Evaluation of the Training Process of three different Prognostic Approaches based on the Gaussian Process
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
Abstract
Data-driven prognostic approaches like Gaussian Process combined with Unscented Kalman Filter (GPUKF) are promising methods for predicting the Remaining Useful Lifetime (RUL) of a degrading component. Whereas the Gaussian Process (GP) is appropriate to derive a suitable degradation model by means of a set of training data, the Unscented Kalman Filter (UKF) employs this model to determine the prediction and its uncertainty.
Since a degradation process is highly stochastic, it is assumed that by applying more sets of training data the accuracy and precision of the GPUKF is increased. In order to examine the performance enhancement two different approaches are investigated in this paper: First, a single GP is trained with all available data sets. The second approach combines several GPs (each created with a data set of one degradation process) by extending the GPUKF with a Multiple Model Method. The development of a third prognostic approach aims at the investigation of the UKF as a suitable tool for the prognostic algorithm. Therefore, a third method applies a Particle Filter in combination with the GP.
For the evaluation of the aforementioned prognosis algorithms according to their precision and accuracy a set of prevalent performance metrics like the Prognostic Horizon and the Mean Average Percentage Error of a prediction is analyzed.
The validity of the determined results is increased by considering the variance of certain metrics over several units under test. Moreover, particular focus is set on the examination of the performance change caused by the use of more training data sets. In order to quantify this process known metrics are extended. The evaluation is based on simulated data sets, which are generated by an exponential degradation model.
The analysis of the implemented algorithms indicates that the applied metrics are in a comparable range. However, the three approaches reveal a different behaviour concerning the convergence
of the performance values according to the number of training data. In particular cases there is even a decline in accuracy and precision attend by a rising number of training data.
How to Cite
##plugins.themes.bootstrap3.article.details##
performance metrics, performance evaluation, unscented Kalman filter, particle filter, Gaussian Process Model, Prognostic Evaluation
Arulampalam, M. S., Maskell, S., Gordon, N., & Clapp, T. (2002). A tutorial on particle filters for online nonlinear/non-gaussian bayesian tracking. IEEE Transactions on Signal Processing, 50(2), 174–188. doi: 10.1109/78.978374
Ferris, B., H¨ahnel, D., & Fox, D. (2006). Gaussian processes for signal strength-based location estimation. In In proc. of robotics science and systems.
Julier, S. J. (2002). The scaled unscented transformation. In American control conference, 2002. proceedings of the 2002 (Vol. 6, pp. 4555–4559).
Ko, J., Klein, D. J., Fox, D., & Haehnel, D. (2007). Gp-ukf: Unscented kalman filters with gaussian process prediction and observation models. In Intelligent robots and systems, 2007. iros 2007. ieee/rsj international conference on (pp. 1901–1907).
Li, X. R., & Jilkov, V. P. (2003). Survey of maneuvering target tracking. part i. dynamic models. Aerospace and Electronic Systems, IEEE Transactions on, 39(4), 1333–1364.
Orchard, M. E., & Vachtsevanos, G. J. (2009). A particle-filtering approach for on-line fault diagnosis and failure prognosis. Transactions of the Institute of Measurement and Control, 31(3-4), 221–246. doi: 10.1177/0142331208092026
Rasmussen, C. E. (2006). Gaussian processes for machine learning.
Saha, B., Goebel, K., & Christophersen, J. (2009). Comparison of prognostic algorithms for estimating remaining useful life of batteries. Transactions of the Institute of Measurement and Control, 31(3-4), 293–308. doi: 10.1177/0142331208092030
Saxena, A., Celaya, J., Balaban, E., Goebel, K., Saha, B., Saha, S., & Schwabacher, M. (2008). Metrics for evaluating performance of prognostic techniques. In Prognostics and health management, 2008. phm 2008. international conference on (pp. 1–17).
Saxena, A., Celaya, J., Saha, B., Saha, S., & Goebel, K. (2009). Evaluating algorithm performance metrics tailored for prognostics. In Aerospace conference, 2009 ieee (pp. 1–13).
The Prognostic and Health Management Society advocates open-access to scientific data and uses a Creative Commons license for publishing and distributing any papers. A Creative Commons license does not relinquish the author’s copyright; rather it allows them to share some of their rights with any member of the public under certain conditions whilst enjoying full legal protection. By submitting an article to the International Conference of the Prognostics and Health Management Society, the authors agree to be bound by the associated terms and conditions including the following:
As the author, you retain the copyright to your Work. By submitting your Work, you are granting anybody the right to copy, distribute and transmit your Work and to adapt your Work with proper attribution under the terms of the Creative Commons Attribution 3.0 United States license. You assign rights to the Prognostics and Health Management Society to publish and disseminate your Work through electronic and print media if it is accepted for publication. A license note citing the Creative Commons Attribution 3.0 United States License as shown below needs to be placed in the footnote on the first page of the article.
First Author et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.