Gaussian Process Regression with Bayesian Optimisation and Uncertainty Propagation for Predicting the Fundamental Period of Masonry-infilled RC Frames

Reinforced Concrete (RC) frames with masonry infills represent a widely adopted structural typology in Algeria. The present study aims to predict the fundamental period of this type of structure using various machine learning algorithms.

Several machine learning models, including Gaussian Process Regression (GPR) applied for the first time to this problem, are employed to assess their performance in predicting the fundamental period of masonry-infilled reinforced concrete frames, using statistical metrics such as the coefficient of determination R² and the Root Mean Square Error (RMSE). An uncertainty propagation analysis is subsequently conducted using the Gaussian Process Regression (GPR) model to evaluate the sources of uncertainty associated with the prediction of the fundamental period of structures.

The results indicate that the GPR model achieves a coefficient of determination R² = 0.9999 on the test data, outperforming all models previously proposed in the literature. The uncertainty analysis reveals that model-related uncertainty accounts for 7.8% of the total uncertainty, whilst input data uncertainty accounts for 92.2%.

This study highlights the relevance of using GPR models to predict the fundamental period of reinforced concrete frames. It also addresses one of the key limitations of purely data-driven models and demonstrates the benefits of resorting to physics-informed machine learning models.

This study demonstrates the superiority of the GPR model over other machine learning models, whilst also outperforming the models previously proposed in the literature. An analysis of the influence of the input variables reveals that their relationships are predominantly non-linear.