Abstract: We present a new method for designing kernel function of H~n(R) using kernel function of H~1(R) and convolution operator.It's possible to select the most suitable kernel function with the method,and its calculation becomes very easy.The method is applied successfully to design the kernel function for kernel principal component analysis using the vibration data of normal,outer race,inner race and ball bearings.The simulation results show the effectiveness of detecting bearings faults.