An improved control-limit-based principal component analysis method for condition monitoring of marine turbine generators

Figures & data

Figure 1. Working flowchart of PCA.

Figure 2. Three of the most important sensors.

Figure 3. Sensors in the monitoring cabinet.

Figure 4. Overall design of the online condition monitoring system for lubricating oil.

Table 1. An example of data structure.

Power (Mw)	Density (g/cm³)	Viscosity (CST)	Dielectric constant	Temperature (°C)	4 um	6 um
333.3368	0.860	33.4620	2.185	38.3	140	31
14um	21um	ISO6um	ISO14um	Capacitance (pF)	Water (%)	NAS 1638
6	1	13	7	2.14	51.56	4

Figure 5. Heatmap of the features correlation.

Figure 6. Principal component scree plot.

Table 2. Total variance explained.

	Initial eigenvalues			Extraction sums of squared loadings
Component	Total	% of variance	Cumulative %	Total	% of variance	Cumulative %
1	8.514	60.813	60.813	8.514	60.813	60.813
2	1.778	12.697	73.511	1.778	12.697	73.511
3	1.177	8.405	81.915	1.177	8.405	81.915
4	0.938	6.701	88.616	0.938	6.701	88.616
5	0.533	3.809	92.425
6	0.459	3.276	95.701
7	0.207	1.480	97.182
8	0.160	1.146	98.327
9	0.096	0.688	99.015
10	0.082	0.583	99.598
11	0.039	0.278	99.876
12	0.013	0.092	99.968
13	0.003	0.023	99.991
14	0.001	0.009	100.000

Figure 7. Flow chart of fault monitoring.

Table 3. Component matrix.

	Component
	1	2	3	4
Power	0.937	0.072	−0.024	−0.022
Density (g/cm^3)	−0.903	0.084	0.099	−0.004
viscosity(CST)	0.158	−0.939	0.183	−0.122
Dielectric constant	0.985	−0.065	−0.058	−0.002
Temperature (°C)	0.461	0.820	−0.220	0.112
4um	0.936	−0.195	−0.088	0.050
6um	0.956	−0.166	−0.075	0.037
14um	0.150	0.347	0.621	−0.624
21um	0.113	0.058	0.667	0.712
ISO6um	0.938	0.060	0.020	−0.063
ISO14um	0.667	0.123	0.438	−0.079
Capacitance (pF)	0.891	−0.003	−0.119	0.004
Water (%)	0.893	−0.017	−0.115	0.002
NAS1638	0.935	0.005	0.133	0.025

Table 4. Monitoring index and its control limit.

Confidence level equals 99%
Monitoring index	$T^2$	Q (SPE)	Hybrid indicator
Values	18.096	3.615	1.702

Figure 8. $T^2$ index monitoring trends.

Figure 9. $Q$ index monitoring trends.

Figure 10. Hybrid indicator monitoring trends.

Figure 11. False alarm rate of statistical indicators.

Table 5. False alarm rate of statistical indicators.

	Fault occurred 1st time	Fault stopped 1st time	False alarm rate 1st time	Fault occurred 2nd time	Fault stopped 2nd time	False alarm rate 2nd time	Total false alarm rate
Actual value	1880	1940	–	2120	2210	–	–
$T^2$ index	1925	1955	0.030	2131	2216	0.043	0.017
Q index	1872	1920	0.014	2119	2189	0.055	0.032
Hybrid indicator	1874	1943	0.005	2121	2208	0.023	0.008