Significance, interpretation, and quantification of uncertainty in prognostics and remaining useful life prediction

Abstract This paper analyzes the significance, interpretation, and quantification of uncertainty in prognostics, with an emphasis on predicting the remaining useful life of engineering systems and components. Prognostics deals with predicting the future behavior of engineering systems, and is affected by various sources of uncertainty. In order to facilitate meaningful prognostics-based decision-making, it is important to analyze how these sources of uncertainty affect prognostics, and thereby, compute the overall uncertainty in the remaining useful life prediction. This paper investigates the classical (frequentist) and subjective (Bayesian) interpretations of uncertainty and their implications on prognostics, and argues that the Bayesian interpretation of uncertainty is more suitable for condition-based prognostics and health monitoring. It is also demonstrated that uncertainty quantification in remaining useful life prediction needs to be approached as an uncertainty propagation problem. Several uncertainty propagation methods are discussed in this context, and the practical challenges involved in such uncertainty quantification are outlined.

[1]  H.-J. Zimmermann Fuzzy set theory , 2010 .

[2]  Rui Kang,et al.  Benefits and Challenges of System Prognostics , 2012, IEEE Transactions on Reliability.

[3]  J. Celaya,et al.  Uncertainty Representation and Interpretation in Model-Based Prognostics Algorithms Based on Kalman Filter Estimation , 2012 .

[4]  Donald L. Iglehart,et al.  Importance sampling for stochastic simulations , 1989 .

[5]  C. Bucher Adaptive sampling — an iterative fast Monte Carlo procedure , 1988 .

[6]  Raphael T. Haftka,et al.  Uncertainty Reduction of Damage Growth Properties Using Structural Health Monitoring , 2010 .

[7]  Enrico Zio,et al.  A data-driven fuzzy approach for predicting the remaining useful life in dynamic failure scenarios of a nuclear system , 2010, Reliab. Eng. Syst. Saf..

[8]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[9]  Lin Ma,et al.  Prognostic modelling options for remaining useful life estimation by industry , 2011 .

[10]  Keung-Chi Ng,et al.  Uncertainty management in expert systems , 1990, IEEE Expert.

[11]  Stephen J. Engel,et al.  Prognostics, the real issues involved with predicting life remaining , 2000, 2000 IEEE Aerospace Conference. Proceedings (Cat. No.00TH8484).

[12]  Daniela Calvetti,et al.  Introduction to Bayesian Scientific Computing: Ten Lectures on Subjective Computing , 2007 .

[13]  O. Alsaç,et al.  Generalized state estimation , 1998 .

[14]  Kwok-Leung Tsui,et al.  Condition monitoring and remaining useful life prediction using degradation signals: revisited , 2013 .

[15]  Enrico Zio,et al.  Particle filtering prognostic estimation of the remaining useful life of nonlinear components , 2011, Reliab. Eng. Syst. Saf..

[16]  Bo-Suk Yang,et al.  Machine performance degradation assessment and remaining useful life prediction using proportional hazard model and support vector machine , 2012, WCE 2010.

[17]  A. N. Kolmogorov,et al.  Foundations of the theory of probability , 1960 .

[18]  N. Zhou,et al.  An Approach to Harmonic State Estimation of Power System , 2009 .

[19]  G. Kacprzynski,et al.  Advances in uncertainty representation and management for particle filtering applied to prognostics , 2008, 2008 International Conference on Prognostics and Health Management.

[20]  Enrico Zio,et al.  Investigation of uncertainty treatment capability of model-based and data-driven prognostic methods using simulated data , 2013, Reliab. Eng. Syst. Saf..

[21]  Zhigang Tian,et al.  A neural network approach for remaining useful life prediction utilizing both failure and suspension histories , 2010 .

[22]  Hugh McManus,et al.  A framework for understanding uncertainty and its mitigation and exploitation in complex systems , 2006, IEEE Engineering Management Review.

[23]  Charles R Farrar,et al.  Damage prognosis: the future of structural health monitoring , 2007, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[24]  Peter Walley,et al.  Towards a unified theory of imprecise probability , 2000, Int. J. Approx. Reason..

[25]  M. Eldred,et al.  Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions , 2008 .

[26]  Sankaran Mahadevan,et al.  Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data , 2011, Reliab. Eng. Syst. Saf..

[27]  M. Rosenblatt Remarks on Some Nonparametric Estimates of a Density Function , 1956 .

[28]  M. Hohenbichler,et al.  Improvement Of Second‐Order Reliability Estimates by Importance Sampling , 1988 .

[29]  Zhigang Tian,et al.  Uncertainty Quantification in Gear Remaining Useful Life Prediction Through an Integrated Prognostics Method , 2013, IEEE Transactions on Reliability.

[30]  Matthew Daigle,et al.  Advanced Methods for Determining Prediction Uncertainty in Model-Based Prognostics with Application to Planetary Rovers , 2013 .

[31]  R. Caflisch Monte Carlo and quasi-Monte Carlo methods , 1998, Acta Numerica.

[32]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[33]  K. Goebel,et al.  Analytical algorithms to quantify the uncertainty in remaining useful life prediction , 2013, 2013 IEEE Aerospace Conference.

