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Model-based prognostics approaches rely on physics-based models that describe the behavior of systems and their components. These models must account for the several different damage processes occurring simultaneously within a component. Each of these damage and wear processes contributes to the overall component degradation. We develop a model-based prognostics methodology that consists of a joint state-parameter estimation problem, in which the state of a system along with parameters describing the damage progression are estimated, followed by a prediction problem, in which the joint state-parameter estimate is propagated forward in time to predict end of life and remaining useful life. The state-parameter estimate is computed using a particle filter and is represented as a probability distribution, allowing the prediction of end of life and remaining useful life within a probabilistic framework that supports uncertainty management. We also develop a novel variance control algorithm that maintains an uncertainty bound around the unknown parameters to limit the amount of estimation uncertainty and, consequently, reduce prediction uncertainty. We construct a detailed physics-based model of a centrifugal pump that includes damage progression models, to which we apply our model-based prognostics algorithm. We illustrate the operation of the prognostic solution with a number of simulation-based experiments and demonstrate the performance of the approach when multiple damage mechanisms are active.