## 3 Experimental Campaign
### Data Processing Procedure  
EMM-ARM [9,12] is an experimental methodology that provides indirect measurements of the Young's modulus of cementitious materials cast inside an acrylic cylindrical beam since the very early ages after casting. Young's modulus is obtained by solving an inverse problem starting from the fundamental natural frequency of the composite beam identified by Operational Modal Analysis [36]. The applied input is, therefore, not measured, but it is assumed to be broadband with a smooth spectrum in the band of interest. In order to continuously and automatically track over time the evolution of the fundamental  
Figure 2: General view of the specimen (**a**) and of the experimental setup (**b**). natural frequency of the composite beam and of the associated Young's modulus of the inner cementitious material, an automated version of the simple Peak-Picking technique is needed. The automatic dynamic identification procedure was implemented in the LabVIEW environment. Acceleration time series were analyzed in 15-min blocks, with a total duration of 120 h for all tests. The Normalized Power Spectral Density (NPSD) [12] was estimated from each record by applying the Welch procedure with 50% overlap and the application of the Hanning window. In the original procedure [12], a pondered average of the 40 highest energy points in the NPSD was used to estimate the fundamental natural frequency. Conversely, in this work, an Automatic Peak Detection (APD) algorithm was used. This automatic procedure is based on an algorithm that fits a quadratic polynomial to sequential groups of data points by setting a suitable threshold. The curves obtained with both methods are compared in Figure 3. The APD curve (in red) is characterized by reduced scatter and, therefore, enhanced results with respect to the original procedure. The estimated natural frequency is used afterward to evaluate the elastic modulus E by iteratively solving Equation (1):  
\[a^{3}[\cosh{(aL)}\cos{(aL)}+1]+\frac{\omega^{2}m_{1}}{EI}[\cos{(aL)}\sinh{(aL) }-\cosh{(aL)}\sin{(aL)}]=0 \tag{1}\]  
where \(E\) is the composite elastic modulus, \(I\) is the second moment of inertia of the composite cross-section, \(\omega=2\pi f\) is the circular natural frequency of the fundamental mode, \(m_{1}\) is the added mass of the sensor at the free end of the cantilever, \(L\) is the free-span length (equal to 400 mm), and the term \(a\) is the coefficient given in Equation (2), in which \(\overline{m}\) is the uniformly distributed mass. \[a=\sqrt[4]{\frac{\omega^{2}\overline{m}}{EI}} \tag{2}\]  
Figure 3: Comparison between the algorithm used by [PERSON] et al. (2011) [12] and the APD procedure used in the present study. An initial value \(\left(EI\right)_{0}\) of the bending stiffness is required to iteratively find the solution of Equation (1), taking into account Equation (2); it can be computed under the assumption that the mass \(m_{1}\) of the sensor is small compared to the cantilever mass:  
\[\left(EI\right)_{0}\cong\frac{\overline{m}L^{4}\omega^{2}}{1.8751^{4}} \tag{3}\]  
Once Equation (1) is iteratively solved to obtain the final value \(EI\) of the bending stiffness of the composite cantilever beam, the elastic modulus of the inner cementitious material \(E_{c}\) can be obtained as per Equation (4):  
\[E_{c}=\frac{64 EI}{\pi\phi_{i}^{4}}-E_{a}\frac{\phi_{e}^{4}-\phi_{i}^{4}}{\phi_{ i}^{4}} \tag{4}\]  
where \(\phi_{e}\) and \(\phi_{i}\) are the outer and inner diameters of the acrylic tube, respectively, and \(E_{a}\) is the elastic modulus of the acrylic tube. This is obtained according to the same testing and data processing procedure but with the acrylic tube filled with water so that the Young's modulus of the inner material is null while the global mass of the beam is well known. The interested reader can refer to [12] for more details. Constant coefficients in Equation (4) (i.e., \(\overline{m}\), \(E_{a}\), \(L\), \(\phi_{e}\), and \(\phi_{i}\)) were individually determined.