PSI - Issue 54

Arvid Trapp et al. / Procedia Structural Integrity 54 (2024) 521–535 Arvid Trapp / Structural Integrity Procedia 00 (2023) 000–000

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the load is characterized by 151x150 data points ( ≈ 1% of 2 million) — the quadratic and symmetric NSM and addi tionally the PSD in same resolution. Then it requires (i) multiplication with transfer function, (ii) Dirlik estimation, and finally (iii) calculation of spectral moments from NSM, which serve as input to the ANN. Exact processing times depend on the chosen parameters, but in generally the statistical approach is several orders faster.

Fig. 12. Depictions of stationary Gaussian (a) and non-stationary (d) excitation realizations, structural transfer function (b), and response signals (c),(e), illustrating the capabilities of the Dirlik and ANN-model in comparison.

5. Conclusion

In this study, we delve into fatigue damage under non-stationary random vibration loading. We compared the statistical approach for assessing fatigue with the classic sampling-based ’non-statistical’ assessment that requires extensive amounts of data. This research is motivated by the severe under prediction of conventional statistical dam age estimators under non-stationary loading conditions. To address this, we propose to extend the loadings statistical characterization using a frequency-domain representation of kurtosis, specifically through the non-stationarity matrix (NSM). This allows the statistical evaluation of non-stationary loading for linear systems. The resulting structural stress responses serve as input for an artificial neural network to predict the discrepancies in fatigue damage aris ing from non-stationarity, benchmarking against the computational e ffi cient Dirlik method. As inverse operation this model is able to reliably predict fatigue damage for non-stationary random vibration loading. These results are very promising. As such, this demonstrates how modern machine learning (ML) can address complex problems with a data-driven approach. The main contributions of our paper include using structural dynamics for non-stationary random loading charac terized by PSD and NSM (’from variance to kurtosis’), introducing NSM-based spectral moments serving as input to an ML model, its e ffi cient training by the ’train-on-Dirlik’ approach, and finally the ML models optimization and val idation. The results are promising and help address the current gap in statistical fatigue assessments for non-stationary random vibration loading. For a practical application in fatigue calculations, certainly key factors are the data gener ation and the choice of adequate parameters, such as the discretization of the frequency axis. Further, the presented research may be a starting point towards multivariate loading and the statistical consideration of multiaxial stress states. Additionally, for more accurate fatigue assessments, it needs to expand the approach to load spectrum estima-