An Extended Time Series Algorithm for Modal Identification from Nonstationary Ambient Response Data Only

Table 7

Results of natural frequency and damping ratio identification of the 20-DOF chain system subjected to a recorded sample of the Chi-Chi Earthquake through the nonstationary base-function ARMA algorithm in conjunction with the proposed modified least-square method.

Mode	Natural frequency (rad/sec)			Damping ratio (%)
	Exact	ARMA	Error (%)	Exact	ARMA	Error (%)
1	3.66	3.63	0.93	5.49	5.49	0.07
2	7.30	7.30	0.03	0.71	0.68	4.79
3	10.90	10.89	0.11	0.94	1.00	6.17
4	14.44	14.41	0.19	0.89	0.82	8.31
5	17.90	17.85	0.27	1.06	1.04	2.08
6	21.26	21.18	0.37	1.17	1.10	5.81
7	24.49	24.37	0.49	1.33	1.30	2.11
8	27.60	27.42	0.67	1.45	1.39	3.86
9	30.54	30.32	0.72	1.59	1.78	11.70
10	33.32	32.97	1.04	1.71	1.68	1.64
11	35.91	35.43	1.33	1.83	1.81	0.87
12	38.30	37.88	1.11	1.94	1.87	3.40
13	40.48	39.90	1.43	2.03	2.14	5.42
14	42.43	41.85	1.38	2.12	1.77	16.32
15	44.14	43.37	1.74	2.20	2.43	10.64
16	45.60	44.78	1.79	2.26	2.01	10.97
17	46.81	45.46	2.88	2.26	2.53	12.04
18	47.76	46.48	2.69	2.20	1.90	13.55
19	48.44	47.14	2.68	2.51	2.67	6.29
20	48.85	48.03	1.67	2.41	2.64	9.54