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The primary objective of this study is to develop a mathematical framework for failure prognostics and uncertainty management based on a state-space degradation model, where unknown parameters are present in the model. Joint state and parameter estimation is carried out by the Sequential Monte Carlo methods. Then, a degradation prediction with uncertainty limits is made. Sequential Monte Carlo methods for joint state and parameter estimation are reviewed, and the effectiveness of the techniques for the prognostics task is assessed. A performance comparison of these algorithms is made based on a numerical study. The results presented in this study show that the state-of-art SMC techniques can provide satisfactory results of joint state and parameter estimation for the prognostics task. The Particle Markov Chain Monte Carlo method provides relatively more accurate estimation results compared with other SMC methods while demanding more computing resources.