###### Abstract  
The uncertainty of rainflow fatigue damage is evaluated for stationary loadings and for non-stationary switching loadings with a finite number of stationary states. The approach is based on confidence intervals constructed after direct analysis of stress-time histories. The accuracy of confidence intervals is verified first by numerical simulations, and then by experimental data measured in a mountain bike traveling under various driving and road surface conditions, yielding stationary and non-stationary switching loadings. Stationarity and non-stationarity of loading records is checked by a statistical method (run test). In experiments, a small set of records (validation set) is also collected and used to approximate the expected damage, which serves for verification purposes. Not only do numerical and experimental results confirm the correctness of the proposed confidence interval for damage, but they also emphasize its usefulness in real engineering applications. uncertainty; rainflow damage; stationary loading; non-stationary loading; confidence interval; statistical run test; mountain bike +
Footnote †: journal: Medical Engineering  
be determined from several statistical properties of the random record, or from its power spectral density function. These approaches are restricted to certain load models (linear oscillator) [6; 7; 8; 9] or to loadings with specific types of power spectral density (narrowband [10; 11], multimodal [12] or wide band [13]). Extension to non-Gaussian loadings has also been proposed recently [14]. Interesting is the method presented in [15] in which the CoV of damage is estimated from only one sample record. The uncertainty in fatigue damage--and its correlation with various sources of randomness--has been investigated, in more recent articles, in a probabilistic and/or reliability framework based on different modeling strategies (e.g., machine learning algorithm [16], surrogate model [17]) and methods (e.g., piecewise stochastic rainflow counting [18], Bootstrap error circle [19]), with applications and case studies spanning various engineering fields (e.g., maritime [20; 21], structural [22], automotive [23; 24]). Differently from the previous methods, an approach--also devised in [13]--used confidence intervals to evaluate the uncertainty of rainflow damage, and specifically to enclose the expected damage when only few stationary stress-times histories, or only one, are available. Although in [13] the approach was positively benchmarked against numerical simulation results, it is only applicable to stationary loadings with time-invariant statistical properties. This characteristic may not fully represent the actual loading conditions in certain structural details, in which random loadings have statistical properties that change over time and, therefore, are non-stationary. Among the broader class of non-stationary loadings, in many engineering applications, the non-stationary loadings are formed by a sequence of stationary states--they are called switching loadings. Examples could be offshore structures and ships exposed to a sequence of stationary sea states; airplanes during the sequence of taxing, taking off, cruising, maneuvering and landing; wind turbines under wind loadings caused by weather conditions; and cars and bikes subjected to different road surfaces and velocities. Evaluating the uncertainty of rainflow damage for such types of switching loadings has therefore a great practical relevance. Starting from this premise, this paper aims to extend the confidence interval of damage for stationary loadings to the case of non-stationary loadings of the switching type. The obtained solution is benchmarked against numerically simulated and measured non-stationary loadings, the latter being recorded in a mountain bike traveling in different riding conditions and over various tracks.