Clustering-based adaptive ground motion selection algorithm for efficient estimation of structural fragilities

Strong earthquakes cause severe structural damage, resulting in significant losses. Accurately predicting seismic demands is crucial for minimizing these losses, a challenge addressed by performance-based earthquake engineering (PBEE). PBEE uses probabilistic assessment frameworks to integrate uncertainties in ground motions and structural responses. A fundamental step in PBEE is assessing the seismic performance of a structure, often described by structural fragility—the conditional failure probability given an earthquake intensity measure (IM). Accurate fragility estimations require a representative set of ground motions, which can be computationally expensive. Existing ground motion selection methods may still require a large number of ground motions. To overcome this computational hurdle without compromising accuracy, this paper proposes a novel clustering-based adaptive ground motion selection algorithm. This algorithm aims to identify a subset of ground motions that yield structural fragility estimations comparable to those obtained using the complete ground motion set. The study assumes an initial set of ground motions has been selected using existing methods (e.g., spectrum-matched records). The algorithm leverages Lasso regression to identify critical ground motion features influencing EDPs (Engineering Demand Parameters) at limit-states and hierarchical clustering to select ground motions adaptively until fragility curve convergence. The paper reviews Incremental Dynamic Analysis (IDA) and fragility evaluation procedures, details the Lasso regression for feature identification, presents the adaptive selection algorithm framework, and demonstrates its efficiency and applicability through numerical examples of various structural systems.

Several ground motion selection procedures exist, aiming for efficient fragility estimations. However, many still necessitate a large number of ground motions to adequately capture seismic hazard uncertainties. Vamvatsikos and Cornell's work uses empirical equations linking static pushover curves with IDA results from SDOF systems, simplifying analysis but limiting the incorporation of higher-mode effects. While modal pushover analysis considers multiple modes, structural system approximation may not capture complex hysteretic behavior. This study addresses this gap by developing a method to reduce computational costs without simplifying the structural model or relying solely on empirical regressions.

The proposed algorithm employs two main stages: feature identification and adaptive ground motion selection. **Feature Identification:** This stage uses Lasso regression to identify critical ground motion features. Lasso regression minimizes a loss function combining mean squared error (MSE) from ordinary least squares (OLS) regression and an ℓ₁ norm penalty term. This penalty shrinks coefficients towards zero, effectively selecting important features. The study considers 28 ground motion features categorized as basic, peak, cumulative, and mixed indices. These features were calculated after scaling ground motions to a consistent IM level (e.g., Sa(T₁) = 1g) for standardization. Lasso regression was performed on a large set of IDA results from bilinear SDOF systems with varying periods, yield strengths, and post-yield stiffness ratios, subjected to 135 ground motions from the NGA-West database. The sensitivity and frequency of each feature's non-zero coefficient were analyzed to determine relative importance. A subset of features achieving 85% of the standard deviation reduction obtained using all features was selected as critical features. **Adaptive Ground Motion Selection:** This stage uses hierarchical clustering to group ground motions based on their values for the critical features identified in the previous step. The ward-linkage method was employed, minimizing the variance within clusters. The algorithm starts with two clusters (K=2) and iteratively increases K until convergence criteria are met. At each iteration, one ground motion per cluster is randomly selected for dynamic analysis. Fragility is estimated assuming that unselected ground motions within a cluster yield similar results to the selected representative ground motion. The convergence criteria are based on fragility differences (FD), measuring the difference between fragility curves at consecutive iterations. The algorithm stops when both FD and the change in FD fall below predefined tolerances.

The Lasso regression identified nine critical ground motion features: S_veff(T), Spectral Shape, S_deff(T), Soil Class, f_strong, S_{a_geo}(T), PGV, CAA, and PGD. These features were effective across various structural systems, ground motion sets, and limit-state definitions. Applying the adaptive selection algorithm to a bilinear SDOF system, a three-story RC frame, a three-story steel MRF, and a nine-story steel MRF showed significant reduction in the number of ground motions required for fragility estimation without sacrificing accuracy. For instance, the three-story RC frame required only 55, 54, and 46 ground motions for serviceability, damage control, and collapse prevention limit states, respectively—a significant reduction from the original 135 ground motions. Similarly, the three-story and nine-story steel MRFs showed a comparable reduction in the number of ground motions needed. Sensitivity analysis showed that the number of iterations and the final FD are inversely and directly proportional to the convergence tolerance, respectively. The algorithm demonstrated robustness to the choice of ground motion set (using either NGA-West or synthetic ground motions) and limit-state definitions (IM-based or DM-based). A modified version of the algorithm using regression-based fragility estimation (cloud analysis) showed improved performance for the nine-story steel MRF, highlighting the potential benefits of combining different fragility assessment methods. However, for the nine-story steel MRF, which exhibited significant higher-mode effects, a slightly less accurate match with the optimal fragility was observed compared to the lower-story buildings unless stricter convergence criteria were employed.

The findings demonstrate the effectiveness of the proposed clustering-based adaptive ground motion selection algorithm for efficiently estimating structural fragilities. The algorithm's ability to reduce computational costs without significantly impacting accuracy has significant implications for performance-based earthquake engineering. The identification of a relatively small set of critical ground motion features simplifies the selection process and makes it more efficient. The algorithm's robustness across different structural types and limit-state definitions broadens its applicability. The results suggest that using a carefully selected subset of ground motions, representing the variability of the full set, is sufficient for accurate fragility estimation. The relatively weak performance for the nine-story steel MRF highlights the need for further research to refine the critical features, potentially incorporating higher-mode effects and more generalized hysteretic behaviors. The use of more stringent convergence criteria might mitigate this issue, but at the cost of increased computational demands.

This paper presents a novel clustering-based adaptive algorithm for efficient ground motion selection in structural fragility analysis. The algorithm effectively identifies critical ground motion features using Lasso regression and selects a representative subset of ground motions using hierarchical clustering. Numerical studies on various structural systems demonstrate significant computational savings without compromising accuracy. Future research should focus on extending the algorithm to handle more complex hysteretic behaviors and structures with significant higher-mode effects. The identified critical features may also inform the development of new intensity measures that improve seismic demand prediction.

The study's critical features were identified based on idealized bilinear SDOF systems. This might limit the algorithm's performance for structures with complex hysteretic behavior (e.g., strength deterioration or pinching effects) and significant higher-mode effects. The algorithm's performance might also be influenced by the specific method used for fragility assessment (e.g., second-moment method versus regression-based method). Further research is needed to address these limitations and develop more generalized critical features applicable to a wider range of structural systems and ground motion characteristics.