) structural models with varying periods in OpenSees. We selected maximum inter-story drift and maximum floor acceleration as critical damage indicators. An Extremely randomized trees (ET) algorithm was then utilized to develop the structural response prediction model. Through feature importance ranking, shapley additive explanations (SHAP) value analysis, and sensitivity analysis, the key IMs governing the structure’s maximum response were systematically identified. The efficacy of the proposed IMs was subsequently validated using three steel frame structures with different periods. The results demonstrate a significant improvement in the accuracy of the machine learning prediction model. The proposed IMs can achieve the same or higher prediction accuracy with fewer parameters. The prediction accuracy of the interstory drift ratio is improved by 34.87%, while the prediction accuracy of floor acceleration is enhanced by 26.58%, compared to previous studies using the same number of IMs. These findings provide crucial guidance for the selection of optimal IMs in machine learning applications for structural seismic response prediction.

Keywords

intensity measures types of seismic waves structural period structural response prediction SHAP analysis

Highlights

• A comprehensive IM–response database is built using three ground-motion types and six structural periods

• Machine-learning interpretability (SHAP, feature importance) is used to identify key IMs for different structural periods

• The prediction accuracy of the interstory drift ratio is improved by 34.87%, while the prediction accuracy of floor acceleration is enhanced by 26.58%, compared to previous studies using the same number of IMs.

Introduction

Earthquakes are sudden, destructive, and unpredictable events that pose serious threats to human safety and economic stability worldwide. Rapid assessment of building damage shortly after an earthquake is essential for governments to formulate effective disaster relief strategies. In recent years, the rapid prediction of structural responses using machine learning algorithms has become a research hotspot in the field of earthquake engineering. The key to accurately predicting structural response lies in establishing a robust mapping relationship between seismic intensity measures (IMs) and structural responses. Existing studies primarily use inter-story drift (Ahmad and Phillips 2022), floor acceleration, and component deformation (Yan et al., 2024) as damage indicators to quantify the degree of structural damage, and these have been incorporated into design specifications (Fang 2021; Han et al., 2019). However, due to the high complexity of ground motion characteristics, it is difficult to quantify seismic actions using a single or even multiple parameters, making the selection of IMs particularly critical. Choosing appropriate IMs is therefore essential for accurately predicting the seismic performance of structures. Numerous scholars have carried out extensive studies on IM selection, which can generally be classified into two main approaches: the correlation coefficient method and machine learning-based methods.

Kostinakis et al. (2015) analyzed the correlation between 19 IMs and the damage states of high-rise frame structures under 64 seismic motions using the Spearman correlation coefficient. The results indicated that the spectral acceleration parameter (S_a) exhibited the highest correlation with structural damage, followed by the velocity spectrum intensity (VSI). Pinzón et al. (2020) evaluated the correlation between various IMs and the maximum inter-story drift of a two-dimensional steel frame based on the determination coefficient (R²), and found that the correlation between peak ground acceleration (PGA) and structural response was the weakest. They also proposed a new parameter that simultaneously considers peak ground velocity (PGV) and energy duration. Other researchers have similarly investigated the relationship between commonly used seismic parameters and structural responses through correlation analysis to identify effective IMs (Yakut and Yılmaz 2008; Yang et al., 2019; Zhai et al., 2013).

Xu et al. (2022a) employed support vector machine (SVM), logistic regression (LR), and decision tree algorithms to develop predictive models and identify optimal IMs for different building types. Morfidis and Kostinakis (2017) applied neural network algorithms to predict the maximum inter-story drift of structures, from which the damage states of reinforced concrete buildings were determined, and the most suitable IM combinations were recommended. Zhang et al. (2023a) selected five IMs to predict maximum inter-story drift and compared the prediction accuracy of an active learning algorithm with that of the Gradient Boosting Trees algorithm. Nguyen et al. (2022) used three different machine learning algorithms to predict the seismic responses of steel frame structures. Ding et al. (2023) considered five seismic parameters: PGA, PGV, acceleration spectrum intensity (ASI), effective peak acceleration (EPA), and S_a, and applied the NGBoost algorithm to predict structural seismic losses. Vazirizade et al. (2017) established a mapping relationship between maximum inter-story drift and component cross-section using an artificial neural network (ANN). Karbassi et al. (2014) employed a decision tree algorithm to predict the structural damage index and assess the damage state. In addition, many other scholars have carried out related studies (Bhatta et al., 2024; Gharagoz et al., 2023; Park et al., 2025; Shen et al., 2025; Xu et al., 2022b; Zhang et al., 2023b; Zhu et al., 2024).

At present, although many researchers have investigated the impact of different IMs on the prediction accuracy of structural seismic response, several research gaps remain:

(1) The influence of different ground motion types on IM selection is not adequately differentiated. When predicting structural seismic response, different IMs should ideally be selected for various types of ground motions (such as near-field, far-field, and pulse-like), yet current research often overlooks this distinction.

(2) Insufficient consideration of the structural period’s effect on the selection of IMs. While existing studies may conduct nonlinear time-history analyses on structures with various periods to build response databases, the final recommendations for IMs often lack a systematic classification or targeted advice based on these structural periods.

(3) Lack of interpretability analysis for the selection of different IMs. Current research primarily emphasizes the predictive performance of machine learning models, neglecting in-depth investigation and interpretability analysis of the underlying mechanisms that justify the choice of one IM over another.

