5.2.3 IDV 3 and IDV 11: single-valued vs. interval-valued multivariate GLR chart

For the final case study, the moving window interval aggregation method is tested for the same fault scenarios tested previously for the TEP: IDV 3 and IDV 11. A smaller sample window size of 10 samples is used for the multivariate GLR chart

in order to highlight the difference between using single and interval-valued data

IDV 3 Intervalvalued multivariate GLR

Fault Detection of Single and Interval Valued Data Using Statistical Process Monitoring…

FAR (%) 05.0 05.0 05.0 05.0

IDV 11 Singlevalued multivariate GLR

IDV 11 Intervalvalued multivariate GLR

The interval aggregation window size was set at 10 samples. The IDV 3 and IDV 11 scenarios for both data types are shown in Figures 12 and 13, and the metrics for

15.1 00.0 02.0 00.0

There are two major observations to be made from the results. First, the use of the multivariate GLR chart allowed for a more stable FAR for all cases due to the presence of a single statistic to monitor for all variables, as opposed to the one for each variable when using the univariate GLR charts. Second, the missed DR when using interval data was significantly lower than that for single-valued data, reaching

The latter observation is attributed to interval data, especially the method of generation, where the centers and radii are used as independent variables in the same dataset. This method of aggregation helps the PCA model account for shifts in the mean and variance respectively, similar to the univariate GLR chart outline in Section 3.1.3. However, it does so without the need to tune any extra parameters, due to the fact that a fault in the centers is likely to be caused by a shift in the mean, while a fault in the radii is likely to be caused by a shift in

In this chapter, the performance of GLR charts were compared to conventional fault detection statistics, specifically the Q and T2 statistics, and the integration of interval-valued data into real-time process monitoring was explored. The performance of different PCA-based univariate GLR charts were examined using singlevalued data through two illustrative examples: simulated synthetic data, and the Tennessee Eastman Process. The performance of the moving window interval aggregation method was evaluated alongside that of single-valued data for the

The results demonstrate that in order to monitor processes that may experience

both shifts in the mean and/or variance, the best performance is achieved by implementing the two respective univariate GLR charts separately in parallel, rather than the single chart designed to simultaneously detect shifts in both, as the simultaneous estimation of two parameters is unable to provide the best possible fault detection performance. Moreover, the moving window interval aggregation method, when combined with the multivariate GLR chart, was able to provide a perfectly stable statistic, with an unwavering false alarm rate, in addition to the best possible performance in detecting shifts in the mean and variance for two scenarios

perfect performance levels of zero missed DR for both scenarios.

Summary of fault detection results (single vs. interval data) for α = 5%.

more clearly.

Missed DR (%)

Table 6.

the variance.

6. Conclusions

multivariate GLR chart as well.

of the Tennessee Eastman Process.

121

each method are tabulated in Table 6.

IDV 3 Singlevalued multivariate GLR

DOI: http://dx.doi.org/10.5772/intechopen.88217

Figure 12. PCA-based multivariate GLR charts (IDV 3).

Figure 13. PCA-based multivariate GLR charts (IDV 11).


Fault Detection of Single and Interval Valued Data Using Statistical Process Monitoring… DOI: http://dx.doi.org/10.5772/intechopen.88217

#### Table 6.

T<sup>2</sup> and Q charts. The improved results can be attributed to the use of MLEs to estimate the values of the unknown parameters used to maximize the GLR statistic, allowing for the best possible DR to be achieved for a fixed FAR. This example also demonstrates that the GLR charts can be easily designed and utilized to monitor

5.2.3 IDV 3 and IDV 11: single-valued vs. interval-valued multivariate GLR chart

For the final case study, the moving window interval aggregation method is tested for the same fault scenarios tested previously for the TEP: IDV 3 and IDV 11. A smaller sample window size of 10 samples is used for the multivariate GLR chart

chemical processes, such as the TEP.

Fault Detection, Diagnosis and Prognosis

Figure 12.

Figure 13.

120

PCA-based multivariate GLR charts (IDV 3).

PCA-based multivariate GLR charts (IDV 11).

Summary of fault detection results (single vs. interval data) for α = 5%.

in order to highlight the difference between using single and interval-valued data more clearly.

The interval aggregation window size was set at 10 samples. The IDV 3 and IDV 11 scenarios for both data types are shown in Figures 12 and 13, and the metrics for each method are tabulated in Table 6.

There are two major observations to be made from the results. First, the use of the multivariate GLR chart allowed for a more stable FAR for all cases due to the presence of a single statistic to monitor for all variables, as opposed to the one for each variable when using the univariate GLR charts. Second, the missed DR when using interval data was significantly lower than that for single-valued data, reaching perfect performance levels of zero missed DR for both scenarios.

The latter observation is attributed to interval data, especially the method of generation, where the centers and radii are used as independent variables in the same dataset. This method of aggregation helps the PCA model account for shifts in the mean and variance respectively, similar to the univariate GLR chart outline in Section 3.1.3. However, it does so without the need to tune any extra parameters, due to the fact that a fault in the centers is likely to be caused by a shift in the mean, while a fault in the radii is likely to be caused by a shift in the variance.

### 6. Conclusions

In this chapter, the performance of GLR charts were compared to conventional fault detection statistics, specifically the Q and T2 statistics, and the integration of interval-valued data into real-time process monitoring was explored. The performance of different PCA-based univariate GLR charts were examined using singlevalued data through two illustrative examples: simulated synthetic data, and the Tennessee Eastman Process. The performance of the moving window interval aggregation method was evaluated alongside that of single-valued data for the multivariate GLR chart as well.

The results demonstrate that in order to monitor processes that may experience both shifts in the mean and/or variance, the best performance is achieved by implementing the two respective univariate GLR charts separately in parallel, rather than the single chart designed to simultaneously detect shifts in both, as the simultaneous estimation of two parameters is unable to provide the best possible fault detection performance. Moreover, the moving window interval aggregation method, when combined with the multivariate GLR chart, was able to provide a perfectly stable statistic, with an unwavering false alarm rate, in addition to the best possible performance in detecting shifts in the mean and variance for two scenarios of the Tennessee Eastman Process.
