# Roll Eccentricity Signal Detection and Its Engineering Application Based on SFFT-IAA
## 4 Simulation Experiments and Result Analysis  
In this study, an actual four-roller reversible cold rolling mill was taken as the object for simulation. The strip steel rolling speed was set as 1 m/s, the roll diameters of a pair of backup rollers were 800 and 808 mm, and the roll diameters of a pair of work rollers were 272 and 278 mm. Assuming that all rollers have elliptical eccentricity and rotational eccentricity, the roll eccentricity signal was constructed as:  
\[ \begin{array}{ll}\mathrm{y}(n)=&0.2\cos(2\pi n\times 0.3981)+0.25\cos(2\pi n \times 0.3915+1.5)\\ &+0.15\cos(2\pi n\times 1.1709+0.7)+0.12\cos(2\pi n\times 1.1456+0.3)\\ &+0.06\cos(2\pi n\times 0.7962+0.8)+0.03\cos(2\pi n\times 0.7883+1.1)\\ &+0.08\cos(2\pi n\times 2.3417+1.6)+0.22\cos(2\pi n\times 2.2917+0.2)+v(n) \end{array} \]  
The above roll eccentricity signal has a relatively close frequency, and its frequency is distributed in a wide range, which is consistent with the characteristics of actual roll eccentricity signals. \(v(n)\) is 0-mean Gaussian white noise, and two sets of data were generated with the signal-to-noise ratio (SNR) of 30 and 10. The initial parameters of the SEFT-IAA algorithm were set as follows: the data sequence length \(N=2048\), the sampling frequency \(f_{s}=50\) Hz, the sparsity \(K=8\), the number of buckets \(B=128\), the number of SEFT iterations \(L=7\), the calculation data length of the IAA algorithm \(N_{I}=256\), the maximum number of IAA iterations \(L_{I}=15\), the frequency grid spacing \(\Delta\omega=0.0001\) Hz, and the power threshold \(P_{TH}=0.01\). The proposed algorithm was verified in the case of \(\mathrm{SNR}=30\). First, SEFT was used to partition the frequency bands. Figure 5 shows the results obtained by the SEFT algorithm. According to Figure 5, the eight frequency points obtained by using the SEFT algorithm were 0.3906, 0.4150, 0.7813, 0.8057, 1.1475, 1.1719, 2.2949, and 2.3438 Hz, respectively. Figure 5: The results obtained by SEFT (SRN = 30). Compared with the original signal, the error rates of the SFFT results are 0.230%, \(-\)4.245%, 0.888%, \(-\)1.193%, \(-\)0.166%, \(-\)0.085%, \(-\)0.140%, and \(-\)0.090%, respectively. Therefore, according to the results obtained by SFFT, the frequency band of the original signal can be divided into four small frequency bands, namely [0.37 Hz 0.43 Hz], [0.76 Hz 0.82 Hz], [1.12 Hz 1.19 Hz], and [2.27 Hz 2.36 Hz]. In the original signal, 256 data points were sampled, and the IAA algorithm was used for computation in the small frequency bands partitioned by SFFT. By combining the above results, the results of the SFFT-IAA algorithm were obtained, as shown in Figure 6.  
According to Figure 6, in the case of SNR = 30, when the proposed method was used to estimate each harmonic frequency component in each frequency band, the method showed high resolution for frequency estimation, and it was not influenced by other frequency components, with sharp frequency spectra peaks, no frequency aliasing, and strong side lobe suppression. Meanwhile, it distinguished the frequency components that were close to each other. Similarly, in the case of SNR = 10, the results obtained by the SFFT-IAA algorithm are presented in Figure 7. It can be seen that SNR was 10, influenced by noise, and the side lobe suppression capability was reduced. Although the frequency spectra peaks were not as sharp as those in the case of SNR = 30, the algorithm can still distinguish the frequency components that were close to each other, and the frequency estimation resolution was also high. To compare the performance of the SFFT-IAA algorithm and the FFT algorithm, simulations using FFT were conducted at an SNR of 10 and 30, respectively. Figure 8 shows the amplitude and frequency characteristics of the eccentricity signal at an SNR of 30 and 10 using FFT. It can be seen from the Figure 8 that the FFT method showed frequency aliasing around 0.39 Hz, 0.79 Hz, and 1.15 Hz for both SNRs, with low resolution, frequency leakage, and fence effect.