# An Energy Efficient Adaptive Sampling Algorithm in a Sensor Network for Automated Water Quality Monitoring

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## Abstract

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## 1. Introduction

- A DDASA for energy conservation in a sensor network for automated water quality monitoring is presented.
- The universal applicability of the algorithm is validated with respect to various parameters with distinct characteristics, making it applicable in other types of practical monitoring situations.
- The proposed method is evaluated with respect to two key water-related parameters.
- The performance of DDASA is compared with the scheme of sampling at a fixed frequency in terms of data accuracy and energy conservation.
- The performance of DDASA is compared to a traditional ASA.

## 2. Related Work

## 3. Data-Driven Adaptive Sampling Algorithm

_{i+}

_{1}and X

_{i}over the average value of a number of N sliding-window based most recent data. Since we are interested in knowing whether there exists a sudden environmental change or not, it is reasonable to compare the latest sensed data X

_{i+}

_{1}with the former data X

_{i}in the signal sequence, and then divide the absolute difference between with the mean value of the most recent N data. If D is sufficiently large, it indicates a sudden environmental change. Then a somewhat higher sampling frequency is desired. Additionally, if the value of D is smaller than the threshold t, which means the value changes are not significant enough, the sampling frequency can be reduced in view of the relative stability of the monitored data. Hence, the theoretical value of y is actually smaller than 2 but greater than y(0), that is, since the smallest value of D will not be a number smaller than 0 in data sensing process, the value of y(0) is essentially greater than 0 regardless of the value of t. A representation of the revised sigmoid function is presented in Figure 1. It is found the value of y in the simulation is mostly a number either slightly smaller than 1 (e.g., when D equals to D

_{1}) when the sensed data numerically remain stable or greater than 1 (e.g., when D equals to D

_{2}) when the sensed data abruptly change.

_{curr}, which is used to acquire latest data, then the new sampling frequency, denoted by f

_{new}is represented as:

Algorithm 1. DDASA | |

1. | Initialize a constant sampling frequency denoted as ${f}_{const}$, sample a number of N for later use; store the samples in a sequence as $S$; |

2. | Predetermine a threshold t according to the characteristics of the monitored parameter; |

3. | Define $D=\frac{\left|{X}_{i+1}-{X}_{i}\right|}{\frac{1}{N}{{\displaystyle \sum}}_{i-N+1}^{i}{X}_{i}}$; |

4. | Define ${f}_{curr}$ = ${f}_{const}$; |

5. | for (i = N; i++) { |

6. | Sample ${X}_{i+1}$ based on ${f}_{curr}$ (or ${f}_{curr}{}^{\prime}$); |

7. | $D=\frac{\left|{X}_{i+1}-{X}_{i}\right|}{\frac{1}{N}{{\displaystyle \sum}}_{i-N+1}^{i}{X}_{i}}$; |

8. | $y(D)=\frac{2}{1+{e}^{-(D-t)}}$ ; |

9. | ${f}_{new}={f}_{curr}\times y\left(D\right)$; |

10. | ${f}_{curr}{}^{\prime}={f}_{new}$; |

11. | $\mathrm{S}\left(i+1\right)={X}_{i+1}$;} |

12. | end |

13. | return S; |

_{curr}to multiply y(D) (greater than 1 but lower than 2) in each iteration for multiple times after comparing the latest acquired data with a set of past-period data. As a result, this data-driven scheme allows the energy to be reasonably either consumed or conserved, as it is the trend of the sensed data rather than certain unusually high or low value data that decides future sampling frequency.

## 4. Illustrative Simulation

## 5. Simulation Results

## 6. Model Validation

_{i}is the sensed data amongst the training set. Afterwards, based on the very threshold value, a NME will be obtained comparing the reconstructed signal against the training set. If each of the five subsets is denoted as A, B, C, D and E separately, the outcome for the cross-validation is presented in Table 4.

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Original dissolved oxygen (DO) Data; (

**b**) Sampled DO data with t = 0.01; (

**c**) Sampled DO data with t = 0.015; (

**d**) Sampled DO data with t = 0.02.

**Figure 5.**(

**a**) Sampled DO data with t = 0.03 and t = 0.07; (

**b**) Frequency trend with t = 0.03 and t = 0.07.

**Figure 6.**(

**a**) Original Turbidity data; (

**b**) Sampled Turbidity data with t = 0.110; (

**c**) Sampled Turbidity data with t = 0.112; (

**d**) Sampled Turbidity data with t = 0.115.

**Figure 10.**(

**a**) Original Temperature data from Intel Berkeley Research Lab; (

**b**) Sampled Temperature data with 0.0016.

t = 0.01 | t = 0.015 | t = 0.02 | t = 0.03 | t = 0.07 | |
---|---|---|---|---|---|

Number of Samples | 1064 | 548 | 421 | 297 | 146 |

Normalized Mean Error (NME) | 1.62% | 5.52% | 8.43% | 9.99% | 11.70% |

t = 0.110 | t = 0.112 | t = 0.115 | t = 0.120 | t = 0.140 | |
---|---|---|---|---|---|

Number of Samples | 1591 | 422 | 320 | 244 | 172 |

NME | 1.14% | 4.26% | 5.33% | 5.39% | 6.16% |

**Table 3.**Performance comparison between ASA and data-driven adaptive sampling algorithm (DDASA) using DO data.

DDASA (t = 0.115) | DDASA (t = 0.112) | ASA | DDASA (t = 0.110) | Fixed Rate Sampling (f = 1/3600 Hz) | |
---|---|---|---|---|---|

Number of Samples | 320 | 422 | 637 | 1591 | 2182 |

NME | 5.33% | 4.26% | 5.31% | 1.14% | 0 |

Remaining Battery Level | 86.03% | 82.86% | 80.72% | 75.19% | 55.37% |

Training Sets | ABCD | ABCE | ABED | ACED | BCED |
---|---|---|---|---|---|

Testing set | E | D | C | B | A |

Threshold | 0.0102 | 0.0113 | 0.0115 | 0.0120 | 0.0136 |

NME | 3.37% | 3.40% | 3.12% | 2.53% | 2.25% |

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**MDPI and ACS Style**

Shu, T.; Xia, M.; Chen, J.; De Silva, C. An Energy Efficient Adaptive Sampling Algorithm in a Sensor Network for Automated Water Quality Monitoring. *Sensors* **2017**, *17*, 2551.
https://doi.org/10.3390/s17112551

**AMA Style**

Shu T, Xia M, Chen J, De Silva C. An Energy Efficient Adaptive Sampling Algorithm in a Sensor Network for Automated Water Quality Monitoring. *Sensors*. 2017; 17(11):2551.
https://doi.org/10.3390/s17112551

**Chicago/Turabian Style**

Shu, Tongxin, Min Xia, Jiahong Chen, and Clarence De Silva. 2017. "An Energy Efficient Adaptive Sampling Algorithm in a Sensor Network for Automated Water Quality Monitoring" *Sensors* 17, no. 11: 2551.
https://doi.org/10.3390/s17112551