**5.4 Online monitoring of PVC batch process**

## **5.4.1 Online monitoring of PVC with DTW-MPCA and DTW-MICA**

On synchronization of DTW operation, all durations of the batches should be 3200. The weight matrix **W**= [1.1527, 1.8648, 0.2390, 1.4778, 0.1742, 0.2118, 0.8186, 0.2760, 0.4592, 3.3258] from Eq.8, 9 for twice iterations. The MPCA model is built and its retained principal number is 8 to show 88.44%the variation of the batch process, whereas MICA retains 3 IC to explain the 93.85% of variation of data. All three solutions of of Nomikos and MacGregor (1995) and GCC are simulated compared with the offline analysis to find which one is the most appropriate in the batch process.

On-Line Monitoring of Batch Process with Multiway PCA/ICA 257

alarm to these batches, so it has to list them in Table 3. GCC performs well that it followed offline with a little difference. OFA-MPCA approach misses the abnormal of #1, #2, #4,

> No. 1 2 3 4 5 MPCA 232.89 101.48 84.305 206.15 153.59 MICA 738.69 844.37 254.93 437.87 301.89 No. 6 7 8 9 10 MPCA 81.499 143.74 81.499 143.74 127.83 MICA 160.76 322.75 160.76 322.75 401.52

SP

Fig. 11. SPE indices of online monitoring solutions, GCC and the mean values of the first

The *D*-statistics of PVC, T2 of OFA-MPCA and *I*2 of OFA-MICA are drawn in Fig.12 as well. GCC performs well in the *D*-statistics in the same way, either T2 or *I*2, which are both close to the counterparts of offline. The first traditional solution can not predict any little variation after the time of detection, and the second one always has too larger error to be drawn in Fig. 12 that the results of the second solution has to be enumerated in Table 4.

> No. 1 2 3 4 5 **T2** 158.23 155.09 143.63 113.78 102.80 **I2** 252.67 926.58 263.94 114.91 104.79 No. 6 7 8 9 10 **T2** 53.445 129.22 53.445 129.22 131.87 **I2** 41.569 70.977 41.569 70.977 110.13

Table 4. The T2 in MPCA and I2 in MICA of the second solution online monitoring

E

2 4 6 8 10

Batch Number

SPE of online monitoring OFA-MICA

off-line

mean value 99 control limits

correlation coefficient

Table 3. The SPE of online monitoring in MPCA and MICA of the second solution

whereas OFA-MICA detects four abnormal all.

2 4 6 8 10

Batch Number

solution, left: OFA-MPCA; right: OFA-MICA

SPE of online monitoring OFA-MPCA

off-line 99 control limits mean value correlation coefficient

SPE

Fig.10 shows several online monitoring SPE indices of the 10 test batches compared with offline in MPCA and MICA, respectively. It can be shown that the MPCA results of first solution always misses faults in abnormal batches because of its smoothing the variation, the MICA result also misses the alarm of #2 and #3; while the results of second and third soltions are too large to alarm by mistake.

Fig. 10. SPE indices of online monitoring solutions, GCC and three solutions, left: DTW-MPCA; right: DTW-MICA

Comparatively, SPE of GCC prediction has adequate information of variations to identify the abnormal, only its MPCA results miss the abnormal of #4, the MICA results perform well.

### **5.4.2 Online monitoring of PVC with OFA-MPCA and OFA-MICA**

After OFA synchronization, the information of original trajectories are extracted. Each variable of each batch run can be transformed into two coefficients, therefore in stead of irregular time length of three-dimensional data block, the two-dimensional coefficients matrix **Θ** (50×18) inherits the main features from the primative three-dimensional data block. Based on the new data of coefficients, the MPCA and MICA are experimented respectively. The online monitoring time point is set to 800 *th* measurement. MPCA algorithm holds 12 PCs to explain the 89.52% variation of the data, whereas MICA reserved 3ICs to illustrate the 51.92% variability in the data. The first two solutions of Nomikos and MacGregor (1995) and GCC are experimented in contrast with the offline analysis to find the best one in the batch process. It is noticed that the third solution does not fit for the coefficients matrix because the loading matrix is not from the coefficients, but from primative variables.

