## 4 Conclusions  
The paper is focused on the post processing procedure of the BTT sensors data in the case where two very close resonance frequencies are present in the dynamic response of the rotating system. Having two close resonance peaks is the typical case of the dynamic response of a bladed disk in presence of mistuning, due for example to an asymmetry of the distribution of the mass in the disk. In this case, having an instrument that can fit the experimental data to obtain the main vibration parameters (resonance frequencies and damping) for both the modes associated to the close resonances is very useful to the experimenter or to the designer. A method based on the nonlinear least square fitting of the sensors data by a 2 DOF dynamic model was here presented. A lumped parameter model representing a rotating mistuned bladed disk assembly was used as a test case. The sensors measurement data were simulated numerically. The results obtained by the 2 DOF fitting method are compared with those obtained by the most classical Sine fitting method employed in the majority of the BTT commercial systems. The following main conclusions can be drawn.  
* The 2 DOF fitting method is more accurate than the Sine fit method in the determination of the maximum response amplitude when the two peaks are very sharp and well separated since the damping is very low (\(\zeta=0.0001\)). In this case, the 2 DOF model can directly estimate the fitting parameters, damping value and resonance frequency, associated to each peak with an accuracy lower than 1%. The Sine fit method is less accurate since it is sensitive to the number of samples of the BTT data which is considerably affected by the rate of acceleration or deceleration, while the 2 DOF method is not so sensitive to the sampling rate since it is based on a mathematical model of the response curve.
* As the damping increases (\(\zeta=0.002\)-0.003), the two peaks have more overlap and appear as a wider peak. In this case the 2 DOF method has the same accuracy as the Sine fitting method in estimating the amplitude of the response. In addition, the 2 DOF method is able to estimate the damping value directly from the fitting with errors still less than 1%. In the presence of noise (with SNR higher than 20 dB) the error remains below 5%. On the contrary the Sine fit method does not get the damping value directly from the fitting but requires to estimate the damping from the width of the peak itself and this estimate can be altered by the fact that there are two overlapped peaks.
* For even higher damping values (\(\zeta=0.006\)) when only one single peak is visible because the two peaks are merged, the two methods (2 DOF and Sine fit) are equivalent. The 2 DOF method can no longer obtain the damping values associated with the two modes with the same accuracy as in the previous cases.  
The 2 DOF method therefore seems to be a valid method to be used in the case of close resonance peaks if the experimenter wants to determine not only the shape and the amplitude of the response peak but also the system parameters (resonance frequencies and damping). Employing this method as  
Figure 14: Effect of noise on the fitting residual, damping ratio and natural frequency for EO = 5, \(\zeta_{1,2}=0.002\) and SD = 0.10, (**a**) fitting residual, (**b**) error in damping ratio, (**c**) error in natural frequency.  
a separate module or as a complementary plugin along with the traditional BTT methods such as Sine fit method can be an added value to the measurement system.  
The three authors together decided the methodology and the test case. [PERSON] performed the numerical simulations and wrote the manuscript. [PERSON] and [PERSON] contributed to final review and manuscript corrections. T.M.B. acquired the necessary funding. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Politecnico di Torino Research Funding \"RIB-Ricerca di base\".  
The authors declare no conflict of interest.