PSI - Issue 54

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

528

8

Fig. 2. Comparison of two switching processes of same second- and fourth-order moments but di ff erent NSM distribution and cycle counts

(a)

(b)

(c)

Loadspectrum RFC[ x sg 1 ( t )]

Loadspectrum RFC[ x sg 2 ( t )]

k=5

130 135 140 145 150 155 160 165

60

( DK ) eq

s

50

( RFC ) eq ( RFC ) eq

1 2

50

s

40

s

40

f m =140 Hz f m =160 Hz f m =180 Hz f m =200 Hz f m =220 Hz f m =240 Hz f m =260 Hz f m =280 Hz

f m =140 Hz f m =160 Hz f m =180 Hz f m =200 Hz f m =220 Hz f m =240 Hz f m =260 Hz f m =280 Hz

2 ]

2 ]

2 ]

30

30

s eq [ m/s

s [ m/s

s [ m/s

20

20

10

10

0

0

10 − 1

10 0

10 1

10 2

10 3

10 4

10 5

10 − 1

10 0

10 1

10 2

10 3

10 4

10 5

140 160 180 200 220 240 260 280 f m [Hz]

cumulated cycles [-] (log)

cumulated cycles [-] (log)

Fig. 3. Parametrization of the mid-frequency f m of the second band for the comparison of two switching processes with di ff erent NSM distributions

generate training data by defining synthetic quasi-stationary processes composed of a set of stationary Gaussian sub processes, alternatively denoted switching process. Quasi-stationary processes can be understood as a simplification of continuous time-dependent processes (Trapp and Wolfsteiner (2021b)). Central motivation is that these are fully characterized statistically and existing statistical ’frequency-domain’ damage-estimators can be used to estimate the damage for each subprocess, which is then accumulated for the resulting non-stationary process using the switching time dependency. This is possible as the basic accumulation rules are invariant to sequence e ff ects. Another essential advantage to this is the extrapolability for arbitrary duration. There would be a large gap between the stress series feasible to process via RFC in the training data generation (e.g. series representing a couple of hours) and stress series that would represent realistic in-service times (e.g. a couple of years). But as the statistical damage estimators use an alytical integration, this approach trades the error of the estimators model against the error that time series limitation would cause. For implementation, these switching processes are defined with R stationary Gaussian subprocesses, denoted { X 1 ( t ) , X 2 ( t ) , ..., X R ( t ) } . Each of these subprocesses is uniquely defined by a PSD G xx r ( f ) and a segment of duration to the assembled process X qs ( t ) with total duration of T = R r T r . The average PSD G xx , stat ( f ) and the NSM can be obtained as a weighted sum of the individual PSDs (outer product for discrete PSDs; Trapp and Wolfsteiner (2021a)):

1 T

3 T

R r

R r T r G xx r ( f 1 ) G xx r ( f 2 )

G xx , stat ( f ) =

T r G xx r ( f ) ;

M xx ( f 1 , f 2 ) =

(6)