Remaining useful life prediction of mechanical system based on improved adaptive fractional Levy stable motion with statistical dependence measurement error

Prediction of remaining useful life (RUL) is a critical component of prognostics and health management (PHM) strategies for mechanical systems. Although some degradation models based on stochastic processes have played a pivotal role in the field of RUL prediction, the diffusion coefficients associated with these models are often fixed values that remain independent of the drift coefficient. Additionally, the measurement error is typically assumed to follow a Gaussian distribution that is independently and identically distributed with respect to the level of degradation. To address these constraints, an RUL prediction framework is proposed based on improved adaptive fractional Levy stable motion (IAFLSM) with statistical dependence measurement error. The established IAFLSM model is capable of effectively characterizing the individual differences and time-varying uncertainties inherent in equipment degradation processes, with the nonlinear drift and diffusion coefficients exhibiting positive correlation in their variability. Moreover, the state space model is employed to realize the synchronous adaptive dynamic update of the drift coefficient and diffusion coefficient, thus accommodating the mechanical equipment degradation trajectory. Furthermore, a statistical dependence measurement error based on fractional Levy stable motion is constructed, and the corresponding scale parameter incorporates a dynamic update mechanism with statistical correlation of degradation incremental behavior. The hidden variables related to performance degradation model are estimated through parameter estimation method and characteristic function. Expanding upon the proposed framework for RUL prediction, the quantification of the uncertainty intrinsic in the forecasting results is accomplished by employing the stability theorem of stable distribution and Monte Carlo technique. The RUL prediction framework is validated through the use of authentic truck rear axle full-life data and benchmark rolling bearing data. The comparative analysis results demonstrate the effectiveness and superiority of the proposed methodology.