Sensitivity Analysis Based on Polynomial Chaos Expansions and Its Application in Ship Uncertainty-Based Design Optimization

Table 3

Sensitivity indices of simplified model of Sobol’ function with 4 variables under different expansion orders.

Sensitivity indices	Analytical solution	Expansion order
		value	error	value	error	value	error
			0.6037	0.6334	4.9%	0.6144	1.8%	0.6085	0.8%
	0.2683	0.2778	3.5%	0.2680	0.1%	0.2683	0
	0.0671	0.0685	2.1%	0.0657	2.1%	0.0666	0.7%
	0.0200	0.0203	1.5%	0.0194	3.0%	0.0198	1.0%
	0.6342	0.6334	1.3%	0.6434	1.5%	0.6412	1.0%
	0.2945	0.2778	5.7%	0.2931	0.5%	0.2967	0.7%
	0.0756	0.0685	9.4%	0.0739	2.2%	0.0756	0
	0.0227	0.0203	10.6%	0.0221	2.6%	0.0225	0.9%
Unknown coefficients		35		126		330