PSI - Issue 54

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

522

2

NSM PDF PSD RFC

non stationarity matrix

probability density function

power spectral density

rainflow counting bias of neurons

b

kurtosis of x

β x

C

material constant

D D

damage rate total damage

G xx ( f ) H xy ( f )

single-sided PSD of x

frequency response function number of stress amplitudes

J

k

S-N curve exponent

n th -order spectral moment of PSD

λ n

th -order spectral moment

Λ I , n ; Λ Θ , n M xx ( f 1 , f 2 )

NSM-based n

non-stationarity matrix (NSM) of x n th -order statistical central moment

µ n

n

order / cycle counts

upward zero crossing rate

ν + 0 ν p

peak rate

p ( x ) Φ [ · ]

probability density function activation function of neurons

R

subprocesses of a quasi-stationary process

s

stress amplitude

s eq

damage equivalent amplitude / pseudo damage

S xxxx ( f 1 , f 2 , f 3 ) fourth-order trispectrum of x ˆ s ( ratio ) eq

ratioof s eq between DK and RFC

σ 2

variance

T w

duration of a realization / process weighting factor of neurons

x ( t ) y ( t )

input / load realization

output / response realization

dampening ratio

ζ

1. Introduction

Fatigue refers to the continuous degradation of materials due to cyclic loading. Consequently, fatigue assessments are conducted to prevent structural failures due to fatigue, depicted schematically in Fig. 1. Common to a sampling based ’time-domain’ and a statistical-based ’frequency-domain’ approach is structural dynamics, as fatigue is deci sively driven by structural resonances. A sampling-based approach (Fig. 1 (a) ) involves the use of counting algorithms to generate load spectra from structural responses y ( t ), more specifically stress states. Load spectra are then com pared with stress-life (S-N) curves to estimate the structural lifetime. Analogously, statistical approaches to a fatigue assessment employ damage- and load spectrum estimators such as Dirlik (Fig. 1 (b) ), founded on the power spectral density (PSD) (Dirlik (1985); Benasciutti (2004)). Both approaches are often termed time-domain (sampling-based) and frequency-domain approach (statistical-based). Compared to the sampling-based ’non-statistical’ approach, which typically involves rainflow cycle-counting, a statistical fatigue assessment o ff ers several advantages. These include the e ff ective representation of random processes in the frequency domain, the extrapolation of load spectra to realistic in service times, statistical variability in experimental testing while reproducibility in numerical simulations, extreme value statistics, and, most notably, the computational advantages, which become crucial when evaluating entire finite-