Inverse problem of aircraft structural parameter identification: application of genetic algorithms compared with artificial neural networks

Figures & data

Figure 1. Pilatus PC-9/A aircraft.

Figure 2. Idealised wing models.

Figure 3. Approach 1 flow chart.

Table 1. Approach 1 – normalised frequencies

		Finite element model
Value	Measured data	N = 1	N = 2	N = 3	N = 4
Normalised frequencies
ω1m/ω1d	1.00	1.00	1.00	1.00	1.00
ω2m/ω1d	2.74	2.74	2.10	2.74	2.74
ω3m/ω1d	3.36	5.47	2.71	2.95	3.04
Percentage error (%)
ω 1m/ω1d	0	−0.27	0.21	0.03	0.18
ω 2m/ω1d	0	0.02	−23.44	0.00	−0.03
ω 3m/ω1d	0	62.89	−19.24	−12.36	−9.54

Figure 4. Approach 1 – design variables vs. element number.

Table 2. Natural frequencies of PC-9/A wing vs. continuous beam

	Normalised frequency (Hz)
Mode	PC-9/A wing	Continuous beam
1	1.00	1.00
2	2.74	2.76
3	3.36	5.40

Figure 5. Flow chart for GA Approach 3.

Figure 6. Flow chart for GA Approach 5.

Figure 7. Approach 5 – design variables vs. element number.

Table 3. Approach 5 – normalised frequencies

		Finite element model
Value	Meas. data	N = 1	N = 2	N = 3	N = 4
Normalised frequencies
ω1m/ω1d	1.00	0.61	1.00	1.00	0.97
ω2m/ω1d	2.74	2.74	2.60	2.69	2.72
ω3m/ω1d	3.36	5.58	3.74	3.60	3.70
Percentage error (%)
ω1m/ω1d	0	−39.04	0.01	−0.04	−3.14
ω2m/ω1d	0	0.00	−5.14	−1.88	−0.72
ω3m/ω1d	0	66.16	11.28	7.25	10.20

Figure 8. Comparison of standard deviation for Approach 5.

Figure 9. Comparison of standard deviation for Approaches 1–5.

Table 4. Material and section properties for experimental model

Property	Element	Value	Units
Bending stiffness
EI	1	6.84 × 10^6	N m^2
EI	2	4.16 × 10^6
EI	3	0.97 × 10^6
Mass per unit length
ρA	1	72.192	kg m^−1
ρA	2	70.421
ρA	3	15.715
Centreline mass
mlm		1266.2	kg