From various on-line monitoring solutions and offline analysis, *Q*-statistics-the SPE indices of 10 test batches are drawn in Fig.11, with MPCA and MICA, respectively. Similarly, the first solution of Nomikos and MacGregor (1995) erases many fine characters of the process so that it cannot detect the problem of many batches correctly, and the values of results of second online monitoring method are too large to be drawn in Fig.11, and always make false 256 Principal Component Analysis

Fig.10 shows several online monitoring SPE indices of the 10 test batches compared with offline in MPCA and MICA, respectively. It can be shown that the MPCA results of first solution always misses faults in abnormal batches because of its smoothing the variation, the MICA result also misses the alarm of #2 and #3; while the results of second and third

Fig. 10. SPE indices of online monitoring solutions, GCC and three solutions, left: DTW-

Comparatively, SPE of GCC prediction has adequate information of variations to identify the abnormal, only its MPCA results miss the abnormal of #4, the MICA results perform

After OFA synchronization, the information of original trajectories are extracted. Each variable of each batch run can be transformed into two coefficients, therefore in stead of irregular time length of three-dimensional data block, the two-dimensional coefficients matrix **Θ** (50×18) inherits the main features from the primative three-dimensional data block. Based on the new data of coefficients, the MPCA and MICA are experimented respectively. The online monitoring time point is set to 800 *th* measurement. MPCA algorithm holds 12 PCs to explain the 89.52% variation of the data, whereas MICA reserved 3ICs to illustrate the 51.92% variability in the data. The first two solutions of Nomikos and MacGregor (1995) and GCC are experimented in contrast with the offline analysis to find the best one in the batch process. It is noticed that the third solution does not fit for the coefficients matrix because the loading matrix is not from the coefficients, but from

From various on-line monitoring solutions and offline analysis, *Q*-statistics-the SPE indices of 10 test batches are drawn in Fig.11, with MPCA and MICA, respectively. Similarly, the first solution of Nomikos and MacGregor (1995) erases many fine characters of the process so that it cannot detect the problem of many batches correctly, and the values of results of second online monitoring method are too large to be drawn in Fig.11, and always make false

SPE

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>10</sup> <sup>0</sup>

Batch Number

x 1012 SPE of online monitoring of DTW-MICA

part loading current deviation mean values 99control limit offline GCC

part loading current values mean values 99control limit offline GCC

soltions are too large to alarm by mistake.

<sup>12</sup> x 104 SPE of online monitoring of DTW-MPCA

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>10</sup> <sup>0</sup>

Batch Number

**5.4.2 Online monitoring of PVC with OFA-MPCA and OFA-MICA** 

2

well.

MPCA; right: DTW-MICA

primative variables.

4

6

SPE

8

10

alarm to these batches, so it has to list them in Table 3. GCC performs well that it followed offline with a little difference. OFA-MPCA approach misses the abnormal of #1, #2, #4, whereas OFA-MICA detects four abnormal all.


Table 3. The SPE of online monitoring in MPCA and MICA of the second solution

Fig. 11. SPE indices of online monitoring solutions, GCC and the mean values of the first solution, left: OFA-MPCA; right: OFA-MICA

The *D*-statistics of PVC, T2 of OFA-MPCA and *I*2 of OFA-MICA are drawn in Fig.12 as well. GCC performs well in the *D*-statistics in the same way, either T2 or *I*2, which are both close to the counterparts of offline. The first traditional solution can not predict any little variation after the time of detection, and the second one always has too larger error to be drawn in Fig. 12 that the results of the second solution has to be enumerated in Table 4.


Table 4. The T2 in MPCA and I2 in MICA of the second solution online monitoring

On-Line Monitoring of Batch Process with Multiway PCA/ICA 259

5

50

0

0

20

I

I

Fig. 14. I2 Contribution plots of 4 monitoring methods in PVC. Upper left: offline; Upper right: online GCC; Lower left: online mean trajectories of first solution; Lower right: online

2 Contribution

2 Contribution

5

100

SPE Contribution

SPE Contribution

Fig. 13. SPE Contribution plots of 4 monitoring methods in PVC. Upper left: offline; Upper right: online GCC; Lower left: online mean trajectories of first solution; Lower right: online

10

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>0</sup>

Variable

OnlineLastValue

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>0</sup>

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> -5

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> -20

Variable

Variable

OnlineLastValue

Variable

Online GCC

Online GCC

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>0</sup>

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>0</sup>

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> -5

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> -5

Variable

Variable

Online Mean

Variable

Offline

Variable

Online Mean

<sup>10</sup> Offline

5

5

SPE Contribution

current values of second solution

0

0

5

I

I

current values of second solution

2 Contribution

2 Contribution

5

10

SPE Contribution

From Fig.12, it can be seen that OFA-MICA misses alarm #1 and #4, but OFA-MPCA has more errors: missed #1 and #3, and has a false alarm about #5, #7, #9 and #10.

