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Additional resources for Applications of Intelligent Control to Engineering Systems: In Honour of Dr. G. J. Vachtsevanos
Le Gland, Improving regularized particle filters, in Sequential Monte Carlo Methods in Practice, A. Doucet, N. De Frietas and N. ), SpringerVerlag, New York, 2001. 9. M. Orchard, B. Wu and G. Vachtsevanos, A particle filter framework for failure prognosis, in Proceedings of World Tribology Congress III, Washington DC, September 12–16, 2005. 10. R. Patrick, M. Orchard, B. Zhang, M. Koelemay, G. Kacprzynski, A. Ferri and G. Vachtsevanos, An integrated approach to helicopter planetary gear fault diagnosis and failure prognosis, in Proceedings of 42nd Annual Systems Readiness Technology Conference, AUTOTESTCON 2007, Baltimore, MD, September 2007.
It is desired for the expected value of this RUL pdf (computed at time t = 320) to be close to the actual time-to-failure. In this sense, the efficacy of the approach can be evaluated using two performance metrics: accuracy and precision. Accuracy measures how close the RUL expectation is to the actual time-to-failure. Precision, on the other hand, indicates the variance associated to RUL estimates. Precise RUL estimates imply a pdf with small variance. The performance of the proposed Particle filtering-based approach has been compared with another implementation that uses the Extended Kalman filter to generate an estimate of the current state pdf.
Furthermore, if the density is Gaussian with unit covariance matrix, the optimal bandwidth is given by hopt = A · N −1/nx +4 , √ A = 8cn−1 · (nx + 4) · 2 π x nx 1/nx +4 . 6) The Epanechnikov kernel is particularly recommended in the special case of equally weighted samples , and thus it is well suited for uncertainty representation in long 2 Particle Filtering Applied to Prognostics 27 term predictions where no future measurements are available for a weight update procedure. N as initial conditions, it is possible to represent the uncertainty inherent to the predicted state pdf by performing an inverse transform resampling procedure for the particle population .