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• The IAFLSM performance degradation model is established that realizes adaptive synchronous dynamic update of diffusion coefficient and nonlinear drift coefficient. • The dynamic updating mechanism for statistical dependence measurement error based on fractional Lévy stable motion is constructed. • The hidden variables are estimated through parameter estimation method and characteristic function, and the uncertainty is quantified by stability theorem and Monte Carlo technique. • The novel truck rear axle dataset conducted by our research group and the benchmark rolling bearing datasets are used to validate the proposed RUL prediction framework. 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 Lévy 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 Lévy 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. [ABSTRACT FROM AUTHOR]

• The RUL prediction framework of mechanical system based on GFLSM with adaptive nonlinear drift is proposed. • The health indicator (HI) based on MD e -CUSUM is constructed, which is more stable and monotonous. • The failure threshold adaptive update method is proposed. • The whole life cycle data including truck drive axle are used to verify the proposed RUL prediction framework. Remaining useful life (RUL) prediction is of great significance for prognostic and health management (PHM). To accurately predict the RUL of mechanical system under complex conditions, an RUL prediction framework is proposed based on performance evaluation and geometric fractional Lévy stable motion (GFLSM) with adaptive nonlinear drift. The early fault identification of degradation process is realized by setting a threshold for the constructed monotonic health indicator (HI). The dynamic updating method of failure threshold depending on confidence interval is proposed to determine the time of zero RUL. The heavy-tailed distribution degradation model based on GFLSM is constructed to overcome the limitation of Gaussian distribution. The multiple degradation stages are mapped to a relatively unified mode through GFLSM. The long-range dependence and self-similarity of degradation process are described through the relationship between Hurst exponent and stability exponent. The adaptive updating method of nonlinear drift coefficient is put forward to satisfy different degradation trajectories, and other parameters of GFLSM are estimated by the characteristic function method. The predicted RUL and corresponding probability density function (PDF) are obtained by Monte Carlo. The proposed RUL prediction framework is verified by the degradation simulation signal and two different practical industrial experiments. The experimental results demonstrate that the proposed framework is more effective and superior to other state-of-the-art techniques in RUL prediction of mechanical system. [ABSTRACT FROM AUTHOR]