Adaptive modeling of reliability properties for control and supervision purposes
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.
- Banjevic, D. (2009). Remaining useful life in theory and practice, Metrika 69(2-3): 337-349.
- Bebbington, M., Lai, C.-D. and Zitikis, R. (2007). A flexible weibull extension, Reliability Engineering & System Safety 92(6): 719-726.
- Castillo, E. and Fernández-Canteli, A. (2006). A parametric lifetime model for the prediction of high-cycle fatigue based on stress level and amplitude, Fatigue & Fracture of Engineering Materials & Structures 29(12): 1031-1038.
- Downing, S.D. and Socie, D.F. (1982). Simple rainflow counting algorithms, International Journal of Fatigue: Materials, Structures, Components 4(1): 31-40.
- Henry, D.L. (1955). A theory of fatigue-damage accumulation in steel, Transactions of the ASME 77(6): 913-917.
- Holmen, J.O. (1979). Fatigue of Concrete by Constant and Variable Amplitude Loading, University of Trondheim, Trondheim.
- Hwang, W. and Han, K.S. (1986). Cumulative damage models and multi-stress fatigue life prediction, Composite Materials 20(2): 125-153.
- Ławryńczuk, M. (2009). Efficient nonlinear predictive control based on structured neural models, International Journal of Applied Mathematics and Computer Science 19(2): 233-246, DOI: 10.2478/v10006-009-0019-1.
- Ławryńczuk, M. and Tatjewski, P. (2010). Nonlinear predictive control based on neural multi-models, International Journal of Applied Mathematics and Computer Science 20(1): 7-21, DOI: 10.2478/v10006-010-0001-y.
- Marco, S.M. and Starkey, W.L. (1954). A concept of fatigue damage, Transactions of the ASME 76(4): 626-662.
- Miner, M.A. (1945). Cumulative damage in fatigue, Applied Mechanics 12(3): 159-164.
- Nelles, O. (2001). Nonlinear System Identification, Springer, Berlin.
- Palmgren, A. (1924). Life time of ball bearing, VDI-Z 68(14): 339-341, (in German).
- 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.
- 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.
- Wöhler, A. (1870). About experimental stress analysis with (low) carbon steel, Zeitschrift für Bauwesen 20: 73-106, (in German).
- Wolters, K. (2008). Formalisms, Simulation, and Potentials of a Dependability Concept for Optimized System Utilization, Dr.-Ing. thesis, Engineering Faculty, University of Duisburg-Essen, Duisburg, (in German).