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Friction and wear processes have their origins in the surface interactions between solid materials with many dynamically important details at the microscale. These details such as the structure of surface roughness, etc. may be framed in terms of macro parameters, but there is necessarily a degree of abstraction and uncertainty in this description. As such, wear models tend to have a significant degree of uncertainty. Moreover, since the physics of contact wear as well as the relevant parameters are uncertain, the damage may be multi-modal and tends to take non-Gaussian Forms. In this work, we address these issues by combining the following elements: a macro-scale physical model of the material wear process under sliding and/or rolling contact, and a rapid algorithm to compute probabilistically valid, non- Gaussian forecasts of the wear. The current state estimate is made using a predictor-corrector method that combines a previous prediction with new sensor information. Based on an input loading forecast (which may be probabilistic), we use the wear model to compute a probability distribution for incremental damage over a time horizon of interest, such as the remaining life of the device of interest. The macro-scale, physics-based wear models are analytic, making the computation of incremental damage very rapid. Combining these incremental probability estimates into a single probability distribution for the future remaining life may be done in realtime using a novel probabilistic damage accumulation algorithm. This algorithm accelerates the probability calculations without making approximations of Gaussianity by operating in the Fourier domain. We apply this approach to the problem of predicting the wear profile of a lead screw actuator accounting for uncertainty in the external demands on the system using a physics-based model for the actuator connected to a 3 degree-of-freedom flight simulator.