This paper systematically investigates the effects of near-field pulse-like ground motions, near-field non-pulse ground motions, and far-field ground motions on the prediction accuracy of structural seismic responses for short-, medium-, and long-period structures. First, correlation analysis and machine learning techniques are employed to identify key IMs influencing structural responses from an initial set of 25 commonly used IMs. Next, a structural response database was established through nonlinear time-history analysis of six steel frames with different fundamental periods. Multiple machine learning algorithms were then evaluated, and a high-precision prediction model was developed using key IMs as inputs. Subsequently, interpretability analysis using feature importance and SHAP values identified the most influential IMs for different structure types and ground motion categories. Finally, validation on three steel frames with distinct periods confirmed the effectiveness and generalizability of the proposed IMs for predicting seismic responses.

Selection of seismic intensity measures

Selection of ground motion

Significant distinctions exist between near-field and far-field ground motions. The velocity time histories of near-field ground motions typically exhibit distinct pulse characteristics, and their spectral properties differ substantially from those of far-field ground motions, often resulting in more severe structural damage. In the selection of ground motion records, this study divides the seismic waves into three categories: near-field non pulse ground motions, near-field pulse-type ground motions, and far-field ground motions. Far-field ground motions are defined as those with a magnitude greater than 6.5 and an epicentral distance greater than 30 km. The selection follows three main criteria: (1) Site type; (2) Whether the epicentral distance exceeds 30 km; (3) Whether the record contains a clear pulse. Based on these criteria, a total of 900 horizontal ground motion records were randomly selected from the pacific earthquake engineering research (PEER) center database, comprising 300 near-field pulse-type ground motions, 300 near-field non-pulse ground motions, and 300 far-field ground motions. The spatial distribution of the selected IMs is presented in Figure 1.

Figure 1.

Spatial distribution of IMs.

Selection of IMs

IMs can be classified into four categories: acceleration-related, velocity-related, displacement-related, and other IMs. In the present study, 25 representative parameters were initially selected to constitute the IM set, encompassing all four categories. The classification and detailed descriptions of these IMs are summarized in Tables 1 –4.

Table 1.

Acceleration-related IMs.

No.	IMs	Detailed interpretation	Definition
1	Peak Ground Acceleration: PGA	Maximum ground acceleration during an earthquake.	$P G A = \max \| {\ddot{u}}_{g} (t) \|$
2	Acceleration RMS: RMSA	Root mean square of acceleration time history, reflecting average acceleration intensity.	$R M S A = \sqrt{\frac{1}{t_{f}} \int_{0}^{t_{f}} {\ddot{u}}_{g}^{2} (t) d t}$
3	Arias Intensity: I_a	Integral of squared acceleration over time, representing seismic energy input.	$I_{a} = \frac{π}{2 g} \int_{0}^{t_{f}} {\ddot{u}}_{g}^{2} d t$
4	Characteristic Intensity: I_c	Indicator combining ground-motion energy and duration, related to damage potential.	$I_{C} = A_{r m s}^{1.5} \times t_{D}^{0.5}$
5	Acceleration Spectrum Intensity: ASI	Integral of acceleration response spectrum over a specified period range.	$A S I = \int_{0.1}^{0.5} S a (T, ζ = 0.05) d T$
6	S_a_avg: S_a	Average acceleration response over multiple frequencies.	$S_{a} = \frac{1}{N} \sum_{T_{1}}^{T_{N}} S a (T_{i}, ζ)$
7	Sustained Maximum Acceleration: SMA	Maximum acceleration sustained over a finite duration.	$S M A = \max (\frac{1}{T} \int_{t_{0}}^{t_{0} + T} \| a (t) \| d t)$

Table 2.

Velocity-related IMs.

No.	IMs	Detailed interpretation	Definition
1	Peak Ground Velocity: PGV	Maximum ground velocity during an earthquake.	$P G V = \max \| {\dot{u}}_{g} (t) \|$
2	Velocity RMS: RMSV	Root mean square of velocity time history, reflecting overall velocity intensity.	$R M S V = \sqrt{\frac{1}{t_{f}} \int_{0}^{t_{f}} {\dot{u}}_{g}^{2} (t) d t}$
3	Velocity Spectrum Intensity: VSI	Intensity measure derived from the velocity response spectrum.	$V S I = \int_{0.1}^{2.0} S v (T, ζ = 0.05) d T$
4	Max Incremental Velocity: MIV	Maximum velocity increment between adjacent time steps.	$M I V = \max \| \int_{t_{1}}^{t_{2}} {\ddot{u}}_{g} d t \|$
5	Sustained Maximum Velocity: SMV	Maximum velocity sustained over a finite duration.	$S M V = \max (\frac{1}{T} \int_{0}^{T} \| v (t) \| d t)$
6	Cumulative Absolute Velocity: CAV	Time integral of absolute acceleration, reflecting intensity and duration effects.	$C A V = \int_{0}^{t} \| {\ddot{u}}_{g} (t) \| d t$

Table 3.

Displacement-related IMs.

No.	IMs	Detailed interpretation	Definition
1	Peak Ground Displacement: PGD	Maximum ground displacement during an earthquake.	$P G D = \max \| u_{g} (t) \|$
2	Displacement RMS: RMSD	Root mean square of displacement time history.	$R M S D = \sqrt{\frac{1}{t_{f}} \int_{0}^{t_{f}} u_{g}^{2} (t) d t}$

Table 4.

Other IMs.

