RAINFLOW CYCLES, MARKOV CHAINS AND ELECTRICAL CIRCUITS

          Igor Rychlik, Matematisk Statistik i Lund


Rainflow cycles are often used to describe variability of loads
and stresses relevant for fatigue of metals. To each cycle
there is attributed a damage, and the total fatigue damage due
to a load is the sum of individual damages caused by rainflow
cycles. For random loads computation of expected damage
intensity is difficult. However, conservative bounds for the
damage intensity can be derived from the upcrossing intensity.
In the special case of Markov loads the explicit formulas for
the oscillation intensities, which is a one to one function of
a rainflow matrix, are known. Here the formulas are derived
using the equivalence between currents flowing in suitable
electrical circuits and the oscillation intensity. An inverse
problem, that is obtaining a time serie for fatigue testing,
from a measured rainflow matrix is also adressed.