A KDE-based non-parametric cloud approach for efficient seismic fragility estimation of structures under non-stationary excitation

With the development of performance-based earthquake engineering, the risk-informed assessment framework has received broad recognition over the world, of which the probability seismic fragility analysis is an important step. The classic seismic fragility adopts the log-normal assumption and forms a parametric derivation. With the development of fragility theory, researchers are hoping to seek out non-parametric approaches to express the intrinsic fragility in a pure analytical form without any distribution assumptions. Besides, how to keep the calculation efficiency (e.g., combining with cloud approach) and how to consider the non-stationary stochastic responses (e.g., combining with non-stationary stochastic excitation model) are critical aspects in fragility that deserve further attention of researchers. In this paper, a kernel density estimation (KDE) based non-parametric cloud approach is proposed for efficient seismic fragility estimation of structures under non-stationary excitation. First, the methodology framework of the efficient approach is illustrated. Then, the procedures of non-stationary stochastic seismic response of structures and KDE-based non-parametric cloud approach for efficient seismic fragility are demonstrated. After that, an application example via a three-span-six-story reinforced concrete frame is given for implementation, followed with a parametric analysis of critical factors. During the process, the classic parametric linear-regression based cloud approach (cloud-LR) and benchmark Monte-Carlo-simulation based cloud approach (cloud-MCS) are also incorporated for validation. In general, the analysis verifies the effectiveness of the non-parametric cloud-KDE approach without requiring more computation work (i.e., same as the parametric cloud-LR approach and much less than the benchmark cloud-MCS approach). Meanwhile, the non-parametric cloud-KDE approach indicates a comparable accuracy with the classic fragility approaches (i.e., less deviation than the parametric cloud-LR approach and much closer to the benchmark cloud-MCS approach), and with the increase of stochastic cloud-point number, the corresponding fitting degree of cloud-KDE approach is growing better. The research provides a new sight for the development of non-parametric seismic fragility approach, and the corresponding findings can be further combined with the probabilistic hazard and risk analysis for a non-parametric assessment procedure in performance-based earthquake engineering.

Automated summary

With the development of performance-based earthquake engineering, the risk-informed assessment framework has gained recognition worldwide, particularly the probability seismic fragility analysis. Researchers are exploring non-parametric approaches to express intrinsic fragility without distribution assumptions, while also considering calculation efficiency and non-stationary stochastic responses. This paper proposes a kernel density estimation-based non-parametric cloud approach for efficient seismic fragility estimation and demonstrates its effectiveness through an application example. The findings provide insights for the development of non-parametric seismic fragility approaches.