PSI - Issue 54

Arvid Trapp et al. / Procedia Structural Integrity 54 (2024) 521–535

533

Arvid Trapp / Structural Integrity Procedia 00 (2023) 000–000

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methodology, combining the characterization of fourth-order, its processing for linear systems theory and the ANN model. From the figures it is evident that the ANN model predicts the damage significantly more accurate than the Dirlik method. This is regardless of the chosen procedure, but — as expected — the latter (Fig. 11) shows larger scatter. Our models prediction remain close to a ratio of one, meaning they align well with the RFC results, even with increasing kurtosis values. In contrast, the Dirlik method tends to underestimate the damage as kurtosis increases.

Fig. 10. Comparison of the equivalent response amplitude ratios derived from Dirlik method and ANN-model, each relative to RFC; data generated by the training procedure for di ff erent S-N curve exponents

Fig. 11. Comparison of the equivalent response amplitude ratios derived from Dirlik method and ANN-model, each relative to RFC; data generated by the test procedure for di ff erent S-N curve exponents

4.2. Real data

As an exemplary showcase, this section considers realistic non-stationary random vibration loading recorded during operation on the axle box of a train, with a kurtosis of β x ≈ 16. We compare this with stationary Gaussian loading of same PSD that has a kurtosis of β x ≈ 3. Both load series are illustrated in Figure 12(a),(d). In this simplified scenario, the loads are considered as single-channel acceleration and the responses as single-channel strain. The loads are used to estimate the NSM, while the response NSM are obtained through linear system theory, using the linear transfer function of a simple dynamic system depicted in Fig. 12(b). The series depicted in Fig. 12(c),(e) show the response series. In the context of a statistical fatigue assessment, these are obtained for the sole purpose of serving as reference, toobtain s ( RFC ) eq and for visualization. The structure has two relevant modes within f < 300 Hz. As shown in Fig. 12(c), the structural dynamic behavior increases the response kurtosis β y ≈ 46 subjected to the recorded loading. This leads to a significant underestimation of the pseudo-damage with the Dirlik method. However, the proposed ANN model predicts the pseudo-damage accurately within small margins of error. For the stationary Gaussian excitation, the Dirlik method is accurate. Considering the computational e ff ort, the referencing realization consisted of two million data points. These are processed via (i) Fourier transform, (ii) multiplication with interpolated transfer function, (iii) inverse Fourier trans form, (iv) rainflow counting (bottleneck), and (v) finally damage accumulation. In the proposed statistical approach