Inverse problem of aircraft structural parameter estimation: application of neural networks

Figures & data

Figure 1. Cantilevered beam model of a real aircraft wing.

Figure 2. FEM/eigenvalue approach using one ANN.

Figure 3. FEM/eigenvalue approach using two ANNs.

Figure 4. Hooke's law/eigenvalue approach using two ANNs.

Figure 5. Evolution of network training/testing error for bending stiffness estimation.

Figure 6. Network post-testing regression analysis for bending stiffness estimation.

Table 1. Natural frequencies of the beam model

Mode	Frequency (Hz)
1	16.41
2	79.62
3	201.87
4	388.89

Table 2. Loading and deformation characteristics

Location (m)	Force (N)	Moment (Nm)	Deflection (mm)	Slope (rad)
0	640	−1170	0	0
1.25	540	390	2.2	0.0039
2.5	−1070	740	11.6	0.0119
3.75	−1610	440	33.4	0.0232
5	1500	120	67.6	0.0296

Table 3. Bending stiffness estimation results

Target (Nm^2)	Estimate (Nm^2)	Error (%)
500,000	500,760	−0.15
360,000	360,540	−0.15
260,000	261,360	−0.52
210,000	209,180	0.39

Table 4. Mass estimation results

Target (kg)	Estimate (kg)	Error (%)
84.2	89.58	−6.39
63.9	65.27	−2.14
49.80	48.25	3.12
32.3	29.99	7.16

Table 5. Accuracy of ANN at estimating beam structural properties

Target (Hz)	Estimate (Hz)	Error (%)
16.4058	15.5049	5.49
79.6216	73.6173	7.54
201.8719	192.6780	4.55
388.8942	375.2358	3.51