A nonparametric degradation modeling method based on generalized stochastic process with B-spline function and Kolmogorov hypothesis test considering distribution uncertainty

Abstract

The increasing reliability requirements of modern industrial products necessitate precise degradation modeling. Stochastic process-based methods are widely employed due to their robust uncertainty quantification capabilities but often rely on the assumption of a predefined degradation distribution, which may not hold in complex scenarios. This study presents a novel degradation modeling framework that integrates nonparametric estimation and stochastic processes into a unified approach. Unlike conventional methods combined nonparametric estimation and stochastic processes by separately modeling, the proposed method employs a nonparametric model to characterize generalized independent increment processes. Utilizing the flexibility of B-spline functions, the method effectively captures the uncertainties of degradation distributions while mitigating errors associated with improper distribution assumptions. The B-spline construction is further formulated as a numerical optimization problem supported by the Kolmogorov hypothesis test, enabling the direct determination of confidence levels for the constructed model. A Monte Carlo-based framework is employed for reliability assessment and lifetime prediction. Validation using simulations and real-world data demonstrates that the proposed method achieves superior accuracy in capturing degradation dynamics and significantly outperforms traditional methods.