Bayesian Hierarchical Models for aerospace gas turbine engine prognostics

Data-driven approach is suitable for gas turbine engine prognostics.Bayesian methods produce predictive results within well defined uncertainty bounds.Bayesian Hierarchical Model (BHM) uses optimally degradation data for prognostics.This integrates effectively multiple unit data to address realistic prognostic challenges. Improved prognostics is an emerging requirement for modern health monitoring that aims to increase the fidelity of failure-time predictions by the appropriate use of sensory and reliability information. In the aerospace industry, it is a key technology to maximise aircraft availability, offering a route to increase time in-service and to reduce operational disruption through improved asset management.An aircraft engine is a complex system comprising multiple subsystems that have dependent interactions so it is difficult to construct a model of its degradation dynamics based on physical principles. This complexity suggests that a statistically robust methodology for handling large quantities of real-time data would be more appropriate. In this work, therefore, a Bayesian approach is taken to exploit fleet-wide data from multiple assets to perform probabilistic estimation of remaining useful life for civil aerospace gas turbine engines.The paper establishes a Bayesian Hierarchical Model to perform inference and inform a probabilistic model of remaining useful life. Its performance is compared with that of an existing Bayesian non-Hierarchical Model and is found to be superior in typical (heterogeneous) scenarios. The techniques use Bayesian methods to combine two sources of information: historical in-service data across the engine fleet and once per-flight transmitted performance measurement from the engine(s) under prognosis. The proposed technique provides predictive results within well defined uncertainty bounds and demonstrates several advantages of the hierarchical variant's ability to integrate multiple unit data to address realistic prognostic challenges. This is illustrated by an example from a civil aerospace gas turbine fleet data.

[1]  A. Gelman Bayes, Jeffreys, Prior Distributions and the Philosophy of Statistics , 2009, 1001.2968.

[2]  Peter E. Rossi,et al.  Bayesian Statistics and Marketing , 2005 .

[3]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[4]  Henry Cohen,et al.  Gas turbine theory , 1973 .

[5]  Rong Li,et al.  Residual-life distributions from component degradation signals: A Bayesian approach , 2005 .

[6]  Lei Xu,et al.  Health management based on fusion prognostics for avionics systems , 2011 .

[7]  H. Jeffreys,et al.  Theory of probability , 1896 .

[8]  Michael G. Pecht,et al.  A prognostics and health management roadmap for information and electronics-rich systems , 2010, Microelectron. Reliab..

[9]  Stephan Staudacher,et al.  Application of Bayesian Forecasting to Change Detection and Prognosis of Gas Turbine Performance , 2009 .

[10]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[11]  Donald A. Berry,et al.  Statistics: A Bayesian Perspective , 1995 .

[12]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[13]  J. Johansson,et al.  Prognostics of thermal fatigue failure of solder joints in avionic equipment , 2012, IEEE Aerospace and Electronic Systems Magazine.

[14]  H. Hecht,et al.  Why prognostics for avionics? , 2006, 2006 IEEE Aerospace Conference.

[15]  Bhaskar Saha,et al.  Prognostics for Electronics Components of Avionics Systems , 2009 .

[16]  Yi-Guang Li,et al.  Gas turbine performance prognostic for condition-based maintenance , 2009 .

[17]  Nagi Gebraeel,et al.  Sensory-Updated Residual Life Distributions for Components With Exponential Degradation Patterns , 2006, IEEE Transactions on Automation Science and Engineering.

[18]  Yibo Li,et al.  Research status and perspectives of fault prediction technologies in Prognostics and Health management system , 2008, 2008 2nd International Symposium on Systems and Control in Aerospace and Astronautics.

[19]  M. Daniels A prior for the variance in hierarchical models , 1999 .

[20]  Justin L. Tobias,et al.  Forecasting Output Growth Rates and Median Output Growth Rates: A Hierarchical Bayesian Approach , 2001 .

[21]  Sw. Banerjee,et al.  Hierarchical Modeling and Analysis for Spatial Data , 2003 .

[22]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[23]  Kai Goebel,et al.  Prognostics for Electronics Components of Avionics , 2008 .

[24]  Simon Rogers,et al.  Hierarchic Bayesian models for kernel learning , 2005, ICML.

[25]  Ruey-Shan Guo A multi-category inter-purchase time model based on hierarchical Bayesian theory , 2009, Expert Syst. Appl..

[26]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[27]  A. Raftery,et al.  How Many Iterations in the Gibbs Sampler , 1991 .

[28]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[29]  E.R. Brown,et al.  Prognostics and Health Management A Data-Driven Approach to Supporting the F-35 Lightning II , 2007, 2007 IEEE Aerospace Conference.

[30]  Bo-Suk Yang,et al.  Application of relevance vector machine and survival probability to machine degradation assessment , 2011, Expert Syst. Appl..

[31]  Munir Ahmad,et al.  Bernstein reliability model: Derivation and estimation of parameters , 1984 .

[32]  Mauro Venturini,et al.  Development of a Statistical Methodology for Gas Turbine Prognostics , 2012 .

[33]  Joseph G. Ibrahim,et al.  Bayesian Survival Analysis , 2004 .

[34]  Michael I. Jordan,et al.  Hierarchical Bayesian Models for Applications in Information Retrieval , 2003 .

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

[36]  M E Robinson,et al.  Bayesian Methods for a Growth-Curve Degradation Model with Repeated Measures , 2000, Lifetime data analysis.

[37]  A. Gelman Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[38]  L. Wasserman,et al.  The Selection of Prior Distributions by Formal Rules , 1996 .

[39]  L. Skovgaard NONLINEAR MODELS FOR REPEATED MEASUREMENT DATA. , 1996 .

[40]  Nagi Gebraeel,et al.  Residual life predictions from vibration-based degradation signals: a neural network approach , 2004, IEEE Transactions on Industrial Electronics.

[41]  S. E. Hills,et al.  Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling , 1990 .

[42]  Pietro Perona,et al.  A Bayesian hierarchical model for learning natural scene categories , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[43]  M. G. Walker,et al.  Next generation prognostics and health management for unmanned aircraft , 2010, 2010 IEEE Aerospace Conference.

[44]  Vishal Sethi,et al.  Towards Development of a Diagnostic and Prognostic Tool for Civil Aero-Engine Component Degradation , 2012 .

[45]  Andrew Gelman,et al.  Data Analysis Using Regression and Multilevel/Hierarchical Models , 2006 .

[46]  Christopher M. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[47]  Ulrich Menzefricke,et al.  Bayesian prediction in growth-curve models with correlated errors , 1999 .

[48]  M. A. Zaidan,et al.  Bayesian framework for aerospace gas turbine engine prognostics , 2013, 2013 IEEE Aerospace Conference.

[49]  Stephen J. Roberts,et al.  A tutorial on variational Bayesian inference , 2012, Artificial Intelligence Review.