Remaining Useful Lifetime Prognosis of Controlled Systems: A Case of Stochastically Deteriorating Actuator

Algorithm 1

Generic particle filter for system state estimation.

Initialization: .

Draw particle according to the initial condition of system

Assign corresponding weight

At step (corresponding to time   ): Given , do

(a) Importance sampling

Based on the system description (derived from (1) to (7)), draw particles

(b) Weight update

Based on the likelihoods of the observations collected (Eq. (8)), assign weights

(c) Weight normalisation

(d) Re-sampling decision

If then perform deterministic re-sampling:

(e) Distribution

Repeat till the prognosis instant    is reached