Explainable probabilistic deep learning framework for seismic assessment of structures using distribution-free prediction intervals

A new probabilistic framework is proposed for providing a distribution-free prediction interval (PI) of seismic responses required for various earthquake engineering applications. The framework overcomes the limitation of point prediction models and avoids the complexity of traditional probabilistic methods. The framework utilizes a few assumptions of probability distributions and requires no prior assumed statistical distribution for the PI. Ensemble probabilistic deep learning models (DLMs) are used to provide quality-driven PIs of seismic responses for low- to mid-rise buildings with limited irregularity. Considering these systems and ground motions with the aid of Monte Carlo simulation and nonlinear time-history analysis (NLTHA), huge datasets are generated for training. To have an insight into the probabilistic DLM, explainable artificial intelligence techniques are used. The superiority of the proposed framework in quantifying uncertainties is validated by comparison with the conventional Bayesian method. In addition, its applicability is investigated by providing bounds of seismic fragility curves, life cycle cost, and resilience index obtained by NLTHA for a benchmark case study model. The results showed that the proposed framework is robust and outperforms the conventional Bayesian method in uncertainty quantification for the considered dataset.