Nonlinear chemical processes fault detection based on adaptive kernel principal component analysis

Figures & data

Figure 1. AKPCA monitoring flowchart.

Figure 2. Monitoring results of KPCA and AKPCA for case 0 in TE process.

Figure 3. Monitoring results of KPCA and AKPCA for case 4.

Figure 4. The mutation probabilities of KPCs at four sample points for fault 4.

Figure 5. The similarity between DV-KPC and other KPCs at four sample points for fault 4.

Figure 6. The monitoring effect diagram of DV-KPC and NDV-KPCs for fault 4.

Table 1. The serial numbers of AKPCs at 150, 200, 400, and 800 sample points.

	150	200	400	800
DV-KPC	11	9	4	30
NDV-KPCs	2, 3, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20	2, 3, 4, 8, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 23	2, 3, 5, 6, 7, 8, 9, 12, 17, 18, 20, 21, 29	1, 2, 3, 4, 6, 20, 28, 29

Figure 7. The monitoring results of KPCA and AKPCA for Case 19.

Figure 8. The monitoring results of KPCA and AKPCA for Case 21.

Table 2. The comparison of missed alarm rates of KPCA, SKPCA, and AKPCA in TE process.

Fault	KPCA	KPCA	SKPCA	AKPCA
number	$T^2$	SPE	$T^2$	$T^2$
1	0.003	0.004	0.001	0.003
2	0.018	0.018	0.008	0.005
3	0.971	0.979	0.806	0.818
4	0.990	0.998	0.004	0.054
5	0.763	0.756	0.003	0.003
6	0.000	0.000	0.000	0.000
7	0.591	0.595	0.002	0.063
8	0.023	0.023	0.012	0.010
9	0.975	0.970	0.811	0.621
10	0.608	0.338	0.078	0.178
11	0.575	0.609	0.139	0.103
12	0.010	0.013	0.001	0.009
13	0.050	0.055	0.045	0.038
14	0.000	0.001	0.002	0.001
15	0.923	0.938	0.717	0.524
16	0.703	0.686	0.040	0.036
17	0.040	0.064	0.025	0.021
18	0.099	0.103	0.087	0.087
19	0.881	0.864	0.478	0.288
20	0.693	0.490	0.187	0.067
21	0.573	0.584	0.453	0.323
Average	0.452	0.433	0.186	0.155

Table 3. The comparison of false alarm rates of PCA, KPCA, SKPCA, and AKPCA in TE process.

Fault	KPCA	KPCA	SKPCA	AKPCA
number	$T^2$	SPE	$T^2$	$T^2$
1	0.012	0.006	0.003	0.001
2	0.012	0.012	0.004	0.003
3	0.018	0.012	0.156	0.004
4	0.000	0.003	0.002	0.004
5	0.018	0.025	0.002	0.005
6	0.006	0.000	0.002	0.000
7	0.006	0.006	0.003	0.012
8	0.006	0.000	0.003	0.001
9	0.118	0.018	0.205	0.003
10	0.012	0.012	0.003	0.006
11	0.025	0.018	0.004	0.023
12	0.012	0.012	0.005	0.001
13	0.000	0.000	0.001	0.000
14	0.006	0.018	0.003	0.002
15	0.006	0.012	0.009	0.001
16	0.112	0.018	0.005	0.003
17	0.006	0.018	0.004	0.003
18	0.000	0.037	0.003	0.002
19	0.006	0.006	0.003	0.002
20	0.000	0.000	0.002	0.000
21	0.006	0.037	0.004	0.003
Average	0.018	0.013	0.026	0.004