When the centrifugal pump is working, if its rotary shaft seal suffers from wear, deformation, thermal cracking and other failures, it will have adverse effects on the system. Employing theoretical and experimental analysis approaches, this study investigates the vibration properties of centrifugal pumps under various states of rotary shaft seals. The aim is to discern rotary shaft seal faults and assess the operational status of the centrifugal pump system. The vibration signal is collected, and the EMD-AR spectrum of the vibration signal is drawn through normalization, window function, anti-aliasing filter, EMD, and AR model establishment. The findings indicate a reduction in both the head and efficiency of the centrifugal pump as the rotary shaft seal experiences failure. The head is notably more affected by this occurrence; To ensure minimal vibration and enhanced stability, it is advisable for centrifugal pumps to operate at design conditions or slightly higher flow rates, avoiding operation at low flow rates; Additionally, the amplitude of the EMD-AR spectrum in the vibration signal progressively increases with the intensification of rotary shaft seal failure. Consequently, the EMD-AR spectrum serves as a reliable indicator for diagnosing damage to the rotary shaft rotary shaft seal.