# Adaptive Kalman Filter Based on Adjustable Sampling Interval in Burst Detection for Water Distribution System

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed Methodology

#### 2.1. Kalman Filtering

#### 2.2. Adaptive Method with Adjustable Sampling Interval

## 3. Results and Discussion

#### 3.1. Effect of Sampling Interval

#### 3.2. Application of Self-Adjusting Method to Virtual Flow Data

#### 3.3. Application of Self-Adjusting Method to Real DMA Flow Data

^{3}/h with a small deviation from the average of 35.3 m

^{3}/h, as shown in Figure 6a. In the measured data, abnormally large flow rates of 92 and 75 m

^{3}/h are observed in May, and many zero values are found over the measurement period. This dataset cannot be regarded as one qualified for detecting bursts with a reasonable accuracy. However, the simulation results can be useful, because the main purpose is to compare the sensitivity and efficiency of sampling intervals. The normalized residuals after low-pass filtering, which are calculated from Equation (9), are plotted in Figure 6b for three types of sampling intervals. As predicted from the many zero flow rates, many bursts are detected over the simulation period. According to the results for a constant 30-min sampling interval, the burst alarm should be provided over almost the whole sampling period. In contrast, the self-adjusting algorithm provides intermittent burst alarms with the distinct magnitude peaks of the normalized residuals. As shown in Figure 6c, the sampling interval remains at 30 min (i.e., the maximum sampling interval) in most of the simulation, but more frequent sampling is requested when detecting bursts.

^{3}/h with a large deviation from the average of 58.1 m

^{3}/h, as shown in Figure 7a. Unlike the flow data observed in DMA MG8, those observed in DMA MG9 are consistent over the sampling period, without missing or abnormal values. In the measured data, a high flow rate in excess of 150 m

^{3}/h is reached, which is a relatively large amount compared with the average flow rate of 58.1 m

^{3}/h. This can be explained by a large amount of commercial water use in the daytime. The potential bursts were clearly detected with normalized residuals at 1-min and adjustable sampling intervals. However, no bursts were detected with a constant 30-min sampling interval, because this is too rough to carry noise information. Although the self-adjusting algorithm overlooked the bursts detected in the 1-min prediction from July to September, its superiority over the 30-min sampling interval can be demonstrated. Moreover, only 9486 samples were utilized for burst prediction, which is only twice as many samples as with 30-min interval (Table 1). As shown in Table 1, the overall results of detecting bursts with the self-adjusting algorithm proved the application successful with respect to accuracy and efficiency that are expressed as numbers of alarms and samples, respectively. The number of alarms was counted by setting the alarm threshold to be 0.01 of the threshold value of $N{R}_{k}$.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Farley, B.; Mounce, S.R.; Boxall, J.B. Field testing of an optimal sensor placement methodology for event detection in an urban water distribution network. Urban Water J.
**2010**, 7, 345–356. [Google Scholar] [CrossRef] - Lambert, A. Accounting for losses: the bursts and background concept. Water Environ. J.
**1994**, 8, 205–214. [Google Scholar] [CrossRef] - Giurco, D.P.; White, S.B.; Stewart, R.A. Smart metering and water end-use data: Conservation benefits and privacy risks. Water
**2010**, 2, 461–467. [Google Scholar] [CrossRef] - Liggett, J.A.; Chen, L.C. Inverse transient analysis in pipe networks. J. Hydraul. Eng.
**1994**, 120, 934–955. [Google Scholar] [CrossRef] - Covas, D.; Ramos, H.; de Almeida, A.B. Standing wave difference method for leak detection in pipeline systems. J. Hydraulic Eng.
**2005**, 131, 1106–1116. [Google Scholar] [CrossRef] - Anderson, J.H.; Powell, R.S. Implicit state-estimation technique for water network monitoring. Urban Water
**2000**, 2, 123–130. [Google Scholar] [CrossRef] - Poulakis, Z.; Valougeorgis, D.; Papadimitriou, C. Leakage detection in water pipe networks using a Bayesian probabilistic framework. Probabilistic Eng. Manag.
**2003**, 18, 315–327. [Google Scholar] [CrossRef] - Puust, R.; Kapelan, Z.; Savic, D.A.; Koppel, T. Probabilistic leak detection in pipe networks using the SCEM-UA algorithm. In Proceedings of the 8th Annual Water Distribution Systems Analysis Symposium, Cincinnati, OH, USA, 27–30 August 2006.
- Palau, C.V.; Arregui, F.J.; Carlos, M. Burst detection in water networks using principal component analysis. J. Water Resour. Plan. Manag.
**2012**, 138, 47–54. [Google Scholar] [CrossRef] - Mounce, S.R.; Machell, J. Burst detection using hydraulic data from water distribution systems with artificial neural networks. Urban Water J.
**2006**, 3, 21–31. [Google Scholar] [CrossRef] - Aksela, K.; Aksela, M.; Vahala, R. Leakage detection in a real distribution network using a SOM. Urban Water J.
**2009**, 6, 279–289. [Google Scholar] [CrossRef] - Mounce, S.R.; Boxall, J.B.; Machell, J. Development and verification of an online artificial intelligence system for detection of bursts and other abnormal flows. J. Water Resour. Plan. Manag.
**2012**, 136, 309–318. [Google Scholar] [CrossRef] - Ye, G.; Fenner, R.A. Kalman filtering of hydraulic measurements for burst detection in water distribution systems. J. Pipeline Syst. Eng. Pract.
**2011**, 2, 14–22. [Google Scholar] [CrossRef] - Ye, G.; Fenner, R.A. Study of burst alarming and sampling frequency in water distribution networks. J. Water Resour. Plan. Manag.
**2014**, 140, 06014001. [Google Scholar] [CrossRef] - Kalman, R.E. A new approach to linear filtering and prediction problems. J. Basic Eng.
**1960**, 82, 35–45. [Google Scholar] [CrossRef] - Mehra, R.K. On the identification of variances and adaptive Kalman filtering. Automatic Control
**1970**, 15, 175–184. [Google Scholar] [CrossRef] - Berthouex, P.M.; Brown, L.C. Statistics for Environmental Engineers, 2nd ed.; Lewis Publishers: Boca Raton, FL, USA, 2002. [Google Scholar]
- US Environmental Protection Agency (US EPA). Data Quality Assessment: Statistical Methods for Practitioners; Report No. EPA QA/G-9S; US EPA: Washington, DC, USA, 2006.

