Nonparametric stochastic degradation modeling under dual uncertainties using a dual B-spline framework

Abstract Faithful representation of stochastic degradation evolution is essential for predicting the future health and service life of engineering systems. Existing approaches commonly prescribe a functional form for the degradation path, an increment distribution, or both, which may introduce structural bias when neither assumption is sufficiently supported by observations. This study develops a dual B-spline degradation framework in which the population-level trend and the residual-increment distribution are represented separately but learned in a coupled manner. The first spline describes the degradation path without imposing a fixed parametric trajectory, whereas the second directly reconstructs the cumulative distribution of residual increments. Their parameters are updated through a common differentiable objective driven by residual-increment feedback. Statistical consistency of the learned distribution is further controlled using a Kolmogorov-Smirnov criterion. The resulting model provides degradation intervals, reliability and lifetime distributions, and rolling RUL estimates. Numerical experiments and sealing O-ring degradation data show improved adaptability to complex trajectories and nonstandard increment distributions compared with the benchmark models.