Damage-based data reduction methods

In fatigue analysis, data is frequently represented by means of uniaxial or multiaxial (that is, single channel or multiple channel) time series. A complete time series or time history such as obtained by a test vehicle on a test track contains much more information that is needed for rate independent fatigue calculations. For efficient calculation and storage of relevant data, it is useful to reduce time series of data to a more compact format.

Formally, time series are functions

Here [T1, T2] is the time interval of some measurement and L is the space of possible values of this measurement,such as forces, strains, and so on. Typically, we have measurements at discrete times; that is, the function f is represented by a series of values at times

ti = T1 + iΔt with i=1,…,N and ,

meaning that the load history is digitized at a constant time interval.

A data reduction method is a mapping acting on the set of time series and transforming it into the set of reduced data as shown in the figure below, for the case of rainflow counting:

Data Reduction Is a Non-Injective Mapping

The mapping is such that more than one time series can be mapped into the same rainflow matrix. For a given reduction method, two time series are called equivalent (f ≈ g), if they are mapped to the same reduced data element (such as the same rainflow matrix).

We will call a data reduction method a damage based data reduction method if all load histories that are mapped to the same reduced data element lead to the same damage.

In terms of fatigue analysis, different time series with equal rainflow matrices (and thus equal fatigue damage) can be considered equivalent time series.

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