No.	IMs	Detailed interpretation	Definition
1	Vmax/Amax: V/A	Ratio of peak velocity to peak acceleration, reflecting spectral characteristics.	$V / A = P G V / P G A$
2	Housner Intensity: HI	Measure based on spectral velocity, reflecting overall structural demand.	$H I = \int_{0.1}^{2.5} PSV (ξ = 0.05, T) d T$
3	Predominant Period: PP	Period corresponding to the dominant frequency of ground motion.	$P P = T [\max S_{a} (ξ = 0.05, T)]$
4	Number of Effective Cycles: NEC	NEC refers to the number of cycles that have a significant impact on the structural response of buildings during an earthquake.	-
5	Specific Energy Density: SED	SED refers to the energy contained within a unit volume, which can be used to assess the distribution of energy from seismic waves under certain site conditions.	-
6	Effective Design Acceleration: EDA	EDA refers to the estimated level of acceleration that a structure may experience under the influence of a design earthquake.	-
7	Mean Period: MP	MP refers to a parameter used to describe the dynamic characteristics of ground motion records.	-
8	IP Index: IP	IP is a parameter used to describe the impulsive characteristics of ground motion records.	-
9	Damage Index: DI	DI is a parameter used to quantify the degree of damage to structures under the action of an earthquake.	-
10	A95 parameter: A95	A95 is the level of acceleration that encompasses 95% of the Arias Intensity.	-

Correlation analysis of seismicmotion parameters

All IMs were computed using the SeismoSignal software. To quantitatively evaluate the correlations among IMs, the Pearson correlation coefficient was calculated between each IM and the remaining 24 IMs. The Pearson coefficient quantifies the linear relationship between two variables and is defined as the ratio of their covariance to the product of their standard deviations, as expressed in equation (1). The Pearson correlation coefficient heatmap among the IMs is shown in Figure 2, where both the horizontal and vertical axes represent IMs. The colour of each grid cell corresponds to the correlation coefficient between a pair of IMs, as indicated by the accompanying colour scale.

ρ_{X, Y} = \frac{cov (X, Y)}{σ_{X} σ_{Y}} = \frac{E ((X - μ_{X}) (Y - μ_{Y}))}{σ_{X} σ_{Y}} = \frac{E (X Y) - E (X) E (Y)}{\sqrt{E (X^{2}) - E^{2} (X)} \sqrt{E (Y^{2}) - E^{2} (Y)}}

(1)

Figure 2.

Pearson correlation coefficient heatmap of IMs.

After obtaining the Pearson correlation coefficients among all parameters, the first round of data dimensionality reduction was conducted following the procedure illustrated in Figure 3. In this study, IMs with a Pearson coefficient greater than 0.8 were considered strongly correlated. To determine which highly correlated parameters should be retained, based on the assumption that ground motion parameters and structural responses exhibit an approximately log-linear relationship, the dataset was transformed into the logarithmic scale. The correlation coefficients between the IMs and two structural response indicators (maximum inter-story drift and maximum floor acceleration) of the two-story MDOF structure were calculated and further screened. Finally, the remaining IMs were identified as the input parameters for subsequent machine learning models. The IMs retained for the three types of ground motions after correlation analysis are summarized in Tables 5 and 6.

Figure 3.

Flowchart of IM screening.

Table 5.

IMs strongly correlated with inter-story drift with different ground motion types.

Ground motion type	IMs
Far-field ground motion	PGV, PGD, V/A, RMSA, RMSV, RMSD, I_a, HI, SMV, PP
Near-field with no pulse ground motion	PGA, PGD, RMSA, RMSV, I_a, I_c, CAV, SMA, PP, NEC
Near-field with pulse ground motion	PGV, PGD, V/A, RMSV, RMSD, SED, VSI, HI, SMV, PP

Table 6.

IMs strongly correlated with floor acceleration with different ground motion types.

Ground motion type	IMs
Far-field ground motion	PGA, PGD, V/A, RMSA, I_a, ASI, SMA, EDA, PP, NEC
Near-field with no pulse ground motion	PGA, PGD, V/A, RMSA, I_a, ASI, HI, SMA, EDA, PP
Near-field with pulse ground motion	PGA, V/A, RMSA, I_a, I_c, SED, VSI, SMA, EDA, PP

Construction of a structural response database

Establishment of numerical model

This study employed OpenSees to develop the numerical models. Considering that building structures are typically MDOF systems exhibiting higher-order mode effects, the definition of the elastic-plastic MDOF system adopted in this study follows the approach proposed in (Ye et al., 2009), as illustrated in Figure 4. In the MDOF analytical model, the inter-story shear force and inter-story drift are described using a bilinear hysteretic constitutive relationship, as shown in Figure 5. All stories in the MDOF system are assumed to have identical story height, mass and lateral stiffness. The mass of each story is taken as 600 t. The initial story stiffness is set to 10⁶ KN/m. The post-yield stiffness ratio is defined as 0.1. Rayleigh damping is adopted to represent structural damping, with a damping ratio of 5%. The material behavior is defined using the Steel01 model. The fundamental period of the structure is varied by changing the number of stories. A total of six MDOF models are established, with 2, 4, 8, 10, 15, and 20 stories. The corresponding fundamental periods are 0.18 s, 0.41 s, 0.89 s, 1.44 s, 1.87 s, and 2.28 s, respectively. These models represent structures with short-, medium-, and long-period characteristics in seismic analysis.

Figure 4.

MDOF system.

Figure 5.

MDOF bilinear hysteresis constitutive model.

