Uncertainty treatment in expert information systems for maintenance policy assessment

This paper proposes a framework based on the Dempster-Shafer Theory of Evidence (DSTE), Possibility Theory (PT) and Fuzzy Random Variables (FRVs) to represent expert knowledge and propagate uncertainty through models. An example of application is given with reference to a check valve of a turbo-pump lubricating system in a Nuclear Power Plant, which is degrading due to mechanical fatigue and undergoes condition-based maintenance interventions. The component degradation-failure model used to evaluate the performance of the maintenance policy contains parameters subject to epistemic uncertainty.

[1]  Nozer D. Singpurwalla,et al.  Survival in Dynamic Environments , 1995 .

[2]  Kalyanmoy Deb,et al.  Reliability-Based Optimization Using Evolutionary Algorithms , 2009, IEEE Transactions on Evolutionary Computation.

[3]  Didier Dubois,et al.  Representing parametric probabilistic models tainted with imprecision , 2008, Fuzzy Sets Syst..

[4]  H. Prade,et al.  An introduction to the fuzzy set and possibility theory-based treatment of soft queries and uncertain or imprecise databases , 1994 .

[5]  Jim W. Hall.  Soft Methods in Earth Systems Engineering , 2006, SMPS.

[6]  Enrico Zio,et al.  An Introduction to the Basics of Reliability and Risk Analysis , 2007 .

[7]  Christian Borgelt,et al.  Possibilistic Graphical Models , 2000, Computational Intelligence in Data Mining.

[8]  Enrico Zio,et al.  Genetic Algorithms in the Framework of Dempster-Shafer Theory of Evidence for Maintenance Optimization Problems , 2015, IEEE Transactions on Reliability.

[9]  Olaf Wolkenhauer,et al.  Possibility theory with applications to data analysis , 1998 .

[10]  Jan M. van Noortwijk,et al.  A survey of the application of gamma processes in maintenance , 2009, Reliab. Eng. Syst. Saf..

[11]  Enrico Zio,et al.  A Comparison Between Probabilistic and Dempster‐Shafer Theory Approaches to Model Uncertainty Analysis in the Performance Assessment of Radioactive Waste Repositories , 2010, Risk analysis : an official publication of the Society for Risk Analysis.

[12]  B. A. White,et al.  Multiobjective fuzzy genetic algorithm optimisation approach to nonlinear control system design , 1997 .

[13]  Magne Jørgensen,et al.  When 90% confidence intervals are 50% certain: on the credibility of credible intervals , 2005 .

[14]  Enrico Zio,et al.  Basics of the Monte Carlo Method with Application to System Reliability , 2002 .

[15]  Hoang Pham,et al.  Some maintenance models and availability withimperfect maintenance in production systems , 1999, Ann. Oper. Res..

[16]  Michael J. Pont,et al.  Application of Dempster-Shafer theory in condition monitoring applications: a case study , 2001, Pattern Recognit. Lett..

[17]  Raymond S. K. Kwan,et al.  A fuzzy genetic algorithm for driver scheduling , 2003, Eur. J. Oper. Res..

[18]  Isabelle Bloch,et al.  Some aspects of Dempster-Shafer evidence theory for classification of multi-modality medical images taking partial volume effect into account , 1996, Pattern Recognit. Lett..

[19]  E. Zio,et al.  A Combined Monte Carlo and Possibilistic Approach to Uncertainty Propagation in Event Tree Analysis , 2008, Risk analysis : an official publication of the Society for Risk Analysis.

[20]  Terje Aven,et al.  Interpretations of alternative uncertainty representations in a reliability and risk analysis context , 2011, Reliab. Eng. Syst. Saf..

[21]  Hongzhou Wang,et al.  A survey of maintenance policies of deteriorating systems , 2002, Eur. J. Oper. Res..

[22]  Didier Dubois.  Possibility Theory, Probability Theory and Multiple-Valued Logics: A Clarification , 2001, Fuzzy Days.

[23]  Frank J. Groen,et al.  Foundations of probabilistic inference with uncertain evidence , 2005, Int. J. Approx. Reason..

[24]  Richard M. Feldman,et al.  A survey of preventive maintenance models for stochastically deteriorating single-unit systems , 1989 .

[25]  Didier Dubois,et al.  Representation, Propagation, and Decision Issues in Risk Analysis Under Incomplete Probabilistic Information , 2010, Risk analysis : an official publication of the Society for Risk Analysis.

[26]  Philippe Smets,et al.  The Transferable Belief Model , 1991, Artif. Intell..

