Likelihood-free Hamiltonian Monte Carlo for modeling piping degradation and remaining useful life prediction using the mixed gamma process

The gamma process is a popular model to characterize the temporal uncertainty in degradation processes. According to this model, degradation occurs in tiny independent increments creating a monotonic non -decreasing trend. Mechanical components or units are often repetitively observed over time for measuring the extent of degradation; apparently, they degrade at different rates although operating in the same environment. The mixed gamma degradation process is suitable for capturing these unexplained differences. However, statistical estimation of its parameters and subsequent prediction of remaining useful life (RUL) turn challenging with limited and noisy measurements.While limited observations bring uncertainties to the model parameters, noisy data turns the likelihood function intractable. In such cases, approximate Bayesian computation (ABC) methods are widely applicable for their ability to bypass the likelihood evaluation and generate samples from an approximate target posterior distribution. The currently available Markov chain Monte Carlo (MCMC) based ABC method shows promising results, although it requires significant thinning due to poor mixing of samples. A new ABC method is derived in this paper which imitates the sampling process of the Hamiltonian Monte Carlo (HMC) method. The proposed ABC-HMC algorithm explores a target probability space more effectively - generating better mixing of samples and requiring less thinning than the MCMC based ABC method. Proof of convergence of ABC-HMC is shown by fulfilling the detailed balance condition. The application of the method is shown using real degradation data of piping components of the heat transport system of a nuclear reactor.

Automated summary

The gamma process is a popular model for characterizing temporal uncertainty in degradation processes, while the mixed gamma degradation process is suitable for capturing differences in degradation rates. Approximate Bayesian computation (ABC) methods are useful for generating samples from a target posterior distribution under limited and noisy measurement conditions.