Gibbs sampler for noisy Transformed Gamma process: Inference and remaining useful life estimation

Abstract

Stochastic processes are widely used to describe continuous degradation, among which the monotonically increasing degradation is most common. However, the observation is often perturbed with undesired noise due to sensor or measurement errors in practice. This paper focuses on predicting the degradation growth and estimating the system’s remaining useful life based on noisy observations. The deterioration is modeled by a Transformed Gamma process, accounting for both time- and state-dependent degradation increments. Measurement error is assumed to follow a normal distribution. We propose to use an improved Gibbs sampler to estimate the hidden degradation states. Combined with Expectation–Maximization, the Gibbs sampler can be used for model parameter estimation. The probability of false/failed alarm and distribution of remaining useful life are also derived. The proposed method is applied to choke valve erosion data collected from NTNU’s laboratory, and the influence of covariates on the degradation rate is discussed.