[27]  Arnold F. Shapiro,et al.  Fuzzy random variables , 2009 .

[28]  Enrico Zio,et al.  Component Ranking by Birnbaum Importance in Presence of Epistemic Uncertainty in Failure Event Probabilities , 2013, IEEE Transactions on Reliability.

[29]  Mary McLeish,et al.  Using certainty factors and possibility theory methods in a tillage selection expert system , 1992 .

[30]  Johan Schubert.  Creating Prototypes for Fast Classification in Dempster-Shafer Clustering , 1997, ECSQARU-FAPR.

[31]  Jon C. Helton,et al.  An exploration of alternative approaches to the representation of uncertainty in model predictions , 2003, Reliab. Eng. Syst. Saf..

[32]  G. Apostolakis.  The concept of probability in safety assessments of technological systems. , 1990, Science.

[33]  Enrico Zio,et al.  Framework for Maintenance Planning , 2010 .

[34]  Philipp Limbourg,et al.  Multi-objective Optimization of Problems with Epistemic Uncertainty , 2005, EMO.

[35]  Didier Dubois,et al.  Possibility theory and statistical reasoning , 2006, Comput. Stat. Data Anal..

[36]  Hamidreza Eskandari,et al.  Handling uncertainty in evolutionary multiobjective optimization: SPGA , 2007, 2007 IEEE Congress on Evolutionary Computation.

[37]  Enrico Zio,et al.  The Monte Carlo Simulation Method for System Reliability and Risk Analysis , 2012 .

[38]  Enrico Zio,et al.  Maintenance policy performance assessment in presence of imprecision based on Dempster-Shafer Theory of Evidence , 2013, Inf. Sci..

[39]  Didier Dubois,et al.  Joint Propagation and Exploitation of Probabilistic and Possibilistic Information in Risk Assessment , 2006, IEEE Transactions on Fuzzy Systems.

[40]  Rommert Dekker,et al.  Modelling and Optimizing Imperfect Maintenance of Coatings on Steel Structures , 2007 .

[41]  Brian White,et al.  Multiobjective fuzzy genetic algorithm optimization approach to nonlinear control system design , 1996 .

[42]  Carlos Guedes Soares,et al.  Even tree uncertainty analysis by Monte Carlo and possibility theory , 2008 .

[43]  Evan J. Hughes,et al.  Evolutionary Multi-objective Ranking with Uncertainty and Noise , 2001, EMO.

[44]  Jerry M. Mendel,et al.  Type-2 fuzzy sets made simple , 2002, IEEE Trans. Fuzzy Syst..

[45]  H. W. Kalfsbeek,et al.  Elicitation, assessment, and pooling of expert judgments using possibility theory , 1995, IEEE Trans. Fuzzy Syst..

[46]  Philipp Limbourg,et al.  Uncertainty analysis using evidence theory - confronting level-1 and level-2 approaches with data availability and computational constraints , 2010, Reliab. Eng. Syst. Saf..

[47]  Enrico Zio,et al.  Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods , 2013 .

[48]  Didier Dubois,et al.  Handling uncertainty with possibility theory and fuzzy sets in a satellite fault diagnosis application , 1996, IEEE Trans. Fuzzy Syst..

[49]  Alessandro Saffiotti,et al.  The Transferable Belief Model , 1991, ECSQARU.

[50]  Enrico Zio,et al.  A framework for the Monte Carlo simulation of degradation and failure processes in the assessment of maintenance programs performance , 2009 .

[51]  Salem Benferhat,et al.  Classification with Uncertain Observations Using Possibilistic Networks , 2009, 2009 21st IEEE International Conference on Tools with Artificial Intelligence.

[52]  Enrico Zio,et al.  Computational Methods for Reliability and Risk Analysis , 2009 .

[53]  A. Wormsen,et al.  A statistical investigation of fatigue behaviour according to Weibull's weakest link theory , 2013 .

[54]  Ziyou Gao,et al.  Railway freight transportation planning with mixed uncertainty of randomness and fuzziness , 2011, Appl. Soft Comput..

[55]  Henri Prade,et al.  An Introduction to the Fuzzy Set and Possibility Theory-Based Treatment of Flexible Queries and Uncertain or Imprecise Databases , 1996, Uncertainty Management in Information Systems.

[56]  R. P. Srivastava,et al.  Belief functions in business decisions , 2002 .

[57]  P. C. Paris,et al.  A Critical Analysis of Crack Propagation Laws , 1963 .