[34]  Matthew Daigle,et al.  A Model-Based Prognostics Approach Applied to Pneumatic Valves , 2011 .

[35]  Habib N. Najm,et al.  Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics , 2009 .

[36]  Noureddine Zerhouni,et al.  CNC machine tool's wear diagnostic and prognostic by using dynamic Bayesian networks , 2012 .

[37]  Donghua Zhou,et al.  Remaining useful life estimation - A review on the statistical data driven approaches , 2011, Eur. J. Oper. Res..

[38]  Matthew Daigle,et al.  Model-based prognostics under limited sensing , 2010, 2010 IEEE Aerospace Conference.

[39]  Jie Gu,et al.  Uncertainty Assessment of Prognostics of Electronics Subject to Random Vibration , 2007, AAAI Fall Symposium: Artificial Intelligence for Prognostics.

[40]  Thomas E Marlin,et al.  Process Control , 1995 .

[41]  Kai Goebel,et al.  Uncertainty Quantification in Remaining Useful Life Prediction Using First-Order Reliability Methods , 2014, IEEE Trans. Reliab..

[42]  Matthew Daigle,et al.  An Efficient Deterministic Approach to Model-based Prediction Uncertainty Estimation , 2012 .

[43]  A. Kiureghian,et al.  Second-Order Reliability Approximations , 1987 .

[44]  Achintya Haldar,et al.  Reliability Assessment Using Stochastic Finite Element Analysis , 2000 .

[45]  Kai Goebel,et al.  Model-Based Prognostics With Concurrent Damage Progression Processes , 2013, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[46]  Zhonghua Han,et al.  Efficient Uncertainty Quantification using Gradient-Enhanced Kriging , 2009 .

[47]  Marvin Rausand,et al.  Remaining useful life, technical health, and life extension , 2011 .

[48]  Sankaran Mahadevan,et al.  Test Resource Allocation in Hierarchical Systems Using Bayesian Networks , 2013 .

[49]  Benoît Iung,et al.  Remaining useful life estimation based on stochastic deterioration models: A comparative study , 2013, Reliab. Eng. Syst. Saf..

[50]  Donghua Zhou,et al.  A Wiener-process-based degradation model with a recursive filter algorithm for remaining useful life estimation , 2013 .

[51]  Kurt Weichselberger The theory of interval-probability as a unifying concept for uncertainty , 2000, Int. J. Approx. Reason..

[52]  László E. Szabó Objective probability-like things with and without objective indeterminism , 2007 .

[53]  Sankaran Mahadevan,et al.  Separating the contributions of variability and parameter uncertainty in probability distributions , 2013, Reliab. Eng. Syst. Saf..

[54]  K. Popper The Propensity Interpretation of Probability , 1959 .

[55]  Chao Hu,et al.  Ensemble of data-driven prognostic algorithms for robust prediction of remaining useful life , 2011, 2011 IEEE Conference on Prognostics and Health Management.

[56]  Wei-Liem Loh On Latin hypercube sampling , 1996 .

[57]  K. Doliński,et al.  First-order second-moment approximation in reliability of structural systems: Critical review and alternative approach , 1982 .

[58]  Achintya Haldar,et al.  Probability, Reliability and Statistical Methods in Engineering Design (Haldar, Mahadevan) , 1999 .

[59]  Chaochao Chen,et al.  Machine remaining useful life prediction: An integrated adaptive neuro-fuzzy and high-order particle filtering approach , 2012 .

[60]  Jay H. Lee,et al.  A least squares formulation for state estimation , 1995 .

[61]  S. S. Wilks,et al.  Probability, statistics and truth , 1939 .

[62]  D. C. Swanson,et al.  A general prognostic tracking algorithm for predictive maintenance , 2001, 2001 IEEE Aerospace Conference Proceedings (Cat. No.01TH8542).

[63]  C. C. Quach,et al.  Optimizing battery life for electric UAVs using a Bayesian framework , 2012, 2012 IEEE Aerospace Conference.

[64]  T. Kailath,et al.  An innovations approach to least-squares estimation--Part II: Linear smoothing in additive white noise , 1968 .

[65]  K. Goebel,et al.  Prognostics approach for power MOSFET under thermal-stress aging , 2012, 2012 Proceedings Annual Reliability and Maintainability Symposium.

[66]  R. Rackwitz,et al.  First-order concepts in system reliability , 1982 .

[67]  Noureddine Zerhouni,et al.  Remaining Useful Life Estimation of Critical Components With Application to Bearings , 2012, IEEE Transactions on Reliability.

[68]  Sankaran Mahadevan,et al.  Uncertainty quantification and model validation of fatigue crack growth prediction , 2011 .

[69]  George Vachtsevanos,et al.  Methodologies for uncertainty management in prognostics , 2009, 2009 IEEE Aerospace conference.

[70]  C. Cornell,et al.  Adaptive Importance Sampling , 1990 .

[71]  B. Saha,et al.  Uncertainty Management for Diagnostics and Prognostics of Batteries using Bayesian Techniques , 2008, 2008 IEEE Aerospace Conference.

[72]  Y.-T. Wu,et al.  COMPUTATIONAL METHODS FOR EFFICIENT STRUCTURAL RELIABILITY AND RELIABILITY SENSITIVITY ANALYSIS , 1993 .