Structural seismic response database

In this study, the inter-story drift and floor acceleration were selected as the damage indices of structural response (Wang and Luo, 2025; Tao et al., 2024; Kaya and Binici, 2025). According to the Code for Seismic Design of Buildings (China), an inter-story drift of 1/50 was adopted as the collapse criterion. The 900 ground motion records documented in the foregoing discussion were used to perform nonlinear time-history analyses of the MDOF structures, resulting in a total of 10,800 data sets of inter-story drift and floor acceleration. The maximum inter-story drift and maximum floor acceleration were extracted as representative damage indices to construct the structural response database. The distributions of these two indices under different types of ground motions are illustrated in Figure 6. As shown in the figure, 6.96% of the maximum inter-story drift data exceed the 1/50 limit, and 26.35% of the maximum floor acceleration data exceed 0.4 g, indicating that the structures experienced significant damage.

Figure 6.

Distribution of maximum structural response.

Establishment of machine learning prediction model

Overview of integrated algorithms

This study employed three commonly used ensemble algorithms as candidate models: Random forest (RF), ET, and AdaBoost. Both RF and ET are bagging-based algorithms that use multiple decision trees for prediction but differ in tree construction. RF randomly selects a subset of features for node splitting to enhance model diversity and generalization, whereas ET introduces additional randomness by selecting both features and split points at random, further improving diversity. AdaBoost, a boosting-based algorithm, iteratively adjusts sample weights according to the performance of weak learners, emphasizing previously misclassified samples to enhance overall model accuracy.

Selection of machine learning model

To ensure that the selected model is suitable for predicting the inter-story drift and floor acceleration of MDOF structures under different types of ground motions, this study established machine learning prediction models based on three algorithms: RF, ET, and AdaBoost. The models were developed using a two-story MDOF structure subjected to nonlinear time history analysis. The input parameters consist of ten seismic IMs screened through correlation analysis, while the outputs are the maximum inter-story drift and maximum floor acceleration. To achieve higher prediction accuracy, a 9:1 ratio was adopted for splitting the training and testing datasets (Kumar et al. 2024). The training set was used to train the models, and the testing set was used to evaluate prediction accuracy. This study adopts mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), mean absolute percentage error (MAPE), and R² as evaluation metrics. The performance results of the models based on different algorithms are presented in Tables 7 and 8.

Table 7.

Comparison of model performance in predicting inter-story drift.

Model	Hyperparameters for the model	MAE	MSE	RMSE	MAPE	R²
ET	n_estimators: 100, max_features: 4, min_samples_leaf: 1	0.0001	0.0000	0.0001	0.1941	0.9985
RF	n_estimators: 200, max_features: 2	0.0002	0.0000	0.0005	0.2233	0.9911
AdaBoost	n_estimators: 200, learning_rate: 0.33	0.0002	0.0001	0.0004	0.1965	0.9961

Table 8.

Comparison of model performance in predicting floor acceleration.

Model	Hyperparameters for the model	MAE	MSE	RMSE	MAPE	R²
ET	n_estimators: 150, max_features: 3, min_samples_leaf: 3	0.0007	0.0000	0.0010	0.3158	0.9836
RF	n_estimators: 200, max_features: 4	0.0010	0.0001	0.0014	0.3595	0.9318
AdaBoost	n_estimators: 150, learning_rate: 0.12	0.0008	0.0000	0.0011	0.3044	0.9663

Although different machine learning models exhibit high correlation in prediction results, comparative analysis among models remains necessary. On the one hand, high prediction accuracy is achieved based on dataset expansion and systematic data preprocessing, while under limited sample sizes or varying structural conditions, noticeable differences in prediction performance still exist among algorithms. On the other hand, models differ in error magnitude, stability, and generalization capability. Through comprehensive evaluation using multiple metrics, models with lower errors and stronger robustness can be identified. In addition, model comparison provides methodological support for subsequent ground motion parameter importance analysis, contributing to the development of a seismic response prediction framework with both high accuracy and interpretability.

It can be seen that the ET algorithm achieved the best overall performance among the three models. It yielded the highest R² value, while the MAE, MSE, RMSE, and MAPE values were all comparatively lower. Therefore, the ET algorithm was selected for subsequent model training.

Structural response prediction results based on the ET algorithm

Prediction results

Based on the ET algorithm, the input parameters were constructed from the results of the correlation analysis, while the output parameters were the maximum inter-story drift and maximum floor acceleration. The dataset was divided into training and testing subsets in a 9:1 ratio. The predicted maximum inter-story drift and maximum floor acceleration of MDOF systems with three different fundamental periods are shown in Figures 7 –12.

Figure 7.

Inter-story drift prediction accuracy of short-period MDOF structures.

Figure 8.

Inter-story drift prediction accuracy of medium-period MDOF structures.

Figure 9.

Inter-story drift prediction accuracy of long-period MDOF structures.

Figure 10.

Floor acceleration prediction accuracy of short-period MDOF structures.

Figure 11.

Floor acceleration prediction accuracy of medium-period MDOF structures.

Figure 12.

Floor acceleration prediction accuracy of long-period MDOF structures.

From the distribution of the scatter plots, it can be observed that most data points are concentrated near the y = x reference line, indicating strong predictive consistency. The prediction accuracy for the maximum inter-story drift is higher than that for the maximum floor acceleration. The R² values for the maximum inter-story drift test set range from 0.9453 to 0.9863, while those for the maximum floor acceleration range from 0.9255 to 0.9787. This difference arises because inter-story drift data are generally smaller in magnitude and more concentrated, leading to better overall prediction accuracy. In contrast, the range of maximum floor acceleration values is wider, with fewer high-value samples, resulting in greater dispersion in the upper-right region of the plots.

