Adaptive modeling of reliability properties for control and supervision purposes

Kai-Uwe Dettmann; Dirk Söffker

International Journal of Applied Mathematics and Computer Science (2011)

  • Volume: 21, Issue: 3, page 479-486
  • ISSN: 1641-876X

Abstract

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Modeling of reliability characteristics typically assumes that components and systems fail if a certain individual damage level is exceeded. Every (mechanical) system damage increases irreversibly due to employed loading and (mechanical) stress, respectively. The main issue of damage estimation is adequate determination of the actual state-of-damage. Several mathematical modeling approaches are known in the literature, focusing on the task of how loading effects damage progression (e.g., Wöhler, 1870) for wear processes. Those models are only valid for specific loading conditions, a priori assumptions, set points, etc. This contribution proposes a general model, covering adequately the deterioration of a set of comparable systems under comparable loading. The main goal of this contribution is to derive the loading-damage connection directly from observation without assuming any damage models at the outset. Moreover, the connection is not investigated in detail (e.g., to examine the changes in material, etc.) but only approximated with a probabilistic approach. The idea is subdivided into two phases: A problem-specific relation between loading applied (to a structure, which contributes to the stress) and failure is derived from simulation, where a probabilistic approach only assumes a distribution function. Subsequently, an adequate general model is set up to describe deterioration progression. The scheme will be shown through simulation-based results and can be used for estimation of the remaining useful life and predictive maintenance/control.

How to cite

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Kai-Uwe Dettmann, and Dirk Söffker. "Adaptive modeling of reliability properties for control and supervision purposes." International Journal of Applied Mathematics and Computer Science 21.3 (2011): 479-486. <http://eudml.org/doc/208062>.

@article{Kai2011,
abstract = {Modeling of reliability characteristics typically assumes that components and systems fail if a certain individual damage level is exceeded. Every (mechanical) system damage increases irreversibly due to employed loading and (mechanical) stress, respectively. The main issue of damage estimation is adequate determination of the actual state-of-damage. Several mathematical modeling approaches are known in the literature, focusing on the task of how loading effects damage progression (e.g., Wöhler, 1870) for wear processes. Those models are only valid for specific loading conditions, a priori assumptions, set points, etc. This contribution proposes a general model, covering adequately the deterioration of a set of comparable systems under comparable loading. The main goal of this contribution is to derive the loading-damage connection directly from observation without assuming any damage models at the outset. Moreover, the connection is not investigated in detail (e.g., to examine the changes in material, etc.) but only approximated with a probabilistic approach. The idea is subdivided into two phases: A problem-specific relation between loading applied (to a structure, which contributes to the stress) and failure is derived from simulation, where a probabilistic approach only assumes a distribution function. Subsequently, an adequate general model is set up to describe deterioration progression. The scheme will be shown through simulation-based results and can be used for estimation of the remaining useful life and predictive maintenance/control.},
author = {Kai-Uwe Dettmann, Dirk Söffker},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {reliability; parameter estimation; damage accumulation; probabilistic simulation},
language = {eng},
number = {3},
pages = {479-486},
title = {Adaptive modeling of reliability properties for control and supervision purposes},
url = {http://eudml.org/doc/208062},
volume = {21},
year = {2011},
}

TY - JOUR
AU - Kai-Uwe Dettmann
AU - Dirk Söffker
TI - Adaptive modeling of reliability properties for control and supervision purposes
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 3
SP - 479
EP - 486
AB - Modeling of reliability characteristics typically assumes that components and systems fail if a certain individual damage level is exceeded. Every (mechanical) system damage increases irreversibly due to employed loading and (mechanical) stress, respectively. The main issue of damage estimation is adequate determination of the actual state-of-damage. Several mathematical modeling approaches are known in the literature, focusing on the task of how loading effects damage progression (e.g., Wöhler, 1870) for wear processes. Those models are only valid for specific loading conditions, a priori assumptions, set points, etc. This contribution proposes a general model, covering adequately the deterioration of a set of comparable systems under comparable loading. The main goal of this contribution is to derive the loading-damage connection directly from observation without assuming any damage models at the outset. Moreover, the connection is not investigated in detail (e.g., to examine the changes in material, etc.) but only approximated with a probabilistic approach. The idea is subdivided into two phases: A problem-specific relation between loading applied (to a structure, which contributes to the stress) and failure is derived from simulation, where a probabilistic approach only assumes a distribution function. Subsequently, an adequate general model is set up to describe deterioration progression. The scheme will be shown through simulation-based results and can be used for estimation of the remaining useful life and predictive maintenance/control.
LA - eng
KW - reliability; parameter estimation; damage accumulation; probabilistic simulation
UR - http://eudml.org/doc/208062
ER -

References

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  13. Palmgren, A. (1924). Life time of ball bearing, VDI-Z 68(14): 339-341, (in German). 
  14. Söffker, D. and Rakowsky, U.K. (1997). Perspectives of monitoring and control of vibrating structures by combining new methods of fault detection with new approaches of reliability engineering, 12th ASME Conference on Reliability, Stress Analysis and Failure Prevention, Virginia Beach, VA, USA, pp. 671-682. 
  15. Troć, M. and Unold, O. (2010). Self-adaptation of parameters in a learning classifier system ensemble machine, International Journal of Applied Mathematics and Computer Science 20(1): 157-174, DOI: 10.2478/v10006-010-0012-8. Zbl1300.68047
  16. Wöhler, A. (1870). About experimental stress analysis with (low) carbon steel, Zeitschrift für Bauwesen 20: 73-106, (in German). 
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