# Water Quality Prediction Model of a Water Diversion Project Based on the Improved Artificial Bee Colony–Backpropagation Neural Network

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## Abstract

**:**

## 1. Introduction

## 2. Research Methods

#### 2.1. Research Area

_{Mn}represents permanganate index, and BOD5 represents the biochemical oxygen demand of five days. The classification can be decided by the model results, and if the classification of the sixth stage is worse than the first stage, it illustrates that there could be pollution that affects the water quality along the transfer route. As shown in Figure 1, the study area is from the first stage to the sixth stage pumping station in Jiangsu Province, and the sixth pumping station at the border of Jiangsu and Shandong is the starting point of the intake area.

#### 2.2. Research Data

_{Mn}, and tBOD5. The data of these parameters which are available for analysis are on a daily basis for a period of about 2 months, there are four periods of water transfer, 1–28 January, 2–15 March, 27 March–9 April and 21 April–10 May. Thus, the corresponding periods of the monitored data of the sixth stage are one day later than the periods mentioned above. According to the principles of accuracy, representativeness, and statistics, the training samples in this study should cover most of the possibilities which means they should occur in all the seasons that the pumping stations operate. They represent most of the cases that may occur and also the number of the training samples should be as many as possible. Thus, in this study, the water quality data of the first 50 days for DO, COD

_{Mn,}and BOD5 were used for model training, because almost all of the possibilities were covered by the first 50 sets. The remaining 16 sets of data were used for verification of the model prediction results. The statistical properties of the water quality time series data are demonstrated in Table 1. The maximum, minimum, mean value, standard deviation, skewness, and kurtosis describe the variability of those parameters. As depicted in Table 2, DL represents detection limited, the potential of hydrogen (pH), ammonia nitrogen (NH

_{3}-N), content of petroleum, and volatile phenol have low skewness coefficients. On the other hand, DO, COD

_{Mn}, BOD5 have comparatively higher skewness coefficients which indicates that there may be a difference between the median and mean value of these variables. It is probable that there are a few extreme values existing to affect the mean value of the parameters.

#### 2.3. Principle of Backpropagation Neural Network

#### 2.4. Principle of the Artificial Bee Colony Algorithm

#### 2.5. ABC-BP Neural Network Model

## 3. Research Design and Process

#### 3.1. An Improved Artificial Bee Colony Algorithm

#### 3.1.1. Defects of the ABC Algorithm

#### 3.1.2. Improvement of ABC Algorithm

#### 3.2. Experiment Setting

#### 3.2.1. Objective Function

#### 3.2.2. Parameters Initialization of the IABC-BP Algorithm

_{Mn,}and BOD5. We extracted 66 monitoring datasets of these parameters according to 2.2. The data of the first 50 days for DO, COD

_{Mn,}and BOD5 were used for model training and the remaining 16 sets of data were used for the verification of the model prediction results. Thus, we obtained the numbers of input and output node as 3 and after the times of the test as shown in Figure 4, the suitable number of neurons in the hidden layer is 7.

#### 3.3. Result Verification

#### 3.3.1. Relative Error

#### 3.3.2. Coefficient of Determination

#### 3.3.3. Nash–Sutcliffe Efficiency Coefficient

## 4. Results and Analyses

#### 4.1. Convergence Performance Analysis

#### 4.1.1. Convergence Accuracy

#### 4.1.2. Convergence Speed

#### 4.2. Results Analysis

#### 4.2.1. Relative Error (RE)

#### 4.2.2. Coefficient of Determination ${R}^{2}$

#### 4.2.3. Nash–Sutcliffe Efficiency Coefficient (NSE)

_{Mn}sometimes would seriously deviate from the actual lines. The BP neural network would become very unstable if the training samples were not enough, because it requires a large number of data for training. However, the ER project has not been completed for a long enough time and the monitoring system of the water quality has not been comprehensive enough to provide sufficient data, so that the amount of available data is limited, thus the forecast would sometimes underperform. Therefore, a more accurate model which has the ability to map nonlinear data, functions better in situations of data deficiency and also is capable of coping with unstable data needs to be further explored.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Performance of IABC-BP models with various parameter settings: (

**a**) MSE distribution at the entire range (3–10) of ${N}_{h}$; (

**b**) MSE distribution at the selected range (4–8) of ${N}_{h}$.

**Figure 6.**The comparison of fitness among the four models. (

**a**) The convergence performance from the first iteration time to the last of four models; (

**b**) The convergence performance from the first iteration time to the twentieth iteration time.

Classifi-cation | pH (Non-Dimensional) | DO ≥ (mg/L) | CODMn ≤ (mg/L) | NH_{3}-N ≤ (mg/L) | Petroleum ≤ (mg/L) | Volatile Phenol ≤ (mg/L) | BOD5 ≤ (mg/L) |
---|---|---|---|---|---|---|---|

