# Mode Shape-Based Damage Detection Method (MSDI): Experimental Validation
## 2 Materials and Methods
### Dynamic Testing of the Plate Model  
To further validate the MSDI method and investigate its robustness, we performed experimental research on a model of a reinforced concrete (RC) plate with plan dimensions 2.3 \(\times\) 1.55 m and 7 cm of thickness. The plate was reinforced with the Q196 reinforcement mesh in the tension zone, and the thickness of the concrete cover was 2.5 cm. The mechanical properties of the concrete, i.e., the characteristic compressive strength (\(f_{\text{ck}}\)) and the modulus of elasticity (\(E\)), were determined on 28-day-old test specimens according to standards EN 12390-3 and EN 12390-13, respectively. The experimentally obtained values were \(f_{\text{ck}}\) = 70 MPa and \(E\) = 36 GPa. The model of an RC plate was divided into rectangular elements (16 cm \(\times\) 15 cm); rows were marked in letters (A-J) and columns in numbers (1-14), as shown in Figure 1. A total of 165 (1-165) measurement points on the RC plate were used for the experimental modal analysis. The operational modal analysis (OMA) [35] was applied for the detection of dynamic properties (natural frequencies, mode shapes, and damping ratios). The measurements were taken with the Bruell&Kjaer Multi-Analyzer system (type 3560-C) using five channels. The modal analysis, including signal processing and modal extraction procedures, was further performed using Pulse software. Five piezoelectric accelerometers (Bruell&Kjaer 4508-B, sensitivity 10 mV/ms\({}^{-2}\)) were used for acceleration measurements. OMA was conducted by moving four accelerometers through 41 measuring stages using one referent measurement point at position no. 155 (41 \(\times\) 4 + 1 = 165 measurement points) (Figure 1). Figure 1: Measurement points on the RC plate. The impact hammer was used to excite the plate randomly. This kind of excitation aims to simulate an operational environment where the excitation is difficult or impossible to measure. Methods of frequency domain decomposition (FDD) [36] and enhanced frequency domain decomposition (EFDD) [37] were used for the estimation of modal parameters. The procedure is based on the singular value decomposition (SVD) of the power spectral density (PSD) matrix of the measured responses. To achieve constant boundary conditions, we suspended the plate using very elastic ropes (Figure 2). The applied boundary conditions, a nearly ideal free-free set-up, were quickly implemented and easily repeated in the laboratory after each testing phase. The plate was tested in an undamaged state and then discrete damages were applied successively by removing parts of the surface from the top of the concrete plate. The plate was again tested after each successive damage simulation. A total of 16 experimentally obtained vertical mode shapes for the undamaged state (Figure 3) and each phase of the damaged state were observed in the analysis. Figure 3: Sixteen mode shapes obtained experimentally on the undamaged plate. Figure 2: Suspended plate with discrete damages. Simulation of Discrete Damages  
In the experimental research, discrete damage was applied by removing a part of the surface from the top of the concrete plate (Figure 4). The size of the discrete damaged rectangle was 15 \(\times\) 16 cm, and the depth varied from 2 to 3 cm. The advantage of discrete damages lies in the fact that the damage location and the change in stiffness are precisely defined. Furthermore, it is possible to simulate a full range of damages, and the MSDI method can be tested using more than one damage location. In sequence, a total of 10 discrete damage cases were simulated on the concrete plate. It is known from the literature that stiffness has a dominant influence on the changes in mode shapes [38]. Therefore, the loss of mass was neglected in the experimental part of this research. Furthermore, the method was previously validated on numerical models [30; 31] based only on the reduction of stiffness without including the effect of changes in mass.