Statistical Modeling of Rainflow Histograms
by
Jason Scott Roth
Abstract
The ability to quantify usage in durability is an important idea, because despite the effectiveness of any fatigue model, if the loads are not representative of the real in-service loadings, that model will inevitably produce results that are uncharacteristic of the actual expected life. The modeling of variable amplitude loading histories is a difficult proposition because the magnitudes of the loadings are random in nature, but when those load histories are placed into a rainflow counted histogram, the data in those histograms forms a pattern which can be statistically modeled.
The models presented involve the use of non parametric density estimation, and in particular the kernel method, to quantify the underlying density in the histograms. Then Monte Carlo simulations are conducted to predict the future results of two different problems. The first problem is given a loading history, model the loadings that could be anticipated if that durability test were to be conducted over longer periods of time. The other problem is given a set of loading histories, from that set, model the loadings that could be expected from the more extreme usages in a similar but much larger set of loading histories. The theory of these models, as well as procedural instructions for implementing the models, and some of the results of these models are presented.
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