PSI - Issue 38

164 6

L. Heindel et al. / Procedia Structural Integrity 38 (2022) 159–167 L. Heindel et al. / Structural Integrity Procedia 00 (2021) 000–000

Fig. 3: The static characteristics of the test setup are obtained by controlling each axis in isolation and measuring the responses.

di ff ering composition between training and validation data was chosen because the handcrafted serviceloads would otherwise introduce a bias into the training dataset. Although the di ff erent service loads do not represent the real appli cation case, they are still used for evaluation purposes to ensure that the trained models produce accurate predictions for realistic load time signals. The total scope of the dataset contains 1 h and 53 min of noise data, as well as 3 h and 9 min of fatigue serviceloads, sampled with a frequency of 1 kHz. The measurement data was then low pass FFT-filtered at 80 Hz to cover only the controllable frequency spectrum of the setup. The entire measurement process was repeated once to ensure constant system behavior over all data samples.

3.2. Error metrics

Depending on the application, di ff erent error metrics have to be taken into consideration to judge the performance of a prediction. In this paper, two commonly error metrics are analyzed, which are commonly used in fatigue analysis. The Root Mean Square (RMS) error RMS y ∗ , y = 1 N N i = 1 y ( t i ) − y ∗ ( t i ) 2 N i = 1 y ( t i ) 2 (8) assesses the average di ff erence between the true and predicted signal channels, denoted by y and y ∗ . In order to judge whether the fatigue damage content of y is preserved in its prediction y ∗ , the RMS error is insu ffi cient, since it weights the prediction error equally for small and large signal amplitudes. For this reason, fictional fatigue damage contents d ( y ) and d ( y ∗ ) are computed for both true and predicted responses. Using the nominal stress concept outlined in Haibach (2002), this process involves a fictitious Wo¨hler curve, the 4-point Rainflow counting algorithm described in McInnes and Meehan (2008) as well as the elementary Palmgren-Miner rule proposed by Palmgren (1924). The experimental setup introduced in subsection 3.1 results in multiaxial stress states, which have to be considered in the fatigue assessment. Following Beste et al. (1992), this is achieved through the Multi-Rain fatigue damage d ψ ( s ) = d ( ψ x s x + ψ y s y + ψ z s z ) | ψ 2 x + ψ 2 y + ψ 2 z = 1 , (9)