Confidence intervals for the expected damage in random loadings: Application to measured time-history records from a Mountain-bike

Abstract

The fatigue damage of a structure is usually estimated by calculating the damage values of a limited number of measured random time-histories. The limited damage values are generally not identical due to the sampling variability. In a recent work, confidence interval expressions have been proposed to bound the expected damage value. The method revealed a good agreement with simulations, thus suggesting its use also with real measurements. The present paper investigates the above-mentioned confidence intervals for expected damage by a real engineering application, in which few measured time-history records, or even only one, are available. This goal is achieved after measuring the random loadings acting on an instrumented Mountain-bike riding in a typical north Italian off-road track. As the whole ensemble of an infinite number of time-histories is not available and the expected damage is thus not known a priori, a sort of calibrator sample damage value, which is computed using a large number of measured time-history records, is used to estimate the expected damage. The obtained results confirm the accuracy of the proposed approach also with real measurements.

Uncertainty of Estimated Rainflow Damage in Stationary Random Loadings and in Those Stationary per partes

“…When fully equ plus rider weighed about 77.2 kg. More details on the bicycle an found in [31]. Two types of circular off-road tracks were chosen for measurements.…”

“…Since each stationary state represents a portion of the whole record z(t), the total time length of z(t) sums the length of individual states as T = ∑ N S i=1 T S,i . In a similar way, the total damage of z(t) is the summation of the damage of individual loading states as [31]. The approximation sign in this equality is due to the fatigue cycles lost when separating the entire stress-time history z(t) into stationary segments and omitting the transitions cycles between them (an example is the range between the global maximum and global minimum if they do not occur within the same segment-typical for the ground-air-ground cycle in the aviation industry).…”

“…The stress-time histories measured on the mountain bike are aimed at verifying the correctness of confidence intervals. The mountain bike (see Figure 6) has a frame of 6061 aluminum alloy, and a front fork of steel [31]. Two Rigida Cyber 10 size 700C wheels are coupled with 700 × 37c S207 semi-slick tires.…”

“…When fully equipped, the mountain bike plus rider weighed about 77.2 kg. More details on the bicycle and on-board system can be found in [31].…”

The use of fractional order statistics for estimating nonparametric confidence intervals for quantiles of the fatigue damage computed in service random loadings

“…A filter was set up with cut-off frequency of 300 Hz, which was above the maximum frequency of interest. The data acquisition system was fixed at the inclined tube of the main "triangle" frame of the bicycle: the rechargeable supply battery was allocated behind the seat, on a welded support [21].…”