# Roll Eccentricity Signal Detection and Its Engineering Application Based on SFFT-IAA
###### Abstract  
The roll eccentricity signal is a weak and complex periodic signal that is difficult to be identified. To improve the detection accuracy of the roll eccentricity signal and to compensate effectively, this study proposed a roll eccentricity signal detection method by combining the sparse fast Fourier transform (SFFT) and the iterative adaptive approach (IAA). The proposed method can rapidly determine the frequency range of the roll eccentricity signal by using the SFFT. Then, it divides the frequency range into several small frequency bands. In each small frequency band, the frequency, amplitude, and phase angle of each harmonic component of the roll eccentricity signal were estimated by using IAA. The simulation results show that the proposed method can find all frequency components, and the frequency estimation accuracy is higher than 99.88%. Finally, the engineering application of this method and the eccentricity compensation control were investigated. In engineering applications, the proposed method can reduce the thickness fluctuation of the finished strip by 89.2%, and the product quality is improved significantly. The simulation results and engineering experiments show that the proposed method has an excellent effect on detecting and compensating roll eccentricity signals. rolling mill; roll eccentricity; roll eccentricity compensation; iterative adaptive approach; sparse fast Fourier transform +
Footnote †: journal: Applied Sciences  
compensate for the fluctuations of the roll gap caused by the roll eccentricity, thus reducing the strip steel thickness error caused by the roll eccentricity. According to the mechanical structure and the operating characteristics of rolling mills and rollers, the following aspects should be considered in roll eccentricity compensation:  
1. A roll eccentricity signal is a complex high-frequency periodic signal mixed with random disturbances and containing multiple harmonics. In addition, the signal is featured with periodicity, variability, complexity, and weakness and cannot be measured directly [2]. 2. The frequency of eccentricity signals changes with the rolling speed, so the detection of eccentricity signals must be quick and be adaptable to the changes in the parameters of eccentricity signals. 3. The same types of rollers (such as upper and lower backup rollers and work rollers) have different but close roll diameters and the frequencies of the harmonic components of their eccentricity signals will be very similar. 4. The roll diameters of different types of rollers differ greatly and the frequencies of the roll eccentricity signals vary in a wide range. From the above analysis, it can be seen that the detection of the roll eccentricity signal is very difficult. First, the eccentricity signal is weak. In the collection of signals containing the eccentricity information, the eccentricity part accounts for a small proportion and it is easily affected by interference signals. Second, the roll eccentricity signal has very similar frequency components and it is difficult to distinguish completely by the commonly used signal process methods under the interference of noise. Furthermore, the roll eccentricity signal cannot be directly measured by the sensors and must be obtained by the method of soft measurement. If the eccentricity signal cannot be detected accurately, the eccentricity compensation control will not only fail to improve the product quality but even cause the deterioration of the product quality. Therefore, rapid and accurate detection of the amplitude, frequency, and initial phase angle of eccentricity signals from complex signals obtained by establishing the corresponding mathematical model are key to compensating and controlling roll eccentricity. The roll eccentricity signal is generated by a series of nonlinear periodic signals with different frequencies superimposed on each other. To detect roll eccentricity signals, scholars have conducted extensive research and made certain achievements.