Bayesian-Informed Fatigue Life Prediction for Shallow Shell Structures

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Model errors of the Co-Kriging predictions for Keff and N, compared to the test dataset_

Model	RRSE (%)	MAPE (%)	MAE	RMSE	R2
Keff	4.613	0.621	0.0511MPam0.0511{\rm{MPa}}\sqrt m	0.065MPam0.065{\rm{MPa}}\sqrt m	0.998
N	12.376	78.035	6.887×104 cycles	1.112×105 cycles	0.985

Convergence results of the inferred mean and standard deviation from Bayesian inference, along with the associated computational cost in terms of CPU time_

					CPU time
Model	θμ	error (%)	θσ	error (%)	Bayesian (s)	MCS (hrs)
True EIFSD	8.470	×	0.424	×	×
ntrial = 30	8.552	0.968	0.503	18.9	7.88	1.15
ntrial = 60	8.440	0.354	0.406	4.02	79.46	4.59
Adaptive (27 steps)	8.465	0.059	0.401	5.20	75.12	2.21

Details of the shell structure parameters and the random variables used in the EIFS inference_

Parameter	Description	Distribution	Mean	COV
W2	Inner width	Lognormal	0.468 m	0.01
L2	Inner length	Lognormal	0.273 m	0.01
R2	Inner radius	Lognormal	0.127 m	0.01
h	Thickness	Lognormal	0.01 m	0.01
RK	Radius of curvature	Lognormal	2.73 m	0.01
α	Crack initiation angle	Lognormal	29.24°	0.05
P	Domain pressure	Lognormal	7.1 Psi	0.04
C	Paris law constant	Lognormal	1.60×10(−11)(m/cycle)(MPam)m1.60 \times {10^{( - 11)}}{{({\rm{m}}/{\rm{ cycle }})} \over {{{\left( {{\rm{MPa}}\sqrt m } \right)}^m}}}	0.1
m	Paris law exponent	Lognormal	3.59	0