## 4 An Experimental Case Study  
The proposed modal parameters estimation scheme was evaluated on a fiberglass wind turbine blade. First, a traditional impact test modal analysis was conducted to determine the presence of non-linearities due to the inherent nature of the composite material used for the base of the blade. Simultaneously, by performing a traditional modal testing on the blade, a reference is obtained and used to evaluate the performance of the proposed scheme. Figure 3 shows the experimental set-up for the traditional modal testing. Two different modal parameter extraction techniques were applied to the experimental data; the classic one degree of freedom peak picking method detailed in [3], and the multiple degrees of freedom rational fractional polynomials method, known as RFP and reported in [31]. Figure 3 shows a clamped free blade used to match boundary conditions for operational conditions of the blade when the brake is applied. The test was performed using single output velocity measurements employing a laser vibrometer model PDV-100 and its corresponding data acquisition hardware connected via USB to a laptop computer. The measured FRF corresponding to velocity measurements of one single output or degree of freedom is shown in Figure 4, where only the first six resonances are considered. The curve in the solid blue line corresponds to the experimental FRF, while the dotted red and black lines correspond to synthesized FRFs obtained by applying the peak picking [3] and RFP methods [2; 31; 32], respectively. Notice that the first modes are difficult to detect and analyse in the frequency domain, even though the deflection of the blade at low frequencies is evident. A second impact hammer test was performed using IEPE accelerometer sensors to compare and validate the former test results. The corresponding FRF for the acceleration measurements case is shown in Figure 5, where the two first bending modes are easily located at a low frequency band [33]. Figure 4: FRF (frequency response function) of the velocity measurements. Figure 3: Blade set-up for modal testing based on impact hammer excitation. In Figure 6, the first 6 modal shapes are shown in a three-dimensional graph. The different deformation patterns were obtained using the traditional impact hammer test described in the literature [3], in six different points of the blade, uniformly spaced. In addition, one point was taken as a reference. In the plane perpendicular to the deformation, the first six modes of vibration are shown in Figure 7, while the corresponding modal vectors obtained are reported in Table 1.  
Figure 5: FRF of the acceleration measurements. Figure 6: Graph of the six bending modes at six first resonant frequencies. Figure 7: First six bending mode shapes of the blade. Remark: It is important to clarify that the reported results are the product of a traditional experimental modal analysis, whose objective is to provide the parameters that serve as a reference to make a comparison of the performance of the proposed online algebraic estimator defined by (21) and (23). The modal shapes were obtained through the excitation technique by using an impact hammer and the synthesis of FRFs employing the methods of extraction of modal parameters peak picking and rational fractional polynomials RFP [2; 3; 31; 32]. The modal assurance criterion known as MAC [33] is a graphic indicator used to indicate the degree of consistency or similarity between modes obtained by two different methods. The expected value of the MAC between two consistent modes is 1. In Figure 8, the modal assurance criterion for the modes obtained by the two sets of measurements, velocity and acceleration, is graphically shown. It is clear to verify the consistency of the data obtained from both tests. In order to determine the influence of non-linearities in the dynamic response of the blade, Hilbert transform analysis of the velocity FRF was performed.