Authors:
Théophile Tshibangu
1
;
Guyh Ngoma
1
;
Martin Gagnon
2
and
Sébastien Carle
3
Affiliations:
1
School of Engineering, University of Quebec in Abitibi-Témiscamingue, 445 Boulevard de l’Université, Rouyn-Noranda, J9X 5E4, Canada
;
2
Hydro-Québec’s Research Institute, 1800, boulevard Lionel-Boulet, Varennes, Quebec, J3X 1S1, Canada
;
3
Hydro-Québec, 1095 Rue Saguenay, Rouyn-Noranda, Quebec, J9X 5B5, Canada
Keyword(s):
Gamma Frailty Model, Reliability, Cracks, Hydraulic Turbine, Censored Historical Data.
Abstract:
All over the world, the need for electrical energy has increased dramatically, forcing hydroelectric power plants to operate under non-standard conditions. This leads to premature fatigue cracking and consequently to multiples crack inspections. In this research, a probabilistic model is developed based on frailty and censoring. The model takes advantage of the use of a Non-Homogeneous Poisson Process (NHPP) because turbine runners are considered as repairable parts. We develop the marginal likelihood expression incorporating frailty effect using gamma frailty distribution and we use the stochastic gradient descent (SGD) algorithm to obtain the optimal parameters. Furthermore, instead of considering the frailty effect z as a random variable, we decide to derive its expression from the individual unconditional likelihood function that has been also optimized. Finally, we compare reliability and cumulative hazard functions between family members. We then confirm the results obtained by
comparing reliability between two families that behaved differently. Results shows that frailty effect, that is fonction of failure statuses and individual final time of observation for a specific component has played an impor tant role in differentiating heterogeneity among groups of the same family. Reliability curves clearly demonstrate heterogeneity within and between families.
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