Fatigue dynamic reliability and global sensitivity analysis of double random vibration system based on Kriging model

Figures & data

Figure 1. The flowchart of the ALK method.

Figure 2. The dynamic reliabilities with different sample numbers calculated by MCS method.

Figure 3. The maximum ERF values at the training points by ALK method in iteration history ($\nu =0.2$).

Figure 4. The true values of training points by ALK method in iteration history ($\nu =0.2$).

Table 1. The dynamic reliabilities of the bar under two conditions.

	MCS	ALK	Error
$R_t\left(\nu =0.1\right)$	0.9878^(10000)	0.9795^(28)	0.84%
$R_t\left(\nu =0.2\right)$	0.9494^(10000)	0.9458^(35)	0.38%

Note: The numbers in brackets indicate the times of performance function evaluation

Figure 5. The GSA indices of variables of bar by MCS and ALK methods.

Figure 6. The dynamic reliabilities with different coefficients of variation.

Figure 7. The schematic diagram of 16-bar structure.

Table 2. The dynamic reliabilities of 16-bar structure with different $t$_.

	MCS	ALK	Error
$R_t\left(t=900\right)$	0.9410^(10000)	0.9444^(35)	0.36%
$R_t\left(t=1000\right)$	0.9353^(10000)	0.9393^(37)	0.43%

Note: The numbers in brackets indicate the times of performance function evaluation

Figure 8. The GSA indices of variables of 16-bar structure by MCS and ALK methods.

Figure 9. The schematic diagram of air pipe with random variation excitations.

Table 3. The input random variables of air pipe.

Input variables(unit)	Distribution type	Mean	Coefficient of variation
${\rho }_p\left(Kg/\phantom{Kg{m}^3}\right)$	Normal	7800	0.01
$E\left(GPa\right)$	Normal	184	0.01
$L\left(m\right)$	Normal	0.21	0.01
$H\left(m\right)$	Normal	0.042	0.01

Figure 10. The acceleration spectrum of PSD.

Figure 11. The GSA indices of variables of air pipe by MCS and ALK methods.

Table 4. The dynamic reliabilities and GSA indices of air pipe.

	$R_f$	${\delta }_{{\rho }_p}$	${\delta }_E$	${\delta }_L$	${\delta }_H$	Times of function evaluation
MCS	0.9692	0.0548	0.703	0.0031	0.0128	40000
ALK	0.9682	0.0511	0.769	0.0032	0.0120	67
Error	0.10%	6.81%	9.41%	5.47%	7.08%