# Data Modeling of Sewage Treatment Plant Based on Long Short-Term Memory with Multilayer Perceptron Network

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## Abstract

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^{2}. The experimental results show that the LMPNet model demonstrates great accuracy in the modeling of the control of WWTPs. A life-long learning strategy is also developed for the LMPNet in order to adapt to the environment that may change over time. By developing performance evaluation metrics, the purification performance can be analyzed, and the prediction reference can be provided for the subsequent control optimization and energy saving plan.

## 1. Introduction

## 2. Methodology

#### 2.1. The Setup of the Studied WWTP

#### 2.2. Dataset and Preprocessing

_{in}, pH

_{in}, NH3-N

_{in}at the influent end, COD

_{out}, pH

_{out}, NH3-N

_{out}at the effluent end, power consumption per hour Power

_{1h}, temperature, instantaneous flow rate at the effluent outflow, DO, fan 1 running status F1

_{run}, and fan 2 running status F2

_{run}. The data cleaning and pre-processing are essential to ensure the optimization of the LMPNet model, and therefore the recorded data were applied with the following steps before being used for the training and testing of the LMPNet:

- In the case of data missing due to failure in sensor communication, the previous value before the missing data will be used.
- In this WWTP setup, the sampling interval of the sensor is one minute, and in most of the time, the data value does not vary obviously within this interval. Therefore, in order to improve the learning efficiency, the mean value of the data within one hour is taken as the sampling point; in this way, there are 24 samples per day that will be recorded.
- For the fan operation status, the on status corresponds to the value 1, and the off status is 0.

_{out}and Power

_{1h}[7,30], such that,

_{out}and NH3-N

_{out}, indicating that the COD content in this WWTP is related to the NH3-N content. F1

_{run}and F2

_{run}are in a regular alternating state of on and off, which presents the maximum negative correlation (−1), while the COD, NH3-N, and pH at the input and output are positively correlated (0.2~0.6) with each other. It can be seen that Power_1h shows the largest positive correlation (0.782) with the influent discharge outflow. The largest negative correlation (−0.468) is between the DO and NH3-N. Pearson’s correlation can only be used for the preliminary analysis of the intra-class correlation and the inter-class discriminability of the training set; however, there may be a very complex nonlinear correlation within the data which cannot be reflected.

## 3. The LMPNet Model

#### 3.1. The Hyperparameters Selection

#### 3.2. The Structure of the LMPNet

**x**

_{t}, such that,

#### 3.3. Performance Evaluation

^{2}) were introduced to evaluate the prediction results of the LMPNet, such that,

^{2}values of the COD

_{out}, pH

_{out}, and NH3-N

_{out}, respectively. The value ranges of Equations (12) and (13) are $\mathrm{M}\mathrm{S}\mathrm{E},\mathrm{M}\mathrm{A}\mathrm{E}$ ∈ [0, +∞) and ${\mathrm{R}}^{2}$ ∈ [0, 1], respectively. The smaller the MSE value, the closer the ${\mathrm{R}}^{2}$ is to 1 and the better the prediction performance that is achieved [38].

#### 3.4. Model Lifelong Learning

## 4. Experimental Results and Discussion

#### 4.1. Output Water Quality Prediction with LMPNet

_{out}, pH

_{out}, and NH3-N

_{out}are [2.129, 0.006, 0.706] and [1.198, 0.054, 0.650], respectively, and the values of the three elements of R

^{2}are [0.799, 0.490, 0.824]. The pH data remain in a small range of around 7, which makes it difficult for the model to learn the nonlinear mapping within the data, and it only learns to output a value very close to 7. The value range of COD

_{out}is the largest (20~34), and the maximum absolute error of prediction is only 2.45. The mean absolute percentage error (MAPE) of the model predictions for COD

_{out}, pH

_{out}and NH3-N

_{out}are 4.6%, 0.8%, and 12.3%. It can be seen that the prediction accuracy of LMPNet meets the engineering requirements, and the prediction output of COD

_{out}, pH

_{out}, and NH3-N

_{out}can effectively indicate a warning to the possible substandard of wastewater purification. The actual and predicted RE results are compared in Figure 7 to evaluate the efficiency of the proposed LMPNet model. The results showed that the curve fit of the RE is satisfactory due to the accurate prediction by LMPNet, which will be useful in the optimization of the automation and control of a WWTP.

#### 4.2. The Ablation of the Input Water Quality Characteristics

_{out}, pH

_{out}, and NH3-N

_{out}values, defined as ${\mathrm{M}\mathrm{A}\mathrm{E}}_{base}$; the absence or distortion of any one of the three parameters resulted in an increase in the MAE values. If the ith element of the input data was removed from the input vector, leaving x

_{t}only 11 elements in the same order, the resulting MAE value vector was denoted as ${\mathrm{M}\mathrm{A}\mathrm{E}}_{i}$, and its deviation from the ${\mathrm{M}\mathrm{A}\mathrm{E}}_{base}$ is given as,

_{out}and COD

_{in}, pH

_{out}and pH

_{in}, and NH3-N

_{out}and NH3-N

_{in}, respectively. The rest of the water quality features have very little influence on the three predicted elements when removed from the input. These results show the effectiveness of the LMPNet on the water quality prediction in a 9-hour time period because these water quality features are always within a relatively stable value range, and any fluctuation in an input parameter will result in an offset of the prediction for the corresponding output feature.

