industrial//maintenance//prognostics//degradation model
A degradation model is a dynamic model of how a unit's health indicator worsens over time, with the unknown and changing rate of worsening carried as a state to be estimated, and it is the core of degradation-based prognosis: estimate where the unit is and how fast it is going, then project forward to the failure threshold. It turns a remaining-life estimate into a calculation with error bars, whenever a health indicator exists.
A degradation model is a dynamic model of how a unit's health indicator worsens over time, with the unknown and changing rate of worsening carried as a state to be estimated, and it is the core of degradation-based prognosis: estimate where the unit is and how fast it is going, then project forward to the failure threshold. It turns a remaining-life estimate into a calculation with error bars, whenever a health indicator exists.
A minimal model, with zkz_kzk the indicator, θk\theta_kθk its rate of degradation, Δt\Delta tΔt the time step and wkw_kwk, ξk\xi_kξk noises that say how far the model is trusted, is
zk+1=zk+θk Δt+wk,θk+1=θk+ξk.z_{k+1}=z_k+\theta_k\,\Delta t+w_k,\qquad \theta_{k+1}=\theta_k+\xi_k .zk+1=zk+θkΔt+wk,θk+1=θk+ξk.
The rate is a state because it is neither known nor constant: it differs from unit to unit and changes with load. A Kalman filter estimates zzz and θ\thetaθ with their uncertainty from the noisy readings (the same state augmentation that lets a filter estimate a sensor's bias); then hundreds of trajectories are launched from the current estimate, each with its own draw of rate and noise, and the time each one crosses the failure threshold zFz_FzF is recorded. The histogram of those crossings is the distribution of the remaining useful life.
Health indicator, evolution model and failure threshold are the three pieces of degradation-based prognosis.
With an indicator that tracks the damage and a model of how it grows, remaining life becomes estimation run forward; without the indicator no model rescues it.
The shape of the model is a choice with consequences far from the data. Linear and exponential growth fit the first months of a bearing's vibration equally well and diverge near the end, exactly where the decision is made; the honest answer often carries both and lets the readings weigh them.
Nonlinear growth and non-Gaussian uncertainty (a distribution of remaining life that is skewed, with a long right tail) are why a particle filter is often preferred over a Kalman filter here: each particle is already a trajectory to project.
Future load is the input the model cannot see in past data: a pump that will run harder next season degrades faster than its history says, and a prognosis is only as good as the assumption about how the unit will be used (prognostics).