Markov based correlations of damage cycles in Gaussian and nonGaussian loads
(1995) In Probabilistic Engineering Mechanics 10(2). p.103115 Abstract
 The sequence of peaks and troughs in a load process acting on a material, contains important information about the damage caused by the load, e.g. on the growth rate of a widening crack. The stress range, i.e. the difference between a peak and the following trough, is one of the variables that is used to describe e.g. fatigue life under random loading. The moments, in particular the mean and variance, of the load range are important variables that determine the total damage caused by a sequence of stress cycles, and they give the parameters in the distribution of the time to fatigue failure. However, for many random load processes, the successive stress ranges can show considerable correlation, which affects the failure time distribution.... (More)
 The sequence of peaks and troughs in a load process acting on a material, contains important information about the damage caused by the load, e.g. on the growth rate of a widening crack. The stress range, i.e. the difference between a peak and the following trough, is one of the variables that is used to describe e.g. fatigue life under random loading. The moments, in particular the mean and variance, of the load range are important variables that determine the total damage caused by a sequence of stress cycles, and they give the parameters in the distribution of the time to fatigue failure. However, for many random load processes, the successive stress ranges can show considerable correlation, which affects the failure time distribution. In this paper we derive the modified failure time distribution under correlated stress ranges, under a realistic approximation that the sequence of peaks and troughs forms a Markov chain. We use the regression method to calculate the transition probabilities of the Markov chain for Gaussian load processes with known spectral density. Simulations of Gaussian processes with PiersonMoscowitz spectrum, and linear and the Duffing oscillators driven by Gaussian white noise, show very good agreement between observed correlations and those calculated from the Markov approximation. Also the numerically calculated transition probabilities lead to good agreement with simulation. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1210443
 author
 Rychlik, Igor ^{LU} ; Lindgren, Georg ^{LU} and Lin, Y.K.
 organization
 publishing date
 1995
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 REGRESSION APPROXIMATIONS
 in
 Probabilistic Engineering Mechanics
 volume
 10
 issue
 2
 pages
 103  115
 publisher
 Elsevier
 external identifiers

 scopus:0029232237
 ISSN
 02668920
 DOI
 10.1016/02668920(95)00001F
 language
 English
 LU publication?
 yes
 id
 2d80f5c553074142b6585995b5e1392b (old id 1210443)
 alternative location
 http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V4M3XY2J0YC1&_cdi=5762&_user=745831&_orig=search&_coverDate=12%2F31%2F1995&_sk=999899997&view=c&wchp=dGLzVzzzSkzS&md5=c04860cd08b6876fcd29cb8d89aebfe6&ie=/sdarticle.pdf
 date added to LUP
 20080916 15:52:18
 date last changed
 20180529 10:20:40
@article{2d80f5c553074142b6585995b5e1392b, abstract = {The sequence of peaks and troughs in a load process acting on a material, contains important information about the damage caused by the load, e.g. on the growth rate of a widening crack. The stress range, i.e. the difference between a peak and the following trough, is one of the variables that is used to describe e.g. fatigue life under random loading. The moments, in particular the mean and variance, of the load range are important variables that determine the total damage caused by a sequence of stress cycles, and they give the parameters in the distribution of the time to fatigue failure. However, for many random load processes, the successive stress ranges can show considerable correlation, which affects the failure time distribution. In this paper we derive the modified failure time distribution under correlated stress ranges, under a realistic approximation that the sequence of peaks and troughs forms a Markov chain. We use the regression method to calculate the transition probabilities of the Markov chain for Gaussian load processes with known spectral density. Simulations of Gaussian processes with PiersonMoscowitz spectrum, and linear and the Duffing oscillators driven by Gaussian white noise, show very good agreement between observed correlations and those calculated from the Markov approximation. Also the numerically calculated transition probabilities lead to good agreement with simulation.}, author = {Rychlik, Igor and Lindgren, Georg and Lin, Y.K.}, issn = {02668920}, keyword = {REGRESSION APPROXIMATIONS}, language = {eng}, number = {2}, pages = {103115}, publisher = {Elsevier}, series = {Probabilistic Engineering Mechanics}, title = {Markov based correlations of damage cycles in Gaussian and nonGaussian loads}, url = {http://dx.doi.org/10.1016/02668920(95)00001F}, volume = {10}, year = {1995}, }