Abstract: Based on the deficiencies of the three-linear parallel factor model in the blind estimation method of the number of me-chanical vibration sources,that is,due to thelimitation of the dimension,only part of the information of the vibration signal can bemodeled,and the time series information in the signal is ignored.In this paper,the estimation method of mechanical vibrationsources number based on the trilinear parallel factor is extended to four dimensions,an estimation method of mechanical vibrationsources number based on the quadrlinear parallel factor is proposed.In the proposed method,the fourth dimension(i.e.time dimension)is added on the basis of three-dimensional,the load matrix is iteratively updated by the four linear alternating leastsquares method,and the number of vibration sources is estimated by the kemel uniform diagnosis method.Compared with the estimation method of mechanical vibration sources number based on the trilinear parallel factor,the proposed method inherits theunique advantages of the trilinear paralel factor,and contains more complete information of the vibration signal.Moreover,underthe condition of the same component number,the quadrlinear parallel factor has higher coincidence value than the trilinear parallelfactor,and has the more accurate estimation.The simulation results show that the proposed method is superior to the estimationmethod of mechanical vibration sources number based on the trilinear paralel factor.The experimental results further verify the effectiveness of the proposed method.