## 6 Verification by Loadings Measured in a Mountain Bike  
### Methods and Data Acquisition  
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 \(\times\) 37c S207 semi-slick tires. The bicycle was equipped with an on-board data acquisition system capable to measure and store the strain-time histories during the bike ride. The on-board system is formed by a data acquisition system (mounted on the inclined tube of the bicycle frame), rechargeable battery (allocated on a support behind the seat), speedometer (with a sensor and a magnet fixed on a spoke) and two half-bridge strain gages (glued onto the fork). The strain gages, placed symmetrically around the left fork tube, are aligned in the longitudinal plane so as to measure the axial strains corresponding to the bending moment in the fork. The sampling frequency was 1000 Hz. After data acquisition, measured strain signals were converted into stress signals as \(x(t)=E\epsilon(t)\), where \(E\) is the elastic modulus of steel. 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]. Figure 6: Instrumented mountain bike used in experiments, with strain gages, data acquisition system, battery and speedometer. Two types of circular off-road tracks were chosen for measurements. The tracks were plane (or almost plane) and made of different road surfaces. Track types and riding conditions were selected so that the measured records were (i) stationary or (ii) non-stationary of switching type. In the stationary case, the mountain bike moved at the approximately constant speed of 15 km/h over the same road made of gravel, see Figure 7a. In the non-stationary case, the bike moved over surfaces of different characteristics such as asphalt, gravel and grass, see Figure 7b, and with a speed varying from 10 to 20 km/h. In both stationary and non-stationary cases, the mountain bike was ridden by a rider of 65 kg, who remained seated for the entire duration of each measurement. It has to be emphasized that the choice of these riding conditions--which are in fact not typical of a mountain bike in off-road use--was primarily dictated by the need to obtain stress-time histories that were stationary or non-stationary of switching type, which are the requirements for applying the confidence intervals. For the same reason, the measured records are not used here for evaluating the structural safety of the bicycle. All measurements, carried out over fourteen consecutive days, gathered an amount of 41 stationary and 21 non-stationary load records, grouped as follows:  
* 10 stationary records used as input for Case M in Section 3.1. * 1 stationary record used as input for Case S in Section 3.2. * 30 stationary records to form the validation set for the stationary case. * 1 non-stationary switching record to be analyzed as in Section 4.2. * 20 non-stationary switching records for the validation set of the non-stationary case. All measured records are available in the section \"Supplementary Materials\". The two validation sets were used to compute a sample mean damage (validation damage) with which to approximate the expected damage as \(E[D(T)]\cong\overline{D}_{\mathit{val}}(T)\). Indeed, \(E[D(T)]\) cannot be measured exactly as it refers to an infinite collection of load records. It is not superfluous to emphasize that the validation damage \(\overline{D}_{\mathit{val}}(T)\) is only used here for verification purposes, that is, to verify whether the confidence intervals enclose the expected damage. The validation sets are not required in real practical situations. Once measured, all stress-time histories (stationary and non-stationary) were scaled so that all data points from 0 to \(T\) had a zero mean and unit variance.