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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Fig. 4. Spectral weighting functions for n = 1 , 2 of introduced NSM-based spectral moments Λ Θ , n and Λ I , n

calculate 4th order spectral moments Λ 0 , Λ I , 1 , Λ I , 2 , Λ Θ , 1 , Λ Θ , 2

timeseries x(t)

ˆ s ( ratio ) eq

M yy ( f 1 , f 2 )

M xx ( f 1 , f 2 )

ANN

H xy ( f )

equivalent stress amplitude s ( NN ) eq = s ( DK ) eq ˆ s ( ratio ) eq

( DK ) eq

G yy ( f )

G xx ( f )

s

Dirlik

Fig. 5. Procedure for prediction of equivalent stress amplitude s ( NN ) eq

by the ANN-model

This substitutes the computational e ff ort for estimating NSM, which would likely be at least as expensive as rainflow counting, depending on the chosen parameters. Following this approach to create a large data base, we generate the sub-PSDs that define the quasi-stationary process randomly. To accomplish this with only few parameters, while preserving physical feasibility, we chose to base the PSDs on the response of simple vibratory systems for obtaining realistic PSDs. The underlying model is based on a modal superposition of single-degree-of-freedom (SDOF) systems with damped natural frequencies f D and damping ratio ζ . The excitation for these systems is broadband noise. The procedure is visualized in Fig. 7. The random data generation process initiates with randomly drawing the number R of sub processes, i.e. PSDs, that characterize the quasi-stationary process. In a first step, the PSDs are generated as band-limited broadband noise for f = [5 , 300] Hz with a random level of σ r = [10 − 4 , 10 6 ]. Then, for each PSD, a number of modes is randomly selected within N modes = 1 , ..., 5, which triggers the respective drawing of the resonance frequencies for f D r = [5 , 300] Hz and damping coe ffi cients ranging from ζ r = [0 . 01 , 0 . 05]. These coe ffi cients fully define the complex-valued transfer functions H xy r ( ω ) = − 1 / ( − ω 2 + 2 ζω 0 i ω + ω 2 0 ) with ω = 2 π f