# Roll Eccentricity Signal Detection and Its Engineering Application Based on SFFT-IAA
## 5 Engineering Implementation and Validation
It can be seen from Figure 11 that the frequency components of the measured data were concentrated around 0.33 Hz, 0.63 Hz, 1.73 Hz, and 2.1 Hz, especially around 0.33 Hz, where the component with the largest frequency spectra peak was located. Considering this, four small frequency ranges were set in this study, which were [0.30 Hz 0.36 Hz], [0.60 Hz 0.66 Hz], [1.70 Hz 1.76 Hz], and [2.07 Hz 2.13 Hz]. In each frequency band, the roll eccentricity parameters were estimated by the IAA algorithm; the results are illustrated in Figure 12.  
As shown in Figure 12, in the range of [0.30 Hz 0.36 Hz], two frequency components were found, i.e., 0.3244 Hz and 0.3343 Hz; in the range of [0.60 Hz 0.66 Hz], one frequency component was found, i.e., 0.6406 Hz; in the range of [1.70 Hz 1.76 Hz], one frequency component was found, i.e., 1.7371 Hz; in the range of [2.07 Hz 2.13 Hz], two frequency components were found, i.e., 2.102 Hz and 2.092 Hz. Usually, the measured data in the industrial field contain strong noise. According to Figures 11 and 12, the proposed method could effectively eliminate the influence of noise to find the accurate frequency components of the roll eccentricity signal, thus showing a strong interference suppression ability. The  
Figure 11: The results of practical data by SFFT. Figure 12: Results of practical data by IAA. The red circles indicate estimated frequencies. (**a**) Frequency band [0.30 Hz 0.36 Hz]; (**b**) frequency band [0.60 Hz 0.66 Hz]; (**c**) frequency band [1.70 Hz 1.76 Hz]; (**d**) frequency band [2.07 Hz 2.13 Hz]. results of the eccentricity signal parameters extracted by the proposed method are presented in Table 2.  
Moreover, to compare the performance of the SFFT-IAA and the FFT in an engineering application, the experiment using the FFT method was carried out. Figure 13 shows the amplitude and frequency characteristics of the practical eccentricity signal using FFT. It can be seen from Figure 13 that the FFT method only found four frequencies of 0.3418 Hz, 0.6348 Hz, 1.7333 Hz, and 2.0996 Hz, and no similar frequencies were found. It showed frequency aliasing around 0.34 Hz and 2.09 Hz, with low resolution, frequency leakage, and fence effect. From this experiment, it can be seen that the performance shown by the FFT has no advantage over the SFFT-IAA. According to the setting of the rolling mill parameters and the production parameters, the roll eccentricity signal comprises the 1\(\times\) rotation frequencies of two backup rollers, the 2\(\times\) rotation frequency of a lower backup roller, the 1x rotation frequency of an upper intermediate roller, and the 2\(\times\) rotation frequencies of two work rollers. This means that the upper backup roller has rotational eccentricity; the lower backup roller has both rotational eccentricity and elliptical eccentricity; the upper intermediate has rotational eccentricity; the two work rolls have elliptical eccentricity. It can be seen that the proposed method is not only meaningful for the accurate detection and compensation control of the eccentricity signal but also for guiding the repair of the rollers. After the parameters of the eccentricity signal were obtained, the roll eccentricity signal could be reconstructed to establish the eccentricity control and the compensation model. The eccentricity control and the compensation model were constructed by sampling the eccentricity signal of the roller with the largest diameter at \(M\) equal intervals after one cycle of rotation, and a sequence \(E\) can be obtained as:  
\[E^{T}=[e(1),\cdots,\,e(M)] \tag{26}\]  
Figure 14 illustrates the eccentricity control model at \(M=128\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline frequency/Hz & 0.3244 & 0.3343 & 0.6406 & 1.7371 & 2.0960 & 2.1003 \\ amplitude/mm & 0.0208 & 0.0220 & 0.0080 & 0.0112 & 0.0051 & 0.0055 \\ phase angle/rad & 0.3504 & 1.5200 & 0.7501 & 1.3301 & 0.4300 & 1.5003 \\ \hline \hline \end{tabular}
\end{table}