Quantifying the Uncertainty of Structural Parameters Using Machine Learning–Based Surrogate Models

Abstract

Uncertainty quantification is crucial for accurately assessing the seismic vulnerability of structures in performance-based earthquake engineering (PBEE). Traditional methods, such as the first order second moment (FOSM) approach, struggle with handling nonlinear structural responses, while Monte Carlo sampling simulations are computationally expensive. Machine learning–based surrogate models offer a more efficient alternative for uncertainty quantification. Despite their widespread use, current research on surrogate models often focuses on model training and predictive accuracy, without fully evaluating their efficiency and overall accuracy in uncertainty propagation. Moreover, selecting the most appropriate model and assessing its overall performance remain challenging. This study addresses these gaps by introducing machine learning–based surrogate models for more efficient uncertainty quantification, with a focus on concrete moment-resisting frames. The study identifies five key quantities of interest and conducts sensitivity analysis to determine influential variables under different seismic intensities. Six surrogate models—Gaussian process regression (GPR), multivariate adaptive regression splines (MARS), moving least squares (MLS), neural networks (NN), linear polynomial regression, and quadratic polynomial regression—are employed to quantify parameter uncertainty. A benchmark of 1,000 Latin hypercube sampling (LHS) finite element simulations is established as benchmark. Results demonstrate that surrogate models significantly reduce computational costs while maintaining high accuracy. The GPR method performs best under all conditions, followed by NN, both of which achieve high accuracy even with a limited sample size. The modeling parameters of engineering structures are often subject to uncertainty, which leads to variability in structural responses under seismic excitation. When quantifying the propagation of this uncertainty, traditional methods such as the first-order second-moment (FOSM) approach and Monte Carlo simulations present notable drawbacks—namely, low accuracy and high computational cost, respectively. Surrogate modeling provides an effective means to overcome these limitations. This study quantifies the uncertainty of modeling parameters for a four-story concrete moment-resisting frame using six commonly applied surrogate models. The models include Gaussian process regression (GPR), multivariate adaptive regression splines (MARS), moving least squares (MLS), neural networks (NN), linear polynomial (LP), and quadratic polynomial (QP) regression. Among these, GPR and NN demonstrate the highest accuracy, with GPR consistently delivering superior performance. The findings of this study offer valuable insights and practical guidance for selecting appropriate surrogate models in engineering applications, supporting more efficient and reliable uncertainty quantification in seismic response analysis.