Application of Stochastic Sensitivity Analysis to Integrated Force Method

Table 1

Comparison of stochastic sensitivities between PM and MCS.

Response sensitivities		Methods
		Perturbation Method			DMCS
		μ ^I	μ ^II	𝜎𝑝	μ	𝜎𝑀
𝐹1 (N/m^2)	A1	−683.95	−691.34	100.42	−690.74	104.30
	A2	−3868.99	−3891.04	429.72	−3892.00	440.63
	A3	−57.00	−55.55	48.46	−55.47	49.28
	A4	−322.42	−312.47	271.84	−312.07	275.60
	A5	−57.00	−55.48	48.44	−55.42	49.09
𝑥1(m/m^2)	A1	0.0781	0.0798	0.0136	0.0798	0.0144
	A2	−0.0442	−0.0451	0.00755	−0.0451	0.00798
	A3	−0.00065	−0.00061	0.000516	−0.00060	0.000541
	A4	−0.00368	−0.00341	0.00288	−0.00339	0.00300
	A5	−0.00065	−0.00061	0.000515	−0.00060	0.000537

Note. μ ^I, μ ^II are the mean value of the first- and second-order approximation of responses, respectively. 𝜎_𝑝 is the standard deviation of the perturbation method of responses.μ is the mean value of direct Monte Carlo simulation of responses. 𝜎_𝑀 is the standard deviation of direct Monte Carlo simulation of responses.