This paper presents the study on the data-driven process monitoring system design for the dynamic processes with periodic rectangular wave disturbance. The basic idea of the proposed methods are to identify the stable kernel representation (SKR) of the dynamic process by projecting the process data into the row subspace of the periodic rectangular wave disturbance. With the help of the projection, the kernel subspace of the system can be further determined. Based on the identified data-driven SKR, fault detection are developed. The performance and effectiveness of the proposed scheme is verified and demonstrated through the numerical study on randomly generated systems.