K-fold cross-validation

K-fold cross-validation is one of the most commonly used validation techniques. In this study, K is set to 10. The cross-validation accuracy results for the inter-story drift prediction model and the acceleration prediction model are presented in Tables 9 and 10, respectively.

Table 9.

Maximum inter-story drift cross-validation accuracy (mean ± std).

Ground motion type	Near-field non-pulse ground motions		Far-field ground motions		Near-field pulse ground motions
Ground motion type	RMSE	MAE	RMSE	MAE	RMSE	MAE
Short-period	0.00030 ± 0.00010	0.00020 ± 0.00000	0.00020 ± 0.00010	0.00010 ± 0.00000	0.00070 ± 0.00030	0.00030 ± 0.00010
Medium-period	0.00070 ± 0.00030	0.00030 ± 0.00010	0.00020 ± 0.00010	0.00010 ± 0.00000	0.00020 ± 0.00010	0.00010 ± 0.00000
Long-period	0.00020 ± 0.00010	0.00010 ± 0.00000	0.00020 ± 0.00010	0.00010 ± 0.00000	0.00030 ± 0.00020	0.00010 ± 0.00010

Table 10.

Maximum floor acceleration cross-validation accuracy (mean ± std).

Ground motion type	Near-field non-pulse ground motions		Far-field ground motions		Near-field pulse ground motions
Ground motion type	RMSE	MAE	RMSE	MAE	RMSE	MAE
Short-period	0.01691 ± 0.01285	0.00599 ± 0.00364	0.01671 ± 0.00933	0.00493 ± 0.00272	0.02114 ± 0.01462	0.00832 ± 0.00478
Medium-period	0.01443 ± 0.00889	0.00501 ± 0.00266	0.01128 ± 0.00487	0.00413 ± 0.00137	0.02164 ± 0.01675	0.00944 ± 0.00271
Long-period	0.01310 ± 0.00563	0.00530 ± 0.00203	0.00902 ± 0.00535	0.00284 ± 0.00129	0.01806 ± 0.01230	0.00737 ± 0.00226

The results of the 10-fold cross-validation indicate that the inter-story drift prediction model achieves high accuracy and good stability across different structural periods and ground motion types. The RMSE and MAE values in all cases are on the order of 10^-4, with relatively small standard deviations. This demonstrates that the model performance is stable under different data partitions. For near-field and far-field ground motions, both the mean values and standard deviations of RMSE and MAE remain low. This suggests that the model effectively captures the variation characteristics of inter-story drifts under typical seismic excitations. In contrast, under pulse-like ground motions, especially in short-period cases, RMSE and MAE increase slightly and their standard deviations become larger. This is caused by the non-stationarity and uncertainty brought by the pulse effect.

Compared with the inter-story drift model, the acceleration prediction model exhibits larger errors, with RMSE and MAE values on the order of 10^-2 and relatively larger standard deviations. Under far-field ground motions, particularly for long-period cases, RMSE and MAE values are lower and the standard deviation is smaller. This indicates better model adaptability to ground motions with smoother spectral characteristics and stronger stationarity. Under pulse-like ground motions, both short-period and medium-period cases show increases in the mean values and standard deviations of RMSE and MAE. The acceleration prediction model maintains acceptable error levels without significant instability across folds.

Analysis of the interpretability of predictive models

The interpretability analysis of predictive models is carried out from two perspectives: feature importance ranking and SHAP value analysis. The feature importance ranking reflects the sensitivity of input parameters to the model’s outputs, while SHAP values reveal the direction and magnitude of each parameter’s influence. Combining these two approaches helps assess the reliability of the prediction model and determine whether its behavior aligns with structural mechanics principles.

Ranking of feature importance coefficients

The rankings of input parameter feature importance coefficients for the prediction models of maximum inter-story drift and maximum floor acceleration in the MDOF system, are shown in Figures 13 –18.

Figure 13.

Feature importance of maximum inter-story drift under near-field non-pulse ground motions.

Figure 14.

Feature importance of maximum inter-story drift under far-field ground motions.

Figure 15.

Feature importance of maximum inter-story drift under near-field pulse ground motions.

Figure 16.

Feature importance of maximum floor acceleration under near-field non-pulse ground motions.

Figure 17.

Feature importance of maximum floor acceleration under far-field ground motions.

Figure 18.

Feature importance of maximum floor acceleration under near-field pulse ground motions.

From Figures 13 –15, it can be seen that, for the prediction of maximum inter-story drift, under near-field non-pulse ground motions, RMSA and RMSV have relatively high importance coefficients, significantly affecting the prediction of maximum inter-story drift. PP exhibits higher importance in short- and medium-period structures, while CAV has a higher importance in long-period structures compared to short- and medium-period structures. Under far-field ground motions, RMSD ranks high in short-, medium-, and long-period structures and is the main parameter influencing maximum inter-story drift. PGD has higher importance in short- and medium-period structures, RMSV in medium- and long-period structures, and HI ranks higher in long-period structures. Under near-field pulse ground motions, RMSA and I_a are the dominant parameters for short-, medium-, and long-period structures. Additionally, HI has a higher importance in long-period structures than in medium- and short-period structures, while PGV has higher importance in short-period structures.

