The synthetic data considered for the tests consist of repetitions of actual measured flow patterns, with in total three sequences of five identical weekdays and two identical weekend days, starting at day 2 and ending at day 22 of an arbitrary month in an arbitrary year. Different datasets were generated from these original data, by adding anomalies with different amplitude and duration, as well as different levels of normally distributed noise. The characteristics of the generated datasets are summarized in Table 2, and the flow patterns corresponding to the unperturbed signal and datasets 1a, 2a and 3a can be seen in Figure 3.
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Table 2
Summary of the generated datasets used to test the CuBOid algorithm
| Anomaly 1 | Anomaly 2 | (%) | |||
|---|---|---|---|---|---|
| Dataset ID | Start-end day | Amplitude (m3/h) | Start-end day | Amplitude (m3/h) | Gaussian noise |
| 0 | None | – | None | – | None |
| 1a | 05–08 | 10 | 15–18 | 5 | None |
| 1b | 05–08 | 10 | 15–18 | 5 | 5 |
| 1c | 05–08 | 10 | 15–18 | 5 | 10 |
| 1d | 05–08 | 10 | 15–18 | 5 | 20 |
| 2a | 04–10 | 10 | 14–20 | 5 | None |
| 2b | 04–10 | 10 | 14–20 | 5 | 5 |
| 2c | 04–10 | 10 | 14–20 | 5 | 10 |
| 2d | 04–10 | 10 | 14–20 | 5 | 20 |
| 3a | 05–15 | 10 | 12–20 | 5 | None |
| 3b | 05–15 | 10 | 12–20 | 5 | 5 |
| 3c | 05–15 | 10 | 12–20 | 5 | 10 |
| 3d | 05–15 | 10 | 12–20 | 5 | 20 |
| Anomaly 1 | Anomaly 2 | (%) | |||
|---|---|---|---|---|---|
| Dataset ID | Start-end day | Amplitude (m3/h) | Start-end day | Amplitude (m3/h) | Gaussian noise |
| 0 | None | – | None | – | None |
| 1a | 05–08 | 10 | 15–18 | 5 | None |
| 1b | 05–08 | 10 | 15–18 | 5 | 5 |
| 1c | 05–08 | 10 | 15–18 | 5 | 10 |
| 1d | 05–08 | 10 | 15–18 | 5 | 20 |
| 2a | 04–10 | 10 | 14–20 | 5 | None |
| 2b | 04–10 | 10 | 14–20 | 5 | 5 |
| 2c | 04–10 | 10 | 14–20 | 5 | 10 |
| 2d | 04–10 | 10 | 14–20 | 5 | 20 |
| 3a | 05–15 | 10 | 12–20 | 5 | None |
| 3b | 05–15 | 10 | 12–20 | 5 | 5 |
| 3c | 05–15 | 10 | 12–20 | 5 | 10 |
| 3d | 05–15 | 10 | 12–20 | 5 | 20 |
Figure 3
Considered flow patterns: (a) original flow pattern, with distinct week and weekend days; (b) flow pattern corresponding to dataset 1a; (c) flow pattern corresponding to dataset 2a; (d) flow pattern corresponding to dataset 3a.
Figure 3
Considered flow patterns: (a) original flow pattern, with distinct week and weekend days; (b) flow pattern corresponding to dataset 1a; (c) flow pattern corresponding to dataset 2a; (d) flow pattern corresponding to dataset 3a.