Prognostic models are built to predict the future evolution of the state or health of a system. Typical applications of these models include predictions of damage (like crack, wear) and
estimation of remaining useful life of a component. Prognostic models may be data based, based on known physics of the system or can be hybrid, i.e., built through a combination of data and physics. To build such models, one needs either data from the field (i.e., real-world operations) or simulations/ tests that qualitatively represent field observations. Often, field data is not easy to obtain and is limited in its availability. Thus, models are built with simulation or test data and then validated with field observations when they become available. This necessitates a procedure that allows for refinement of models to better represent real-world behavior without having to run expensive simulations or tests repeatedly. Further, a single prognostic model developed for an entire fleet may need to be updated with measurements obtained from individual units. In this paper, we describe a novel methodology, based on the Unscented Kalman Filter, that not only allows for updating such “fleet” models, but also guarantees improvement over the existing model.
unscented Kalman filter, Kalman Filtering, Model Updating
Brown, R., & Hwang, P. (1992). Introduction to random signals and applied kalman filtering. John Wiley and Sons, Inc.
Daum, F. (2005). Nonlinear filters: beyond the kalman filter. IEEE Aerospace and Electronic Systems Magazine, 20(8), 57-69.
Eykhoff, P. (1974). System identification. Wiley.
Houtekamer, P. L., & Mitchell, H. (2001). A sequential ensemble kalman filter for atmospheric data assimilation. Monthly Weather Review, 129(1), 123-137.
Isidori, A. (1995). Nonlinear control systems. Springer.
Jazwinski, A. (1970). Stochastic processes and filtering theory. Academic Press.
Julier, S., & Uhlmann, J. (1997). A new extension of the kalman filter to nonlinear systems. In The 11th intl. symp. on aerospace/defense sensing, simulation and controls, multi sensor fusion, tracking and resource management.
Julier, S., Uhlmann, J., & Durrant-Whyte, H. (1995). A new approach for filtering nonlinear systems. In Proceedings of american control conference.
Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Transactions of the ASME - Journal of Basic Engineering, 82(Series-D), 35-45.
Kalman, R. E., & Bucy, R. S. (1961). New results in linear filtering and prediction theory. Transactions of the ASME - Journal of Basic Engineering, 83(Series-D), 95-108.
Nijmeijer, H., & Fossen, T. (1999). New directions in nonlinear observer design. Lecture Notes in Control and Information Sciences, Springer Verlag.
Ning, L., & Oliver, D. (2005). Ensemble kalman filter for automatic history matching of geologic facies. Journal of Petroleum Science and Engineering, 47(34), 147 -161.
Swerling, P. (1959). First order error propagation in a stagewise smoothing procedure for satellite observations. Journal of the Astronomical Sciences, 6(3).
Volponi, A., Ganguli, R., & Daguang, C. (2003). The use of kalman filter and neural network methodologies in gas turbine performance diagnostics: A comparative study. ASME Journal of Engineering for Gas Turbines and Power, 125(4), 917-924.
Zhan, R., & Wan, J. (2007). Iterated unscented kalman filter for passive target tracking. IEEE Transactions on Aerospace and Electronic Systems, 43(3), 1155-1162.