**Figure 1.**Procedure for detecting bursts with adaptive Kalman filter incorporating adjustable sampling interval.

**Figure 2.**Virtual flow data: (

**a**) sine curve; (

**b**) virtual leakage; (

**c**) random noise; and (

**d**) composite virtual flow.

**Figure 3.**Burst detection results with respect to sampling interval for virtual flow data: (

**a**) flow residual; (

**b**) normalized residual after low-pass filtering; and (

**c**) relative accuracy versus sampling interval.

**Figure 4.**Burst detection results with adjustable sampling interval for virtual flow data: (

**a**) flow; (

**b**) normalized residual after low-pass filtering; and (

**c**) sampling interval variation.

**Figure 6.**Burst detection results with adjustable sampling interval for DMA MG8: (

**a**) flow; (

**b**) normalized residual after low-pass filtering; and (

**c**) sampling interval variation.

**Figure 7.**Burst detection results with adjustable sampling interval for DMA MG9: (

**a**) flow; (

**b**) normalized residual after low-pass filtering; and (

**c**) sampling interval variation.

DMA | Alarms | Samples | ||||
---|---|---|---|---|---|---|

1 min | 30 min | Self-Adjusted | 1 min | 30 min | Self-Adjusted | |

MG8 | 38 | 5 | 19 | 132,481 | 4416 | 21,003 |

MG9 | 73 | 0 | 20 | 132,481 | 4416 | 9486 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Choi, D.Y.; Kim, S.-W.; Choi, M.-A.; Geem, Z.W. Adaptive Kalman Filter Based on Adjustable Sampling Interval in Burst Detection for Water Distribution System. *Water* **2016**, *8*, 142.
https://doi.org/10.3390/w8040142

**AMA Style**

Choi DY, Kim S-W, Choi M-A, Geem ZW. Adaptive Kalman Filter Based on Adjustable Sampling Interval in Burst Detection for Water Distribution System. *Water*. 2016; 8(4):142.
https://doi.org/10.3390/w8040142

**Chicago/Turabian Style**

Choi, Doo Yong, Seong-Won Kim, Min-Ah Choi, and Zong Woo Geem. 2016. "Adaptive Kalman Filter Based on Adjustable Sampling Interval in Burst Detection for Water Distribution System" *Water* 8, no. 4: 142.
https://doi.org/10.3390/w8040142