From Figures 16 –18, it can be observed that, for the prediction of maximum floor acceleration, under near-field non-pulse ground motions, PGA, EDA, and ASI are the primary parameters influencing floor acceleration. RMSA ranks relatively high in short-period structures, while V/A plays a key role in medium- and long-period structures. Under far-field ground motions, RMSA and PGA consistently rank high and serve as the main predictors of floor acceleration. SMA is particularly important for short-period structures, whereas EDA dominates in medium- and long-period structures. Under near-field pulse ground motions, RMSA, PGD, and PGA are among the most influential parameters across all three period ranges. ASI has higher importance for short-period structures, while EDA is more influential in medium- and long-period structures. The key IMs are presented in Tables 11 and 12.

Table 11.

Key IMs affecting inter-story drift of structures with different periods.

Ground motion type	Short-period	Medium-period	Long-period
Far-field ground motion	RMSD, PGD, SED	RMSD, RMSV, PGD	RMSD, RMSV, HI
Near-field with no pulse ground motion	RMSA, RMSV, CAV	RMSA, RMSV, PP	RMSA, RMSV, PP
Near-field with pulse ground motion	RMSA, I_a, PGV	RMSA, I_a, RMSV	RMSA, I_a, HI, RMSV

Table 12.

Key IMs affecting floor acceleration of structures with different periods.

Ground motion type	Short-period	Medium-period	Long-period
Far-field ground motion	PGA, RMSA, SMA	PGA, RMSA, EDA	PGA, RMSA, EDA
Near-field with no pulse ground motion	PGA, EDA, ASI, RMSA	PGA, EDA, ASI, V/A	PGA, EDA, ASI, V/A
Near-field with pulse ground motion	RMSA, PGD, PGA, ASI	RMSA, PGD, PGA, EDA	RMSA, PGD, PGA, EDA

For short-period structures, the overall stiffness is high and the vibration frequency is large. Their dynamic responses are mainly governed by the high-frequency components and instantaneous amplitude of ground motions. Therefore, for floor acceleration responses, peak-based and acceleration energy-related IMs, such as PGA, RMSA, and ASI exhibit high importance.

For inter-story drift responses, RMSA and RMSV dominate under near-field and pulse-like ground motions. This indicates that short-duration and high-intensity pulse inputs significantly increase deformation demand. As the structural period increases to the medium-period range, the sensitivity to velocity-related features and cumulative energy effects becomes more pronounced. In this case, RMSV, EDA, and CAV, which reflect both ground-motion duration and energy input, show higher importance in the SHAP analysis. This suggests that the response of medium-period structures is controlled by both peak effects and the overall energy level of ground motions.

For long-period structures, the deformation capacity is larger and the vibration period is longer. Their inter-story drift responses are more sensitive to low-frequency components and displacement-related IMs. Under far-field ground motions, the importance of RMSD and PGD increases significantly. Under pulse-like ground motions, HI and I_a, which characterize pulse features and energy concentration become dominant. This reflects the amplification effect of velocity pulses on the displacement demand of long-period structures.

Overall, the variation in IM importance across different period ranges originates from the matching between structural dynamic characteristics and ground-motion spectral features. The SHAP results are consistent with the feature importance rankings. This confirms the reliability and physical interpretability of the proposed prediction model in identifying key ground-motion parameters.

SHAP value analysis

The SHAP method is a post-hoc model interpretation technique (Lundberg and Lee 2017) for explaining complex machine learning models. It calculates the contribution of each input feature to the model output (Štrumbelj and Kononenko 2014). The distribution of input parameter SHAP values for the structural seismic response prediction model developed in this study is shown in Figures 19 -24.

Figure 19.

SHAP analysis of maximum inter-story drift under near-field non-pulse ground motions.

Figure 20.

SHAP analysis of maximum inter-story drift under far-field ground motions.

Figure 21.

SHAP analysis of maximum inter-story drift under near-field pulse ground motions.

Figure 22.

SHAP analysis of maximum floor acceleration under near-field non-pulse ground motions.

Figure 23.

SHAP analysis of maximum floor acceleration under far-field ground motions.

Figure 24.

SHAP analysis of maximum floor acceleration under near-field pulse ground motions.

By examining the SHAP plots of inter-story drift-related parameters for MDOF structures under near-field non-pulse ground motions, it can be observed that the SHAP values of RMSA and RMSV are widely distributed across short-, medium-, and long-period structures and are mainly positively correlated with inter-story drift. This indicates that these parameters are highly sensitive to inter-story drift, and as their values increase, the maximum inter-story drift also increases, consistent with the previously discussed feature importance rankings. The SHAP value distribution of CAV in short-period structures is wider than in medium- and long-period structures, suggesting that CAV is another key parameter influencing inter-story drift in short-period MDOF structures, primarily exhibiting a negative correlation. Similarly, the SHAP value distribution of PP in medium- and long-period structures is wider than in short-period structures, indicating that PP significantly affects inter-story drift in these structures. The SHAP diagrams clearly illustrate the sensitivity of other parameters to inter-story drift as well. Analysis of SHAP plots for both inter-story drift and floor acceleration under other types of ground motions shows consistency with the feature importance rankings, confirming that the prediction model is reliable and effective.

According to the ranking of feature importance coefficients and SHAP analysis, RMSA, RMSV, RMSD, PDA, and PGA can be used as the key ground motion parameters affecting different periodic structures under different types of ground motion.

