This paper explores how the remaining useful life (RUL) can be assessed for complex systems whose internal state variables are either inaccessible to sensors or hard to measure under operational conditions. Consequently, inference and esti- mation techniques need to be applied on indirect measurements, anticipated operational conditions, and historical data for which a Bayesian statistical approach is suitable. Models of electrochem- ical processes in the form of equivalent electric circuit parame- ters were combined with statistical models of state transitions, aging processes, and measurement fidelity in a formal frame- work. Relevance vector machines (RVMs) and several different particle filters (PFs) are examined for remaining life prediction and for providing uncertainty bounds. Results are shown on battery data.1

Index Terms—Battery health, Bayesian learning, particle filter, prognostics, relevance vector machine, remaining useful life.