Bayesian Model Calibration and Model Selection of Non-destructive Testing Instruments

Concrete acquires a major share of infrastructure and building stock. However, degradation and deterioration of reinforced concrete (RC) structures have been a major concern for the construction industry in recent years. Evaluating the current health of the structure is important for taking a decision regarding future action on the structure. Structural health monitoring (SHM) becomes an essential step for an engineer to gain knowledge about the health of the structure. SHM faces various challenges due to site conditions as well as the limitations present in the NDT tool itself. SHM compromises of collecting health data using NDT tools and analyzing it with the physical or empirical model. These models are fitted using various techniques to develop the relationship between the NDT readings and the corresponding actual quantity of interest. Before the NDT tool is taken on site for actual investigation, the model should be calibrated in the laboratory. The model calibration of the NDT tool is prone to measurement uncertainties which are not properly incorporated in the commonly adopted regression method of calibration. This paper focuses on the model calibration and selection of the best model using Bayesian inference. Bayesian inference helps to quantify the measurement uncertainties. For this, a measurement error model (MEM) is adopted to relate the NDT readings to the property being estimated. An illustration of the calibration and selection process is demonstrated for the proposed approach. For the demonstration, we adopt rebound hammer which is one of the most common NDT tools used to evaluate the present strength of concrete by relating the NDT readings to the crushing strength values obtained in the laboratory. As multiple models are available in the literature for both the cases, Bayesian model selection method is used for selecting the most plausible model from all available models. This will help us to identify which model represents the NDT instrument in the best possible way.