Validation of the proposed method

In this section, three concentrically braced steel frame (CBF) structures are established using OpenSees, with 4, 8, and 16 stories, respectively. Their fundamental periods are 0.8 s, 1.5 s, and 2.1 s. These three models cover short-, medium-, and long-period structural systems (Zhao et al., 2023), and can comprehensively represent the seismic response characteristics of structures with different fundamental periods under earthquake excitation. The story height of each floor is 3.6 m, and the bay width is 7.2 m. Two braced frames are arranged in each horizontal direction. The seismic fortification intensity is set to 7, and the site condition corresponds to Site Class II. The standard values of dead load for floors and roofs are 5.0 kN/m, and the live load is 3.5 kN/m. The constitutive behavior of the structural steel is represented by the Steel02 material model in OpenSees, with a Poisson’s ratio of 0.3. Both beam and column members are modeled as elastoplastic elements.

Elastic-plastic time-history analyses were performed in OpenSees under different types of ground motions, using the seismic records obtained earlier in this study. The maximum inter-story drifts and maximum floor accelerations were extracted to form the sample database. By comparing the key IMs identified in the foregoing analysis with findings from three other studies (Poreddy et al., 2022; Xu et al., 2022b; Zhang et al., 2024), the accuracy of the results was verified. The structural plan and elevation views are shown in Figure 25.

Figure 25.

Structural configuration of steel frame structures.

Prediction of the maximum structural response

To verify whether the ET algorithm is the optimal approach for predicting the maximum responses of centrally braced steel frame structures, machine-learning prediction models were developed using the ET, RF, and AdaBoost algorithms. The model performance was evaluated using MAE, MSE, RMSE, MAPE, and R² as evaluation metrics. The input parameters included RMSA, RMSV, RMSD, PGV, and PGA, which effectively represent the main characteristics of ground motions. The output parameters were the maximum inter-story drift and floor acceleration of the centrally braced steel frame structure. It should be noted that the dataset was not grouped by ground-motion type or structural period during model training and prediction. This strategy was adopted to examine whether the ET based model can accurately predict the maximum inter-story drift and floor acceleration without considering differences in ground-motion characteristics or structural periods. This design helps to validate the robustness and general applicability of the proposed model. It also provides broader reference value for practical engineering applications. The performance results of different models are summarized in Tables 13 and 14.

Table 13.

Comparison of evaluation indicators for the model of maximum inter-story drift.

Model	MAE	MSE	RMSE	MAPE	R²
ET	0.0002	0.0000	0.0003	0.2135	0.9655
RF	0.0002	0.0003	0.0006	0.2688	0.9437
AdaBoost	0.0002	0.0001	0.0008	0.2956	0.9308

Table 14.

Comparison of evaluation indicators for the model of maximum floor acceleration.

Model	MAE	MSE	RMSE	MAPE	R²
ET	0.0015	0.0016	0.0013	0.2565	0.9536
RF	0.0027	0.0019	0.0015	0.2849	0.9211
AdaBoost	0.0028	0.0015	0.0020	0.3155	0.9007

Based on the prediction results and evaluation metrics of the three algorithms, the model constructed using the ET algorithm remains the optimal one. It shows higher accuracy and lower prediction errors than the other models. Therefore, the ET algorithm is adopted to develop the subsequent machine-learning prediction models. The input parameters consist of five ground-motion IMs, namely RMSA, RMSV, RMSD, PGV, and PGA. These parameters were selected through analysis in the present study. They effectively represent the main characteristics of earthquake ground motions. They also provide sufficient information for predicting the maximum structural responses. The output features include the maximum inter-story drift and the maximum floor acceleration of centrally braced steel frame structures. The evaluation metrics remain MAE, MSE, RMSE, MAPE, and the coefficient of determination R². These metrics reflect the prediction accuracy and stability of the model from different perspectives. The final training results of the model are presented in Tables 15 and 16.

Table 15.

Prediction results of the maximum inter-story drift of the central support steel frame structure.

Floors	MAE	MSE	RMSE	MAPE	R²
4	0.0010	0.0011	0.0015	0.1941	0.9646
8	0.0012	0.0013	0.0013	0.2233	0.9587
16	0.0009	0.0010	0.0013	0.1965	0.9566

Table 16.

Prediction results of the maximum floor acceleration of the central support steel frame structure.

Floors	MAE	MSE	RMSE	MAPE	R²
4	0.0021	0.0023	0.0032	0.2535	0.9527
8	0.0025	0.0023	0.0029	0.2988	0.9375
16	0.0029	0.0026	0.0031	0.2965	0.9331

Tables 15 and 16 list the predicted maximum inter-story drifts and floor accelerations for centrally braced steel frames with different structural periods. The prediction accuracy for the maximum inter-story drift exceeds 0.95. The prediction accuracy for the maximum floor acceleration is higher than 0.93. In addition, the values of MAE, MSE, RMSE, and MAPE are all relatively low. The low MAE values indicate small deviations between the predicted and actual results. The low MSE and RMSE values further confirm the concentration and stability of the prediction errors. The low MAPE values demonstrate reliable prediction performance across different response magnitudes. Overall, the ET based prediction model for maximum structural responses exhibits excellent performance in terms of accuracy and error control. This highlights the high precision and strong robustness of the proposed model.

Result verification

Based on a review of relevant references, three selected IMs were compared with those proposed in this study. The key earthquake motion parameters identified in the three references are summarized in Table 17. The prediction accuracy of different IMs was evaluated by using varying numbers of IMs as model inputs. This section uses the forward stepwise method to identify the optimal combination of IMs, aiming to achieve high prediction accuracy with minimal input variables.

Table 17.

IM values suggested by different references.

