The adjoint method coupled with the modal identification method for nonlinear model reduction

Figures & data

Figure 1. Test case configuration.

Figure 2. Heat flux density U(t) used for RM identification.

Figure 3. The DM's temperature responses at the three points when the input signal shown in figure 2 for the RM identification is applied. These temperature points along with the corresponding signal are used as data for the RM identification.

Table 1. The RM identification results. Comparison between the FDM and the AM for the computation of ∇j(u).

	(K)		Number of iterations		Computing time (s CPU)		Average time per iteration (s CPU)
Reduced model order n	FDM	AM	FDM	AM	FDM	AM	FDM	AM
1	1.396	1.396	12	10	7	34	0.6	3.4
2	0.187	0.187	73	76	134	368	1.8	4.8
3	1.92 × 10^−2	1.96 × 10^−2	343	207	1646	967	4.8	4.7
4	9.29 × 10^−3	1.02 × 10^−2	277	111	9263	849	33.4	7.6
5	8.98 × 10^−3	1.01 × 10^−2	4	1	364	17	91	17

Figure 4. Test heat flux density U(t) used for RM validation.

Figure 5. The DM's temperature responses at Points No. 1, 2 and 3 when the test input signal U(t) is applied.

Figure 6. Discrepancies between DM's and RM's (FDM) responses when test function is applied.

Figure 7. Discrepancies between DM's and RM's (AM) responses when test function is applied.