Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T09:23:52.148Z Has data issue: false hasContentIssue false
  • English
  • Français

Rainflow Cycles for Switching Processes with Markov Structure

Published online by Cambridge University Press:  27 July 2009

Pär Johannesson
Pär Johannesson
Affiliation:
Department of Mathematical Statistics, Lund Institute of Technology at Lund University, P.O. Box 118, S-221 00 Lund, Sweden
Get access Rights & Permissions [Opens in a new window]

Abstract

The concept of rainflow cycles is often used in fatigue of materials for analyzing load processes. Methods are developed for computation of the rainflow matrix for a random load that is changing properties over time due to changes of the system dynamics; for example, for a random vehicle load it could reflect different driving conditions. The random load is modeled by a switching process with Markov regime; that is, the random load changes properties according to a hidden (not observed) Markov chain.

An algorithm is developed for a switching process where each part of the load is modeled by a Markov chain. As only the local extremes are of importance for rainflow analysis, another approach is to model the sequence of turning points by a Markov chain. The main result of this paper is an algorithm for computation of the rainflow matrix for a switching process where each part is described by a Markov chain of turning points. The algorithms are illustrated by numerical examples.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 12 , Issue 2 , April 1998 , pp. 143 - 175
Copyright
Copyright © Cambridge University Press 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bishop, N.W.M. & Sherrat, F. (1990). A theoretical solution for the estimation of ‘rainflow’ ranges from power spectral density data. Fatigue & Fracture of Engineering Materials & Structures 13: 311–326.CrossRefGoogle Scholar
2.Collins, J.A. (1981). Failure of materials in mechanical design. New York: Wiley-Interscience.Google Scholar
3.Dowling, N.E. (1972). Fatigue predictions for complicated stress-strain histories. Journal of Materials 7: 71–87.Google Scholar
4.Elliot, R.J., Aggoun, L., & Moore, J.B. (1995). Hidden Markov models. Berlin: Springer-Verlag.Google Scholar
5.Frendahl, M. & Rychlik, I. (1993). Rainflow analysis: Markov method. International Journal of Fatigue 15: 265–272.CrossRefGoogle Scholar
6.Johannesson, P., Lindgren, G., & Rychlik, I. (1995). Rainflow modelling of random vehicle fatigue loads. ITM-report 1995: 5.Google Scholar
7.Krenk, S. & Gluver, H. (1990). Markov models and range counting in random fatigue. In Krätzig, et al. (eds.). Structural dynamics. Rotterdam: Balkema, pp. 683–690.Google Scholar
8.Lindgren, G. & Rychlik, I. (1987). Rain flow cycle distribution for fatigue life prediction under Gaussian load processes. Fatigue & Fracture of Engineering Materials & Structures 10: 251–260.CrossRefGoogle Scholar
9.Matsuishi, M. & Endo, T. (1968). Fatigue of metals subjected to varying stress. Paper presented to the Japan Society of Mechanical Engineers, Fukuoka, Japan, pp. 37–40.Google Scholar
10.Miner, M.A. (1945). Cumulative damage in fatigue. Journal of Applied Mechanics 12: A159–A164.CrossRefGoogle Scholar
11.Palmgren, A. (1924). Die Lebensdauer von Kugellagern. VDI-Zeitschrift 68: 339–341.Google Scholar
12.Rabiner, L.R. (1989). A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE 77: 257–284.CrossRefGoogle Scholar
13.Rychlik, I. (1987). A new definition of the rainflow cycle counting method. nternational Journal of Fatigue 9: 119–121.CrossRefGoogle Scholar
14.Rychlik, I. (1988). Rain-Flow-Cycle distribution for ergodic load processes. SIAM Journal of Applied Mathematics 48: 662–679.CrossRefGoogle Scholar
15.Rychlik, I. (1989). Simple approximations of the Rain-Flow-Cycle distribution for discretized random loads. Probabilistic Engineering Mechanics 4: 40–48.CrossRefGoogle Scholar
16.Rychlik, I. (1996). Extremes, rainflow cycles and damage furictionals in continuous random processes. Stochastic Processes and Their Applications 63: 97–116.CrossRefGoogle Scholar
17.Rychlik, I. (1996). Fatigue and stochastic loads. Scandinavian Journal of Statistics 23: 387–404.Google Scholar
18.Rychlik, I. (1996). Simulation of load sequences from rainflow matrices: Markov method. International Journal of Fatigue 18: 429–438.CrossRefGoogle Scholar
19.Rychlik, I. & Lindgren, G. (1995). WAVE Analysis Toolbox—A tutorial. Department of Mathematical Statistics, Lund University.Google Scholar
20.Scheutzow, M. (1994). A law of large numbers for upcrossing measures. Stochastic Processes and Their Applications 53: 285–305.CrossRefGoogle Scholar
21.Silverman, B.W. (1986). Density estimation for statistics and data analysis. London: Chapman and Hall.Google Scholar
22.Sobczyk, K. & Spencer, B.F. Jr, (1992). Random fatigue: From data to theory. New York: Academic Press.Google Scholar