Reference	IMs
Xu	S_a, EPA, HI, EPV, PGV
Zhang	S_a, PGA, PGV, S_v, PP
Poreddy	PGA, PGV, AI, MIV, SED

Currently, relevant studies may consider the structural period or ground motion type when establishing databases, but the key IMs recommended in their conclusions do not differentiate between ground motion types or structural periods. This study verifies the reliability of the proposed key IMs under these two factors. First, ground motion types and structural periods are classified, and the prediction accuracy of structures with different periods using varying numbers of IMs under different ground motions is compared, as shown in Figures 26 and 27. The results indicate that the IMs proposed in this study consistently achieve higher prediction accuracy than those suggested in the three referenced studies.

Figure 26.

Comparison of prediction accuracy for maximum inter-story drift.

Figure 27.

Comparison of prediction accuracy for maximum floor acceleration.

From Figures 26 and 27, when one to three parameters are used as inputs, the proposed method shows substantial accuracy improvements, with increases of 11.42%–34.87% in the prediction of maximum inter-story drift and 2.89%–26.58% in the prediction of maximum floor acceleration. Even when four parameters are considered, the prediction accuracy remains 6.41%–17.02% and 4.79%–14.78% higher than that of the other studies, respectively. Notably, using the four recommended parameters yields prediction accuracies of approximately 90% or higher, with maximum values of 94.65% and 92.47%, while incorporating all five parameters further increases the accuracy to around 95%, reaching peak values of 97.08% and 97.89%, respectively. The line chart clearly shows that the IMs proposed in this study provide significantly higher accuracy, particularly when only a small number of parameters are used.

This study systematically considers the effects of near-field, far-field, and pulse-like ground motions on the maximum structural responses. The influence of structural period is explicitly incorporated. Prediction models are developed to relate IMs to structural responses across different periods. As a result, the proposed IMs demonstrate superior performance in terms of prediction accuracy. It should be noted that differences in datasets, structural models and evaluation metrics exist across studies. Therefore, these comparisons should be interpreted as indicative rather than strictly equivalent.

Conclusion

Existing research has shown that, although many studies have investigated the influence of different IMs on the accuracy of structural seismic response prediction, there has been no comprehensive consideration of the effects of different types of ground motions on structures with varying periods. This study systematically examines the impact of near-field pulse ground motions, near-field non-pulse ground motions, and far-field ground motions on the prediction accuracy of short-, medium-, and long-period structural responses. Key IMs were identified through correlation analysis. Machine learning prediction models were established using the ET algorithm, with the selected IMs as input and maximum inter-story drift and floor acceleration as outputs. Feature importance and SHAP value analyses were subsequently performed. The effectiveness of the proposed approach was validated using typical structural examples.

(1) Under far-field ground motions, RMSD and PGD are identified as key ground motion parameters for predicting the maximum inter-story drift of MDOF structures with short, medium, and long fundamental periods. In addition, SED is recommended for short-period structures, RMSV for medium-period structures, and HI for long-period structures. For the prediction of the maximum floor acceleration, PGA and RMSA are dominant parameters for all structural periods. SMA is suggested for short-period structures, whereas EDA is more suitable for medium- and long-period structures.

(2) Under near-fault ground motions, RMSA and RMSV are the key parameters for predicting the maximum inter-story drift across different structural periods. CAV is recommended for short-period structures, while PP is preferred for medium- and long-period structures. For the prediction of the maximum floor acceleration, PGA, EDA, and ASI are identified as the dominant parameters. RMSA is suitable for short-period structures, whereas V/A performs better for medium- and long-period structures.

(3) Under pulse-like ground motions, I_a and RMSA play a dominant role in predicting the maximum inter-story drift for all structural periods. PGV is recommended for short-period structures, RMSV for medium-period structures, and HI for long-period structures. For the prediction of the maximum floor acceleration, RMSA, PGD, and PGA are identified as key parameters. ASI is recommended for short-period structures, while EDA is preferred for medium- and long-period structures.

(4) When using the same number of seismic parameters as inputs, the recommended parameter sets RMSA, RMSV, RMSD, PGV, and PGA in this study provide higher prediction accuracy for structural response. This improvement is observed both with and without distinguishing ground motion types and structural periods. Compared with three related studies, the proposed parameters improve the prediction accuracy of the maximum inter-story drift by up to about 34.87% and that of the maximum floor acceleration by up to about 26.58% when such distinctions are considered.

Although this study has made some progress, there are still some limitations. The study uses a uniform MDOF structural model, assuming that the mass, stiffness, and floor height are the same across all floors. This simplification helps highlight the influence of seismic motion characteristics and structural period, but it ignores variations in mass, stiffness, and floor height. Future research will expand this work by incorporating structures with non-uniform property distributions and severe vertical irregularities. This will broaden the applicability of the proposed prediction framework.

Footnotes

ORCID iDs

Zhenyu Tong

Haifeng Yu

Author contributions

Yong Li: Writing – original draft, Validation, Methodology, Investigation, Formal analysis, Conceptualization. Hongru Ma: Methodology, Validation, Formal analysis, Writing - original draft. Zhenyu Tong: Conceptualization, Formal analysis, Writing - review & editing. Haifeng Yu: Formal analysis, Software, Funding acquisition. Junhai An: Methodology, Validation, Data curation. Jiangxing Zhang: Software, Data curation.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was financially supported by the Natural Science Foundation of Hebei Province (Grant Numbers: E2023208069 and E2025208016), and the Science and Technology Project of Hebei Education Department (Grant Number: QN2024054).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

Data will be made available on request.*

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