Research on Vibration Fatigue Damage Locations of Offshore Oil and Gas Pipelines Based on the GA-Improved BP Neural Network

Table 4

Error comparison of the finite element model modified by the neural network.

Modal degree	Modal testing	Initial finite element model		First-step correction		Second-step correction
	Measured value (Hz)	Simulation value (Hz)	Relative error (%)	Simulation value (Hz)	Relative error (%)	Simulation value (Hz)	Relative error (%)
1	11.694	9.2847	−20.60	11.787	0.80	11.689	−0.04
2	14.089	13.246	−5.98	14.715	4.44	14.515	3.02
3	20.411	19.044	−6.70	21.724	6.43	21.792	6.77
4	29.892	26.676	−10.76	27.691	−7.36	28.753	−3.81
5	36.045	35.218	−2.29	35.484	−1.56	36.122	0.21
6	39.111	37.017	−5.35	37.921	−3.04	38.341	−1.97
7	40.715	42.536	4.47	42.699	4.87	42.847	5.24
8	61.765	57.739	−6.52	65.384	5.86	65.348	5.80
9	72.592	71.31	−1.77	73.869	1.76	72.275	−0.44
10	90.633	89.325	−1.44	90.319	−0.35	90.183	−0.50
Average	—	—	6.59	—	3.65	—	2.78