# Hybridised Artificial Neural Network Model with Slime Mould Algorithm: A Novel Methodology for Prediction of Urban Stochastic Water Demand

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## Abstract

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## 1. Introduction

- The employment of 10 climatic factors over 16 years to assess the impact of climate change on urban water demand.
- Development and analysis of a new hybrid algorithm SMA-ANN for the water demand optimisation problem, and choosing the optimal hyperparameters of the ANN approach.
- The application of two hybrid algorithms, MVO-ANN and BSA-ANN, for analysing and validating the proposed SMA-ANN algorithm.
- Using the novel methodology, which contains data pre-processing techniques (EMD and tolerance) and hybrid SMA-ANN algorithm, to simulate the monthly stochastic pattern of water demand based on the best scenario of climatic factors over 16 years.
- Minimising the uncertainty by applying three metaheuristic algorithms for more validation, and using the ANN (stand-alone) to confirm the results of the SMA-ANN model. Additionally, employing 10 climatic factors that give scientific insight (i.e., to what extent climate change has driven water demand) for policymakers to achieve sustainability.

## 2. Case Study and Data Used

^{2}area, and the company has approximately 72,700 customers, categorised into residential, industrial and commercial [45].

^{2}), potential evapotranspiration (FA-O56) (mm), vapour pressure (VP) (hpa), rainfall (Rain) (mm), evaporation (Eva) (mm), maximum relative humidity (RHmax) (%) and minimum relative humidity (RHmin) (%) from 2000 to 2015. Figure 1 shows the time series and box plot of monthly water consumption for SEW utility. The figure reveals the decrease in water consumption due to drought, and water-conserving policies and initiatives. After that, the consumption increased, possibly because restrictions were eased after the impact of the drought lessened. It may also be due to the strategies that Melbourne Corporation pursued by upgrading the dams and relying on other resources, such as water desalination and water recycling [44].

## 3. Proposed Methodology

#### 3.1. Data Pre-Processing

- The maximum difference between the number of local maxima and minima is one.
- The mean value of an IMF is zero.

- Assume h
_{k − 1}(t) = x(t), and h_{i,k − 1}(t) = x(t), where i and k refer to the IMF number and the iteration number for finding the accurate ith IMF, respectively. - Identify all the maxima and minima points of the series h
_{i,k − 1}(t). - Connect the maxima points by cubic spline interpolation and do the same thing for the minima points. The linked maxima points are called the upper envelope, U
_{i,k − 1}(t), while the linked minima points are called the lower envelope, L_{i,k − 1}(t). - The mean of the upper and lower envelopes is found using this formula: m
_{i,k − 1}(t) = (U_{i,k − 1}(t) − L_{i,k − 1}(t))/2. - Form the following formula: h
_{i,k}(t): = h_{i,k − 1}(t) − m_{i,k − 1}(t). The component h_{i,k}(t) is primarily described as the first IMF. To determine the first IMF accurately, the h_{i,k}(t) is considered as a new signal, and the mean of upper envelope, lower envelope and the mean (i.e., U_{I,k}(t), L_{i,k − 1}(t) and m_{i,k}of the h_{i,k}(t)) are calculated. The new component h_{i,k}(t) is checked to see whether it has IMF properties or not. If it does, then it (i.e., h_{k}(t)) is identified as an IMF. If not, the process will be repeated until IMF properties are obtained. The number of the repetitions to identify an IMF is called iterations and is notated by k, while the IMF number is notated by i. - When the ith IMF is obtained, the residue is obtained: res
_{i}= h_{i,k − 1}− IMF_{i.} - The residue res
_{i}is now treated as the signal h_{i+1,k − 1}and the same steps 2–6 are repeated until no more IMFs can be extracted.

#### 3.2. Slime Mould Algorithm (SMA)

- a.
- Approaching food

_{b}represents the current individual location corresponding to high odour concentration.

