Distribution Free Prediction Interval for Uncertainty Quantification in Remaining Useful Life Prediction

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Huimin Chen

Abstract

Remaining useful life (RUL) prediction is an important component for system health monitoring and prognosis. Ideally, one expects the prediction algorithm to provide the complete distribution of the RUL prediction over time taking various uncertainties into account. However, the dynamic model be- ing used to characterize state estimation and future loading uncertainties is often simplified through various approximations, leading to non-credible predicted distribution. Nevertheless, certain algorithm may only provide a point estimate of the RUL, making it difficult to quantify the uncertainty of the prediction. In this paper, we focus on interval prediction with high probability that guarantees finite sample validity without the knowledge of statistical distribution of the noise. The key idea is to leverage the newly proposed conformal pre- diction framework with non-parametric conditional density estimation. Under certain regularity conditions, the proposed interval estimator converges to an oracle band at a minimax optimal rate. In addition, we apply a data driven method to automatically select the bandwidth in the kernel density estimator. We discuss practical approximations to speed up the computation. The proposed method can be used to predict the RUL interval with physics-based model in a distribution free manner. It can also be applied to assess the validity of other prognostic algorithms from experimental data. We demonstrate the effectiveness of the RUL prediction for Li-Ion batteries using both simulated and experimental data.

How to Cite

Chen, H. . (2013). Distribution Free Prediction Interval for Uncertainty Quantification in Remaining Useful Life Prediction. Annual Conference of the PHM Society, 5(1). https://doi.org/10.36001/phmconf.2013.v5i1.2249
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Keywords

Remaining useful Life, battery health management, conformal prediction, non-parametric density estimation

References
Charkhgard, M., & Farrokhi, M. (2010). State-of-charge estimation for lithium-ion batteries using neural networks and ekf. Industrial Electronics, IEEE Transactions on, 57(12), 4178–4187.

Chen, H. (2012). Adaptive cubature kalman filter for non- linear state and parameter estimation. In Information fusion (fusion), 15th international conference on (pp. 1413–1420).

Chiasson, J., & Vairamohan, B. (2005). Estimating the state of charge of a battery. Control Systems Technology, IEEE Transactions on, 13(3), 465–470.

Efron, B., & Tibshirani, R. (1993). An introduction to the bootstrap (Vol. 57). CRC press.

Fisher, R. (1954). Statistical methods for research workers. Oliver and Boyd.

Justel, A., Pena, D., & Zamar, R. (1997). A multivariate kolmogorov-smirnov test of goodness of fit. Statistics & Probability Letters, 35(3), 251–259.

Kim, J., & Cho, B. H. (2011). State-of-charge estimation and state-of-health prediction of a li-ion degraded battery based on an ekf combined with a per-unit system. Vehicular Technology, IEEE Transactions on, 60(9), 4249–4260.

Klein, R., Chaturvedi, N. A., Christensen, J., Ahmed, J., R., F., & Kojic, A. (2013). Electrochemical model based observer design for a lithium-ion battery. Control Systems Technology, IEEE Transactions on, 21(2), 289– 301.

Lei, J., Robins, J., & Wasserman, L. (2011). Efficient non- parametric conformal prediction regions. Manuscript. http://arxiv.org/abs/1111.1418..

Luo, J., Namburu, M., Pattipati, K., Liu, Q., Kawamoto, M., & Chigusa, S. (2003). Model-based prognostic techniques. In Ieee systems readiness technology conference (pp. 330–340).

Plett, G. L. (2004a). Extended kalman filtering for battery management systems of lipb-based hev battery packs part 2 – modeling and identification. Journal of Power Sources, 134(2), 262–276.

Plett, G. L. (2004b). Extended kalman filtering for battery management systems of lipb-based hev battery packs part 3 – state and parameter estimation. Journal of Power Sources, 134(2), 277–292.

Rosenblatt, M. (1956). Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics, 27(3), 832–837.

Saha, B., & Goebel, K. (2011). Model adaptation for prognostics in a particle filtering framework. International Journal of Prognostics and Health Management, 2(006).

Saha, B., Goebel, K., & Christophersen, J. (2009). Comparison of prognostic algorithms for estimating remaining useful life of batteries. Transactions of the Institute of Measurement & Control, 31(3-4), 293–308.

Sankararaman, S., & Goebel, K. (2013). Uncertainty quantification in remaining useful life of aerospace components using state space models and inverse form. In Aiaa/asme/asce/ahs/asc structures, structural dynamics and materials conference.

Saxena, A., Celaya, J., Saha, B., Saha, S., & Goebel, K. (2009). On applying the prognostic performance metrics. In Annual conference of the prognostics and health management society.

Shafer, G., & Vovk, V. (2008). A tutorial on conformal prediction. Journal of Machine Learning Research, 9,371–421.

Tsybakov, A. (2009). Introduction to nonparametric estimation. Springer.
Section
Technical Papers