# Assessment of Concrete Strength Using the Combination of NDT--Review and Performance Analysis
## Combining NDT Techniques Using the SonReb Method for Concrete-Strength Evaluation
### Bivaried Regression Model for the SonReb Method
#### 2.2.2 Efficiency of the SonReb Method  
The SonReb method is widely used in real practice; however, until now, there has been no general agreement about the efficiency of this method (i.e., whether the use of ultrasonic and rebound hammer techniques together is more efficient than the application of only one of these two techniques). Some studies indicate that using the SonReb method leads to a better assessment of the compressive strength [19; 38]. However, other studies did not find an important improvement in the quality of assessment when using the SonReb method [39; 40].  
In real practice, to study the efficiency of the SonReb method, the coefficient of determination \(r^{2}\) for the case of combination is compared with \(r^{2}\) values that correspond to cases of single NDT techniques. Table 2 compares \(r^{2}\) values obtained from using SonReb with the values obtained from using the ultrasonic pulse velocity technique only (single \(V\)) or rebound hammer only (single \(R\)) and for several datasets selected from the literature. It is clear that, for each dataset, the value of \(r^{2}\) for SonReb is always greater than the corresponding values for the cases of single \(V\) and single \(R\). However, from the principles of statistics, adding a new term to the model (as is the case for SonReb) will increase the value of \(r^{2}\)[41]. As a result, the coefficient of determination is a misleading indicator about the efficiency of SonReb. Table 2 also shows the values of the RMSE (root mean square error) calculated at the prediction stage, i.e., for the part of dataset that was not used in the model identification (fitting stage). From these values, it is clear that for some datasets, the minimum errors are obtained from using a single NDT technique, while for other datasets, the minimum errors are provided by the SonReb method. This indicates that the combination is not always efficient. Furthermore, [42] has studied the efficiency of the SonReb method using synthetic datasets and highlighted that the efficiency of SonReb depends on the qualities of the two techniques combined (in other words, the uncertainties of measurements) and on the number of samples or cores used in the model identification process.  
Figure 1: Graphical representation of the SonReb model using Equation (1) [7].  
In summary, the SonReb method is not always efficient, and its efficiency is affected by factors such as the quality of pulse velocity and rebound hammer measurements, the number of samples/cores used in the model identification, and probably the concrete quality (strength, variability, moisture variation, etc.). To analyze the efficiency of SonReb, it is necessary to do so at the prediction stage and not at the fitting stage. This consists of splitting the data in two groups, one for fitting models and the second for testing the model (prediction on data not used for fitting). Moreover, to deepen the analysis of the efficiency, it is important to compare the cost of the SonReb with that of using a single technique in order to derive conclusions that are more realistic.  
\[RMSE=\sqrt{\sum_{i=1}^{\text{NC}}(f_{\textit{core }i}-f_{\textit{cost }i})^{2}/NC} \tag{3}\]  
where \(f_{\textit{core }i}\) is the true in situ strength, \(f_{\textit{cost }i}\) is the estimated compressive strength, and \(NC\) is the number of cores.