PSI - Issue 38

Arvid Trapp et al. / Procedia Structural Integrity 38 (2022) 260–270

267

8

A. Trapp / Structural Integrity Procedia 00 (2021) 1–11

(a) for ν ∗ p and k = { 1 , 5 }

(b) for ν ∗

0 and k

= { 1 , 5 }

Fig. 5: Conformity of pseudo damage for ν ∗ 0 and ν ∗ p considering synthetic PSDs

3.4. Analysis of realistic PSDs

So far only series representing synthetic PSDs are analyzed. This section continues the investigation for realistic PSDs. Therefore, PSDs are estimated from recorded random vibration and analyzed following the approach from the former section using the CPD. To generate a large set of PSDs, a collection of recordings from the axle box of a train’s wheel set are chosen. These are highly non-stationary and therefore o ff er a large variety of di ff erent PSDs when evaluated by the short-time Fourier transform. Thus, for each second of recording a PSD was estimated. These are used to generate (description in [18]) stationary Gaussian realizations. Each realization was then analyzed as a referencing and as an up-sampled series with ζ = 20 to calculate the CPD (Eq. 12). A set of them is visualized in Fig. 6 for ν ∗ p and ν ∗ 0 .

(a) for ν ∗ p and k = { 1 , 5 , 9 }

(b) for ν ∗

0 and k

= { 1 , 5 , 9 }

Fig. 6: Conformity of pseudo damage for ν ∗ 0 and ν ∗ p considering realistic PSDs

The results are once again noteworthy. Fig. 6(b) shows that ν ∗ p seems to be an adequate descriptor for the CPD with k = 1, likewise to the prior section (Fig. 5). On the other hand, larger Miner exponents lead to a wide spread for the CPD via ν ∗ p . Using ν ∗ 0 (Fig. 6a) generates opposing results. For larger Miner exponents, e.g. k = 5 and k = 9, the CPD shows relatively narrow spread across the di ff erent PSDs, while the Miner exponent k = 1 produces wide spread. This visual appearance suggests that each parameter seems to have its sweet spots. As a consequence the next section considers a three dimensional representation for the CPD for ν ∗ 0 and ν ∗ p (Fig. 7a).