- b.
- Warp food

#### 3.3. Artificial Neural Network (ANN)

#### 3.4. Hybrid Metaheuristic Algorithm-Based Artificial Neural Network

#### 3.5. Model Evaluation

^{2}, Equation (10)). In addition, a Bland–Altman scatterplot is used to graphically represent the upper and lower limits of agreement area between (actual data–simulated data) on the y-axis, and ((actual data + simulated data)/2) on the x-axis. Moreover, Augmented Dickey–Fuller (ADF) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests are used to examine the stationarity of the stochastic component for dependent and independent variables.

## 4. Results and Discussion

#### 4.1. Preparation of Dependent and Independent Variables

#### 4.2. Model Configuration

#### 4.3. Performance Evaluation

^{2}) for the SMA-ANN and ANN models. The values of R

^{2}delivered information for the linear relationship between the actual water consumption (Target, ML) and predicted water demand (Output, ML) for both models. Similar to the error tests (absolute and relative), both models offered good results according to Dawson et al. [56]. However, the value of R

^{2}for the SMA-ANN model was 0.9, which is more accurate than that of the ANN model (0.87). Additionally, the scatter data for the SMA-ANN model were falling closer to the ideal line than the scatter data for the ANN model.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**(

**A**) Monthly time series, (

**B**) box plot of normalised and cleaned municipal water consumption data.

**Table 1.**Correlation coefficients between water consumption and climatic factors in the raw and stochastic stage.

Data | Tmax | Tmin | Tmean | Rain | Eva | Srad | VP | RHmax | RHmin | FA-O56 |
---|---|---|---|---|---|---|---|---|---|---|

Raw | 0.63 | 0.61 | 0.62 | −0.10 | 0.61 | 0.60 | 0.55 | −0.59 | −0.54 | 0.63 |

Stochastic | 0.93 | 0.91 | 0.92 | −0.53 | 0.88 | 0.83 | 0.88 | −0.89 | −0.75 | 0.88 |

Climatic Factors | Tolerance Value |
---|---|

Tmax | 0.322 |

RHmin | 0.344 |

Rain | 0.867 |

Models | MAE | RMSE | MARE |
---|---|---|---|

SMA-ANN | 0.012 | 0.015 | 0.001 |

ANN | 0.013 | 0.017 | 0.015 |

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## Share and Cite

**MDPI and ACS Style**

Zubaidi, S.L.; Abdulkareem, I.H.; Hashim, K.S.; Al-Bugharbee, H.; Ridha, H.M.; Gharghan, S.K.; Al-Qaim, F.F.; Muradov, M.; Kot, P.; Al-Khaddar, R.
Hybridised Artificial Neural Network Model with Slime Mould Algorithm: A Novel Methodology for Prediction of Urban Stochastic Water Demand. *Water* **2020**, *12*, 2692.
https://doi.org/10.3390/w12102692

**AMA Style**

Zubaidi SL, Abdulkareem IH, Hashim KS, Al-Bugharbee H, Ridha HM, Gharghan SK, Al-Qaim FF, Muradov M, Kot P, Al-Khaddar R.
Hybridised Artificial Neural Network Model with Slime Mould Algorithm: A Novel Methodology for Prediction of Urban Stochastic Water Demand. *Water*. 2020; 12(10):2692.
https://doi.org/10.3390/w12102692

**Chicago/Turabian Style**

Zubaidi, Salah L., Iqbal H. Abdulkareem, Khalid S. Hashim, Hussein Al-Bugharbee, Hussein Mohammed Ridha, Sadik Kamel Gharghan, Fuod F. Al-Qaim, Magomed Muradov, Patryk Kot, and Rafid Al-Khaddar.
2020. "Hybridised Artificial Neural Network Model with Slime Mould Algorithm: A Novel Methodology for Prediction of Urban Stochastic Water Demand" *Water* 12, no. 10: 2692.
https://doi.org/10.3390/w12102692