# Dissolved Oxygen Forecasting in Aquaculture: A Hybrid Model Approach

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## Abstract

**:**

## 1. Introduction

## 2. Related Literature Review

## 3. Methodology

#### 3.1. Proposed Model Design

#### 3.1.1. Ensemble Empirical Mode Decomposition

#### 3.1.2. LSTM Neural Network

- (a)
- Forget gate equation:$${F}_{t}=\sigma \left({W}_{f}\times \left[{h}_{t-1},{X}_{t}\right]+{b}_{f}\right)$$
- (b)
- Input gate equations:$${I}_{t}=\sigma \left({W}_{i}\times \left[{h}_{t-1},{X}_{t}\right]+{b}_{i}\right)$$$${\widehat{I}}_{t}=\mathrm{tanh}\left({W}_{i}\times \left[{h}_{t-1},{X}_{t}\right]+{b}_{i}\right)$$
- (c)
- Output gate equations:$${O}_{t}=\sigma \left({W}_{o}\times \left[{h}_{t-1},{X}_{t}\right]+{b}_{o}\right)$$$${h}_{t}={O}_{t}\times \mathrm{tanh}\left({C}_{t}\right)$$
- (d)
- Cell state equation:$${C}_{t}=\left\{\left({F}_{t}\times {C}_{t-1}\right)+\left({I}_{t}\times {\widehat{I}}_{t}\right)\right\}$$

#### 3.1.3. Novel Hybrid EEMD-Based LSTM model

## 4. Experiments and Results

#### 4.1. Water Quality Dataset Acquisition

#### 4.2. Data Normalization

#### 4.3. Problem Formulation

#### 4.4. Performance Evaluation Metrics

## 5. Discussions

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The structure of long short-term memory (LSTM) neural networks (NN) blocks with their corresponding symbols and meanings.

**Figure 5.**Non-stationary continuous signal composed of sinusoidal waves with a distinct change in frequency.

**Figure 6.**Short-term (6 h) forecast result measured against actual dissolved oxygen (DO) concentration values.

Error Statistics | 12 Hour Forecast | 1 Month Forecast |
---|---|---|

MAE | 0.0753 | 0.1666 |

MSE | 0.0065 | 0.0385 |

RMSE | 0.0807 | 0.1962 |

MAPE | 0.0093 | 0.0206 |

Error Statistics | LSTM NN | BPNN | SAE-LSTM NN | SAE-BPNN | EEMD-LSTM NN |
---|---|---|---|---|---|

Run Time(s) | 23.2 | 3.6 | 29.6 | 9.1 | 2.37 |

MAE | 0.1590 | 0.4530 | 0.1260 | 0.4060 | 0.0753 |

MSE | 0.0398 | 0.3013 | 0.0242 | 0.2428 | 0.0065 |

RMSE | 0.1995 | 0.5489 | 0.1556 | 0.4927 | 0.0807 |

MAPE | 0.0160 | 0.0450 | 0.0130 | 0.0419 | 0.0093 |

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**MDPI and ACS Style**

Eze, E.; Ajmal, T.
Dissolved Oxygen Forecasting in Aquaculture: A Hybrid Model Approach. *Appl. Sci.* **2020**, *10*, 7079.
https://doi.org/10.3390/app10207079

**AMA Style**

Eze E, Ajmal T.
Dissolved Oxygen Forecasting in Aquaculture: A Hybrid Model Approach. *Applied Sciences*. 2020; 10(20):7079.
https://doi.org/10.3390/app10207079

**Chicago/Turabian Style**

Eze, Elias, and Tahmina Ajmal.
2020. "Dissolved Oxygen Forecasting in Aquaculture: A Hybrid Model Approach" *Applied Sciences* 10, no. 20: 7079.
https://doi.org/10.3390/app10207079