For the prediction of complex nonlinear time series with fractal characteristics, the key problem is the influence of initial condition sensitivity on the dynamic model of the system. This sensitivity also determines the maximum dependable prediction time. The prediction of the finite discrete vibration amplitude obtained by ignoring the maximum dependable prediction time is of little significance for the feature recognition of periodic oscillation trend signal and lifespan analysis. The prediction time was calculated from the viewpoint of information entropy and established the K Nearest Neighbor (KNN) nonparametric improved prediction algorithm based on the local mean decomposition (LMD) of the vibration time series. The LMD main PF component and the influence weight were selected from the energy point of view, and the phase space and the prediction sequence of PF components were reconstructed. To realize the variable parametric optimization, the reconstruction of the different characteristic modal phase space was carried out by using the maximum dependable prediction time as the reconstruction interval. Using the above prediction algorithm, the bearing vibration sequence of 2D12 reciprocating compressor was calculated, and the fault characteristic component was extracted. The comparative analysis results show that the algorithm can accurately predict the evolution trend of the sequence and provide effective support for the lifespan prediction.