Open Access

ARTICLE

A Machine Learning Surrogate Framework for Bayesian Calibration of Nonlinear Concrete Damage Models

Yi Chen, Xiaodan Ren^*

Department of Structural Engineering, College of Civil Engineering, Tongji University, Shanghai, China

* Corresponding Author: Xiaodan Ren. Email:

(This article belongs to the Special Issue: AI-Enhanced Computational Methods in Engineering and Physical Science)

Computer Modeling in Engineering & Sciences 2026, 148(1), 9 https://doi.org/10.32604/cmes.2026.083966

Received 14 April 2026; Accepted 17 June 2026; Issue published 27 July 2026

Abstract

Concrete exhibits significant stochasticity and nonlinearity, making the calibration of nonlinear damage models challenging for high-precision structural analysis. To address the high computational cost of finite element model calibration and the influence of model bias, this study proposes a machine learning surrogate framework for Bayesian calibration of nonlinear concrete damage models. The framework integrates a bi-scalar damage constitutive model, support vector regression based surrogate modeling, response-level finite element model bias representation, and adaptive Markov Chain Monte Carlo sampling within a unified probabilistic setting. The surrogate models are constructed to approximate the nonlinear mapping from constitutive parameters to force-displacement responses, thereby replacing repeated high-cost finite element evaluations during posterior sampling. Meanwhile, the model bias term is explicitly incorporated into the likelihood formulation to distinguish structural model inadequacy from observational noise. The proposed framework is validated using experimental force-displacement responses of reinforced concrete columns. The results show that the surrogate models provide accurate predictions and substantial computational acceleration. The posterior predictions agree well with the experimental responses, and the incorporation of model bias leads to more realistic uncertainty representation in both parameter inference and structural response prediction. The proposed framework provides an efficient and robust strategy for Bayesian calibration and uncertainty quantification of nonlinear concrete damage models.

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