I | 6~9 | 7.5 | 2 | 0.15 | 0.05 | 0.002 | 3 |

II | 6~9 | 6 | 4 | 0.5 | 0.05 | 0.002 | 3 |

III | 6~9 | 5 | 6 | 1.0 | 0.05 | 0.005 | 4 |

IV | 6~9 | 3 | 10 | 1.5 | 0.5 | 0.01 | 6 |

V | 6~9 | 2 | 15 | 2.0 | 1.0 | 0.1 | 10 |

Parameters | Max | Min | Mean | Std. Dev. | Skewness | Kurtosis |
---|---|---|---|---|---|---|

Water temperature (°C) | 19.00 | 6.80 | 14.29 | 4.3245 | 0.0048 | −1.8145 |

Potential of Hydrogen | 8.21 | 7.76 | 7.99 | 0.1135 | 0.0267 | −0.9186 |

Dissolved oxygen (mg/L) | 12.40 | 6.30 | 9.19 | 1.5658 | −0.2266 | −0.8880 |

Permanganate index (mg/L) | 6.00 | 3.00 | 4.81 | 0.6107 | −0.2669 | 0.6001 |

Biochemical Oxygen Demand of five days (mg/L) | 3.70 | 0.23 | 2.91 | 0.4986 | −0.1729 | −1.2901 |

Ammonia nitrogen (mg/L) | 0.93 | 1.90 | 0.49 | 0.1206 | 0.0223 | 2.6669 |

Content of petroleum (mg/L) | <DL | <DL | - | - | - | - |

Content of volatile phenol (mg/L) | <DL | <DL | - | - | - | - |

Iteration Times | Fitness_{BP} | Fitness_{PSO-BP-} | Fitness_{ABC-BP} | Fitness_{IABC-BP} |
---|---|---|---|---|

1 | 0.6770 | 0.7678 | 0.9103 | 0.9606 |

2 | 0.9372 | 0.9515 | 0.9271 | 0.9611 |

3 | 0.9443 | 0.9515 | 0.9272 | 0.9644 |

4 | 0.9461 | 0.9533 | 0.9341 | 0.9667 |

5 | 0.9469 | 0.9537 | 0.9341 | 0.9667 |

10 | 0.9493 | 0.9554 | 0.9501 | 0.9678 |

20 | 0.9507 | 0.9572 | 0.9578 | 0.9681 |

50 | 0.9514 | 0.9574 | 0.9616 | 0.9690 |

100 | 0.9515 | 0.9576 | 0.9632 | 0.9693 |

200 | 0.9515 | 0.9577 | 0.9648 | 0.9702 |

300 | 0.9515 | 0.9577 | 0.9652 | 0.9704 |

400 | 0.9515 | 0.9577 | 0.9656 | 0.9705 |

500 | 0.9515 | 0.9577 | 0.9657 | 0.9705 |

Name of Model | BP | PSO-BP | ABC-BP | IABC-BP |
---|---|---|---|---|

${R}^{2}$ | 0.658 | 0.918 | 0.942 | 0.981 |

Name of Model | BP | PSO-BP | ABC-BP | IABC-BP |
---|---|---|---|---|

$NSE$ | 0.134 | 0.296 | 0.541 | 0.805 |

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**MDPI and ACS Style**

Chen, S.; Fang, G.; Huang, X.; Zhang, Y.
Water Quality Prediction Model of a Water Diversion Project Based on the Improved Artificial Bee Colony–Backpropagation Neural Network. *Water* **2018**, *10*, 806.
https://doi.org/10.3390/w10060806

**AMA Style**

Chen S, Fang G, Huang X, Zhang Y.
Water Quality Prediction Model of a Water Diversion Project Based on the Improved Artificial Bee Colony–Backpropagation Neural Network. *Water*. 2018; 10(6):806.
https://doi.org/10.3390/w10060806

**Chicago/Turabian Style**

Chen, Siyu, Guohua Fang, Xianfeng Huang, and Yuhong Zhang.
2018. "Water Quality Prediction Model of a Water Diversion Project Based on the Improved Artificial Bee Colony–Backpropagation Neural Network" *Water* 10, no. 6: 806.
https://doi.org/10.3390/w10060806