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

Table 5

Numerical simulation results and comparison between the numerical simulation and measured modal results.

Modal order number	Model no. 1		Model no. 2		Model no. 3		Model no. 4
	Frequency (Hz)	Relative error (%)	Frequency (Hz)	Relative error (%)	Frequency (Hz)	Relative error (%)	Frequency (Hz)	Relative error (%)
1	11.689	−0.04	11.597	−1.04	11.388	1.60	10.559	−1.02
2	14.515	3.02	14.314	1.78	13.385	0.78	14.230	1.19
3	21.792	6.77	21.713	6.89	21.371	6.33	20.785	6.42
4	28.753	−3.81	27.456	−7.00	26.002	−4.99	28.360	−3.42
5	36.122	0.21	36.097	0.44	33.307	6.52	35.986	0.13
6	38.341	−1.97	37.873	−1.07	37.696	4.22	37.696	0.17
7	42.847	5.24	42.846	5.47	42.617	4.90	42.767	5.27
8	65.348	5.80	65.332	5.85	65.328	6.37	64.319	6.25
9	72.275	−0.44	71.442	−0.51	71.080	0.10	72.044	0.02
10	90.183	−0.50	89.383	−1.23	90.177	−0.37	90.068	−0.27
Average		2.78	—	3.13	—	3.62	—	2.42