Missing value recovery for encoder signals using improved low-rank approximation

Rotary encoders have been increasingly equipped in high precision machinery, and their data missing may pose great challenges for both numeric control and health monitoring. In view of this limitation, a new methodology, termed improved low-rank approximation (ILRA), is proposed for encoder signal recovery. In this approach, phase space representation (PSR) is first introduced to transform the one-dimensional encoder signal into a matrix for low-rank exploration. Bidirectional centralization with cumulative energy ratio is then proposed to identify and extract the principal components embedded in phase space. Finally, an improved low-rank approximation scheme is employed to recover the missing values in an iterative manner. The performance of the proposed ILRA is evaluated by both simulation and experimental analysis. The results show that the proposed method can recover the missing values efficiently. Furthermore, the method yields satisfactory results for subsequent instantaneous angular speed estimation. Therefore, it may offer a promising tool for numerical data recovery in industrial applications.