#### 4.3. Influence of Different Time Delays on Prediction

_{out}, pH

_{out}, and NH3-N

_{out}with a delay of Δt = 9 h, this section tests the LMPNet with different time delays of Δt = 6, 8, 10, 12, 14, and 16 h, respectively. Table 3 shows the performance analysis metrics of the MAE and MSE between the predicted and true values of the model. The experimental results show that LMPNet can maintain a good prediction performance within a range of time spans. The variation in prediction accuracy is related to the HRT of the wastewater treatment process.

#### 4.4. Energy Efficiency Analysis for Wastewater Purification

_{in}and NH3-N

_{in}is relatively low; the energy efficiency can be improved by adjusting the real-time power of the pumps and fans according to the R factor.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic diagram of the wastewater treatment system based on dual-mode dynamic separation.

**Figure 2.**The original values of the 12 water quality parameters measured by sensors from February to June 2022 and used for the preparation of the training and validation sets, including COD

_{in}, COD

_{out}, pH

_{in}, pH

_{out}, NH3-N

_{in}, NH3-N

_{out}, F1

_{run}, F2

_{run}, DO, temperature, Power

_{1h}, and outflow.

**Figure 5.**The decrease in the MSE loss value during training at each epoch iteration; the red curve is the training loss, while the blue curve is the validation loss. The minimum validation loss occurs at the 108th epoch with a loss value of 0.183.

**Figure 6.**Comparison of the model-predicted and actual values for the untrained testing set with 351 samples at a prediction interval Δt: 9 h.

**Figure 7.**Comparison of the predicted and actual RE for the untrained testing set with 351 samples at a prediction interval Δt: 9 h.

**Figure 8.**The chart of water quality characteristics in the ablation experiment. The Y-axis is the output features of the LMPNet model, and the X-axis is the input features that were deleted, respectively. The value in the graph is the increase in the output error ($\u2206{\rm E}$) after ignoring the corresponding feature, and the larger the value indicates that the input feature is more important to the prediction of the output feature.

**Figure 9.**The purification efficiency factor η and the synthesized purification factor R over the hours of the testing set for the WWTP.

Water Characteristics and Operating Parameters | ||||
---|---|---|---|---|

Variables | Units | Statistics | ||

Range | Mean | Std | ||

COD_{in} | mg/L | 53.2–231.6 | 131.6 | 41.5 |

COD_{out} | mg/L | 14.8–33.16 | 27.0 | 3.5 |

NH3-N_{in} | mg/L | 27.5–14.2 | 27.5 | 14.2 |

NH3-N_{out} | mg/L | 0.9–10.4 | 7.2 | 2.1 |

pH_{in} | – | 6.7–7.0 | 6.9 | 0.05 |

pH_{out} | – | 6.7–7.0 | 6.9 | 0.05 |

DO | mg/L | 16.3–17.1 | 17 | 0.1 |

temperature | °C | 25–34.3 | 29.2 | 2.9 |

Power_{1h} | kW·h | 6.9–15.4 | 10.2 | 1.9 |

outflow | L/s | 2.5–12.7 | 7.4 | 2.3 |

F1_{run} | – | 0–1 | 0.52 | 0.48 |

F2_{run} | – | 0–1 | 0.52 | 0.48 |

Hyperparameters | Optimum Values |
---|---|

Batch size | 512 |

Dropout rate | 0.5 |

Epoch | 120 |

Optimizer | Adam |

Learning rate | 0.0003 |

Weight decay | 0.0001 |

Train and validation set split ratio | 0.8 |

Loss function | MSELoss |

**Table 3.**The prediction errors of the LMPNet on the output water quality characteristics for different time delays.

Predicted Water Quality Parameters | ||||||
---|---|---|---|---|---|---|

COD_{out} | pH_{out} | NH3-N_{out} | ||||

Δt (hour) | MAE | MSE | MAE | MSE | MAE | MSE |

6 | 1.299 | 2.440 | 0.053 | 0.005 | 0.761 | 0.958 |

8 | 1.143 | 1.936 | 0.055 | 0.006 | 0.645 | 0.671 |

10 | 1.306 | 2.584 | 0.054 | 0.005 | 0.698 | 0.800 |

12 | 1.67 | 4.346 | 0.051 | 0.005 | 0.905 | 1.388 |

14 | 1.992 | 6.146 | 0.046 | 0.004 | 1.116 | 2.086 |

16 | 2.342 | 8.287 | 0.038 | 0.003 | 1.415 | 3.075 |

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## Share and Cite

**MDPI and ACS Style**

Wei, Z.; Wu, N.; Zou, Q.; Zou, H.; Zhu, L.; Wei, J.; Huang, H.
Data Modeling of Sewage Treatment Plant Based on Long Short-Term Memory with Multilayer Perceptron Network. *Water* **2023**, *15*, 1472.
https://doi.org/10.3390/w15081472

**AMA Style**

Wei Z, Wu N, Zou Q, Zou H, Zhu L, Wei J, Huang H.
Data Modeling of Sewage Treatment Plant Based on Long Short-Term Memory with Multilayer Perceptron Network. *Water*. 2023; 15(8):1472.
https://doi.org/10.3390/w15081472

**Chicago/Turabian Style**

Wei, Zhengxi, Ning Wu, Qingchuan Zou, Huanxin Zou, Liucun Zhu, Jinzhan Wei, and Hong Huang.
2023. "Data Modeling of Sewage Treatment Plant Based on Long Short-Term Memory with Multilayer Perceptron Network" *Water* 15, no. 8: 1472.
https://doi.org/10.3390/w15081472