Probabilistic models for prediction of the yield stress of rebars and compressive strength of concrete based on Bayesian linear regression

This paper proposes probabilistic models for predicting the yield stress of reinforcing steel bars and the compressive strength of concrete used in Iran’s construction industry. The importance of this research stems from recognition that the strength of construction materials is one of the main parameters in performance-based design, in calibration of load and resistance factor design (LRFD) provisions, and in risk and resilience analysis of civil infrastructure. Moreover, due to the common practice of on-site casting of the concrete and a large number of rolling mill companies producing reinforcing steel bars, there is a considerable amount of uncertainty in the compressive strength of concrete and the yield stress of steel bars. In this paper, first an extensive database is compiled from concrete and steel laboratory tests. One key field of data for developing the concrete strength model is the nominal design strength of concrete, which was unavailable for a notable portion of the collected data. The database was augmented to account for the missing data using classification algorithms of k-nearest neighbors (KNN) and RBF-Kernel based on machine learning. Next, a probabilistic model is developed using Bayesian linear regression using the Rtx software to predict the compressive strength of concrete as a function of its nominal strength, curing duration, and the quality grade of the concrete manufacturer. The models are Subsequently are diagnosed for the quality of prediction, heteroskedasticity, and normality of the errors to ensure they are statically sound and well represent the underlying data. Next, a model reduction procedure is implemented to discard the inconclusive predictors from the model and to eliminate high correlations among the model parameters to achieve the final model form. Finally, the yield stress of reinforcing steel of Grades A-III and A-IV are modeled using Bayesian random variables whose distribution parameters are also random are inferred from the collected data. Bayesian inference enables the quantification of epistemic uncertainties in the model parameters and hence, makes it possible to update the model using Bayesian updating as new data emerge.