Consquently, it is proved that the effect of OFA-MICA is better than ones of OFA-MPCA on both of *Q*-statistics and *D*-statistics in Fig.11 and Fig.12.

Fig. 12. T2 or I2 indices of online monitoring solutions, GCC and the mean values of the first solution, left: OFA-MPCA; right: OFA-MICA

#### **5.5 Contribution plot of SPE and I2 in OFA-MICA**

The contribution plots can be used to dignose the event from non-conforming batches so as to assign a cause of abnormal by indication of which variables are predominatly responsible for the deviations (Jackson and Mudholkar, 1979). For instance, based on the approach of OFA-MICA, when the 800 *th* measurements of a diseased batch #3, the online SPE and *I*<sup>2</sup> contribution plots of 9 process variables are shown in Fig. 13 and Fig.14. It is obvious that the ratio of GCC (upper right) looks like the one of offline (upper left) which is different from the others (lower) distinctly. From Fig.13, The comparative larger ones of SPE is temperature of the baffle outlet (variable 4), flow rate of jacket water (variable 8) and stirring power (variable 9). Meanwhile we can find that the notable contribution of *I*2 in Fig.14 are temperature of the reactor jacket inlet (variable 2), baffle outlet (variable 4) and flow rate of jacket water (variable 8). Therefore, contrasted with the report from plant in Table 2, the root cause is lower stirring power (the most conspicuous one in bar plot of Fig.13), which decreased other variables such as variable 4 and variable 8 consequently. It is inferred that lower stirring power decreased the rate of the reaction and generated less heat and needed smaller quantity of cooling water.

258 Principal Component Analysis

From Fig.12, it can be seen that OFA-MICA misses alarm #1 and #4, but OFA-MPCA has

Consquently, it is proved that the effect of OFA-MICA is better than ones of OFA-MPCA on

0

5

10

15

I

2

Fig. 12. T2 or I2 indices of online monitoring solutions, GCC and the mean values of the first

 **in OFA-MICA** 

The contribution plots can be used to dignose the event from non-conforming batches so as to assign a cause of abnormal by indication of which variables are predominatly responsible for the deviations (Jackson and Mudholkar, 1979). For instance, based on the approach of OFA-MICA, when the 800 *th* measurements of a diseased batch #3, the online SPE and *I*<sup>2</sup> contribution plots of 9 process variables are shown in Fig. 13 and Fig.14. It is obvious that the ratio of GCC (upper right) looks like the one of offline (upper left) which is different from the others (lower) distinctly. From Fig.13, The comparative larger ones of SPE is temperature of the baffle outlet (variable 4), flow rate of jacket water (variable 8) and stirring power (variable 9). Meanwhile we can find that the notable contribution of *I*2 in Fig.14 are temperature of the reactor jacket inlet (variable 2), baffle outlet (variable 4) and flow rate of jacket water (variable 8). Therefore, contrasted with the report from plant in Table 2, the root cause is lower stirring power (the most conspicuous one in bar plot of Fig.13), which decreased other variables such as variable 4 and variable 8 consequently. It is inferred that lower stirring power decreased the rate of the reaction and generated less heat and needed

20

25

I 2

2 4 6 8 10

 of Online monitoring OFA-MICA off-line mean value 99 control limits correlation coefficient

Batch Number

more errors: missed #1 and #3, and has a false alarm about #5, #7, #9 and #10.

both of *Q*-statistics and *D*-statistics in Fig.11 and Fig.12.

of Online monitoring OFA-MPCA

off-line 99 control limits correlation coefficient

mean value

2 4 6 8 10

Batch Number

solution, left: OFA-MPCA; right: OFA-MICA

**5.5 Contribution plot of SPE and I2**

smaller quantity of cooling water.

0

5

10

15

T

2

20

25

30

T 2

Fig. 13. SPE Contribution plots of 4 monitoring methods in PVC. Upper left: offline; Upper right: online GCC; Lower left: online mean trajectories of first solution; Lower right: online current values of second solution

Fig. 14. I2 Contribution plots of 4 monitoring methods in PVC. Upper left: offline; Upper right: online GCC; Lower left: online mean trajectories of first solution; Lower right: online current values of second solution

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