A Thrust Allocation Method for Efficient Dynamic Positioning of a Semisubmersible Drilling Rig Based on the Hybrid Optimization Algorithm

Table 2

Optimization result for 14 time steps.

Time steps	Input from the control system			Thrusters																GA only [A]	Hybrid [B]; (GA + SQP)	Ratio; (B/A)
				Thruster 1		Thruster 2		Thruster 3		Thruster 4		Thruster 5		Thruster 6		Thruster 7		Thruster 8
	Required force		Required moment	RPM	Angle	RPM	Angle	RPM	Angle	RPM	Angle	RPM	Angle	RPM	Angle	RPM	Angle	RPM	Angle	Total power	Total power
	(KN)		(KN⋅m)	(rpm)	(deg)	(rpm)	(deg)	(rpm)	(deg)	(rpm)	(deg)	(rpm)	(deg)	(rpm)	(deg)	(rpm)	(deg)	(rpm)	(deg)	(kW)	(kW)
(s)																						—
1	50	−600	−64,000	3.10	−93	0.62	−91	0.09	85	0.55	−103	2.2	37	0.18	178	0.22	17.3	1.66	167	9,859	8,250	0.84
2	−500	1,500	−25,000	2.51	115	1.02	171	1.29	152	0.79	93	0.03	−64	1.90	78	1.52	81	2.28	114	12,882	10,824	0.84
3	100	−800	17,000	0.78	−35	1.57	−78	1.02	−2	0.54	−13	2.61	−95	0.26	−15	0.17	−92	0.45	20	7,186	6,580	0.92
4	750	−550	63,000	2026	34	0.61	−177	0.76	170	0.07	32	0.62	−78	1.99	−78	0.03	40	2.64	−48	11,800	9,172	0.78
5	175	560	−32,500	0.08	13	0.92	147	0.05	41	0.73	−128	2.74	74	1.11	−35	0.15	−41	0.29	−146	7,121	7,107	1.00
6	−50	−1,080	3,000	2.17	−116	0.04	129	0.89	−65	0.32	−136	2.45	−85	1.42	−70	0.09	−141	0.04	−4	8,840	7,360	0.83
7	−300	1,560	12,000	0.58	129	2.18	68	2.29	97	0.26	54	1.98	108	1.28	−180	0.07	−65	2.29	112	13,749	9,522	0.70
8	1,050	250	−36,000	0.80	−84	0.52	144	0.64	29	2.40	9	0.1	165	2.78	11	1.32	51	0.13	−143	9,623	7,519	0.78
9	−600	−850	−22,000	2.09	−120	0.38	91	0.34	173	2.42	−102	0.21	17	1.97	−180	0.20	−106	0.8	−91	9,687	7,380	0.76
10	−1,200	250	−11,000	1.27	−165	1.31	169	2.28	−176	0.03	39	2.08	146	0.29	134	1.82	161	0.07	−37	9,206	8,140	0.88
11	−500	1,200	−10,000	0.03	125	0.94	148	2.47	97	0.13	−150	1.89	86	1.10	153	0.20	−9	2.32	138	11,280	10,277	0.91
12	600	550	−7,000	0.36	−10	1.93	26	0.04	−72	2.26	1	2	111	1.38	139	1.4	0	0.24	139	9,575	4,855	0.50
13	50	−930	1,000	1.10	−120	1.18	−92	1.72	−78	0.84	−89	2.07	−107	0.96	−88	1.4	2	0.16	62	6,541	3,949	0.60
14	−700	75	−26,000	1.23	−137	1.04	57	0.18	−12	0.18	−34	0.53	−8	0.06	9	2.27	168	1.86	180	6,243	4,802	0.77
—	—	—	—	—	—	—	—	—	—	—	—	—	—	—	—	—	—	—	—	—	Mean	0.79