Relevance of control theory to design and maintenance problems in time-variant reliability: The case of stochastic viability

Reliability Engineering and System Safety

Volumn 132, Issue 1, 2014, Pages 250-260

  Rougé, Charles ^a,b   Mathias, Jean Denis ^a   Deffuant, Guillaume ^a  

^a Cemagref   (France)

^b UNIVERSITÉ LAVAL   (Canada)

Author keywords

Design and maintenance problems; Dynamic programming; Dynamical systems; Reliability kernel; Time variant reliability; Viability theory

Indexed keywords

COMPUTATION THEORY; CONTROL THEORY; DESIGN; DYNAMICAL SYSTEMS; MAINTENANCE; RELIABILITY; RELIABILITY THEORY; STOCHASTIC SYSTEMS;

CONFIDENCE LEVELS; MAINTENANCE PROBLEM; MAINTENANCE STRATEGIES; PROBABILITY OF FAILURE; RELIABILITY PROBLEMS; STOCHASTICITY; TIME-VARIANT RELIABILITY; VIABILITY THEORY;

DYNAMIC PROGRAMMING;

EID: 84925386927     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2014.07.025     Document Type: Article

References (54)

1. Doyen L, De Lara M. Stochastic viability and dynamic programming. Syst Control Lett 2010;59:629-34.
2. Rackwitz R. Reliability analysis-a review and some perspectives. Struct Saf 2001;23:365-95.
3. Mathias JD, Lemaire M. Reliability analysis of bonded joints with variations in adhesive thickness. J Adhes Sci Technol 2012:1-11. http://dx.doi.org/10.1080/01694243.2012.727176.
4. Rausand M. Reliability centered maintenance. Reliab Eng Syst Saf 1998;60(2): 121-32.
5. Naeem S. Species redundancy and ecosystem reliability. Conserv Biol 1998;12(1): 39-45.
6. Aliev TA, Kartvelishvili LN. Principles of evaluating the ecological reliability of irrigation systems. Hydrotech Constr 1993;27(5):297-304.
7. Melching CS. An improved fi rst-order reliability approach for assessing uncertainties in hydrologic modeling. J Hydrol 1992;132:157-77.
8. Ditlevsen O, Madsen HO. Structural reliability methods. Chichester: John Wiley & Sons; 1996.
9. Lemaire M. Structural reliability. New York: John Wiley & Sons; 2009.
10. Rice SO. Mathematical analysis of random noise. Bell Syst Tech J 1944;23: 282-332.
11. Li C, Der Kiureghian A. Mean out-crossing rate of nonlinear response to stochastic input. In: Lemaire M, Favre J, Mébarki A, editors. Proceedings of the international conference on the application of statistics and probability ICASP7, vol. 1; 1995. p. 295-302.
12. Guedes Soares C, Garbatov Y. Reliability of maintained ship hull girders subjected to corrosion and fatigue. Struct Saf 1998;20:201-19.
13. Sudret B. Analytical derivation of the outcrossing rate in time-variant reliability problems. Struct Infrastruct Eng 2008;4(5):353-62.
14. Kuschel N, Rackwitz R. Optimal design under time-variant reliability constraints. Reliab Eng Syst Saf 2000;22:113-27.
15. Sudret B. Probabilistic models for the extent of damage in degrading reinforced concrete structures. Reliab Eng Syst Saf 2008;93:410-22.
16. Hagen O, Tvedt L. Vector process out-crossing as parallel system sensitivity measure. J Eng Mech 1991;117(10):2201-20.
17. Andrieu-Renaud C, Sudret B, Lemaire M. The phi2 method: a way to compute time-variant reliability. Reliab Eng Syst Saf 2004;84:75-86.
18. Burgazzi L. About time-variant reliability analysis with reference to passive systems assessment. Reliab Eng Syst Saf 2008;93:1682-8.
19. Petryna YS, Pfanner D, Stangenberg F, Krätzig WB. Reliability of reinforced concrete structures under fatigue. Reliab Eng Syst Saf 2002;77:253-61.
20. Schotanus MIJ, Franchin P, Lupoi A, Pinto PE. Seismic fragility analysis of 3d structures. Struct Saf 2004;26:421-41.
21. Wang Z, Wang P. A new approach for reliability analysis with time-variant performance characteristics. Reliab Eng Syst Saf 2013;115:70-81.
22. Savage GJ, Son YK. The set-theory method for systems reliability of structures with degrading components. Reliab Eng Syst Saf 2011;96:108-16.
23. Quigley J, Walls L. Mixing Bayes and empirical Bayes inference to anticipate the realization of engineering concerns about variant system designs. Reliab Eng Syst Saf 2011;96:933-41.
24. Targoutzidis A. A Monte Carlo simulation for the assessment of Bayesian updating in dynamic systems. Reliab Eng Syst Saf 2012;100:125-32.
25. Val DV, Stewart MG. Life-cycle cost analysis of reinforced concrete structures in marine environments. Struct Saf 2003;25:343-62.
26. Sørensen JD, Svensson S, Stang BD. Reliability-based calibration of load duration factors for timber structures. Struct Saf 2005;27:153-69.
