Prediction is initiated at a given time kP. Using the current state estimate, the goal is to compute probability distributions for EOL and RUL. The particle filter computes
We can approximate a prediction distribution n steps forward as
Similarly, we can approximate the EOL as
To compute EOL, then, we propagate each particle forward to its own EOL and use that particle's weight at kP for the weight of its EOL prediction.
The pseudocode for the prediction procedure is given as the algorithm below. Each particle is propagated forward until the EOL threshold TEOL evaluates to 1, at this point EOL has been reached for this particle. The predictions rely on hypothesized inputs, which must be chosen carefully.
The figure below shows results from the prediction of friction damage with 100 particles. Initially, the particles have a very tight distribution of friction parameter values, but the distribution of the wear parameter, wr, is relatively large. As a result, the individual trajectories for the different wear parameter values are easily distinguishable as EOL is approached. The different EOL values along with particle weights form an EOL distribution approximated by the probability mass function shown in the figure.