27. Biondini F, Frangopol DM. Lifetime reliability-based optimization of reinforced concrete cross-sections under corrosion. Struct Saf 2009;31:483-9.
28. Aubin JP. Viability theory. Boston: Birkhäuser; 1991.
29. Aubin JP, Bayen A, Saint-Pierre P. Viability theory. Regulation of uncertain systems. Berlin: Springer-Verlag; 2011.
30. Saint-Pierre P. Approximation of the viability kernel. Appl Math Opt 1994;29:187-209.
31. Bonneuil N. Computing the viability kernel in large state dimension. J Math Anal Appl 2006;323:1444-54.
32. Deffuant G, Chapel L, Martin S. Approximating viability kernel with support vector machines. IEEE Trans Autom Control 2007;52(5):933-7.
33. Deffuant G, Gilbert N, editors. Viability and resilience of complex systems. London: Kluwer Academic Publishers; 2011.
34. De Lara M, Doyen L. Sustainable management of natural resources. Berlin: Springer-Verlag; 2008.
35. Sudret B, Defaux G, Pendola M. Time-variant finite element reliability analysis -application to the durability of cooling towers. Struct Saf 2005;27:93-112.
36. Hsiao E, Schuster M, Juang C, Kung G. Reliability analysis and updating of excavation-induced ground settlement for building serviceability assessment. J Geotech Geoenviron Eng 2008;134(10):1448-58.
37. Clarke FH, Ledyaev YS, Stern RJ, Wolenski PR. Qualitative properties of trajectories of control systems: a survey. J Dyn Control Syst 1995;1(1):1-48.
38. Aubin JP, Saint-Pierre P. An introduction to viability theory and management of renewable resources. In: Kropp J, Scheffran J, editors. Decision making and risk management in sustainability science. New York: Nova Science; 2002. p. 43-80.
39. Perreira MVF, Pinto LMVG. Stochastic optimization of a multireservoir hydroelectric system: a decomposition approach. Water Resour Res 1985;21(6): 779-92.
40. Shapiro A. Analysis of stochastic dual dynamic programming method. Eur J Oper Res 2011;209:63-72.
41. Abate A, Prandini M, Lygeros J, Sastry S. Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems. Automatica 2008;44: 2724-34. http://dx.doi.org/10.1016/j.automatica.2008.03.027.
42. Summers S, Lygeros J. Verification of discrete time stochastic hybrid systems: a stochastic reach-avoid decision problem. Automatica 2010;49:1951-61. http://dx.doi.org/10.1016/j.automatica.2010.08.006.
43. Hashimoto T, Stedinger J, Loucks D. Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation. Water Resour Res 1982;18(1):14-20.
44. Moy W, Cohon J, ReVelle C. A programming model for analysis of the reliability, resilience, and vulnerability of a water supply reservoir. Water Resour Res 1986;22(4):489-98.
45. Kundzewicz Z, Laski A. Reliability-related criteria in water supply studies. In: New uncertainties concepts in hydrology and water resources. Cambridge, UK: Cambridge University Press; 1995.
46. Oviedo-Salcedo DM. Accounting for parameter uncertainty and temporal variability in coupled groundwater-surface water models using component and systems reliability analysis [Ph.D. thesis]. University of Illinois at Urbana-Champaign; 2012.
47. Skaggs TH, Barry DA. The first-order reliability method of predicting cumulative mass flux in heterogeneous porous formations. Water Resour Res 1997;33(6): 1485-94.
48. Naeem S, Li S. Biodiversity enhances ecosystem reliability. Nature 1997;390: 507-9.
49. Rastetter EB, Gough L, Hartley AE, Herbert DA, Nadelhoffer KJ, Williams M. A revised assessment of species redundancy and ecosystem reliability. Conserv Biol 1999;13(2):440-3.
50. Doyen L, Lara MD, Ferraris J, Pelletier D. Sustainability of exploited marine ecosystems through protected areas: a viability model and a coral reef case study. Ecol Model 2007;208:353-66.
51. De Lara M, Martinet V. Multi-criteria dynamic decision under uncertainty: a stochastic viability analysis and an application to sustainable fishery management. Math Biosci 2009;217:118-24.
52. Doyen L, Thébaud O, Béné C, Martinet V, Gourguet S, Bertignac M, et al. A stochastic viability approach to ecosystem-based fisheries management. Ecol Econ 2012;75:32-42.
53. Rougé C, Mathias JD, Deffuant G. Extending the viability theory framework of resilience to uncertain dynamics and application to lake eutrophication. Ecol Indic 2013;29:420-33. http://dx.doi.org/10.1016/j.ecolind.2012.12.032.
54. Maier HR, Lence BJ, Tolson BA, Foschi RO. First-order reliability method for estimating reliability, vulnerability, and resilience.Water Resour Res 2001;37(3): 779-90.