# Application of Artificial Neural Networks for Natural Gas Consumption Forecasting

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Dataset

#### 2.2. Feature Engineering

## 3. Methodology

#### 3.1. Artificial Neural Networks (ANN)

#### 3.2. Long Short-Term Memory Networks (LSTM)

#### 3.3. Deep Neural Networks (DNN)

#### 3.4. Process Flow

#### 3.4.1. Preprocessing

#### 3.4.2. Data Split

#### 3.4.3. Standardization

#### 3.4.4. Processing

## 4. Evaluation metrics

^{2}) are all being used in order to determine the best performing model [5,7,43].

^{2}value close to 1 is preferred, signifying better performance for the model and that the regression curve is well fit on the data. A coefficient of determination value of 1 would signify that the regression line fits the data perfectly; however, this could also denote overfitting on the data.

## 5. Results

^{2}were used.

#### 5.1. Results from ANN

#### 5.2. Results from LSTM

^{2}values. LSTMs can offer excellent accuracy for single-variable time series; however, it is evident that they are highly susceptible to the depth of the forecasting period, as well as to the data that are required for proper training.

#### 5.3. Results from DNN

#### 5.4. Comparison (Cities)

^{2}. Seven out of fourteen cities achieved an accuracy of >90%, however, for the other seven cities, the performance of the model is disappointing.

^{2}as the primary metric. Here, six cities achieved an accuracy of >94%, with the rest achieving higher accuracy when compared to the ANN.

^{2}. For seven out of fourteen cities, the proposed methodology achieved an accuracy of >94%, which is considered very satisfactory for prediction, considering that the MSE of these models is also very low.

#### 5.5. Sensitivity Analysis

## 6. Discussion

^{2}for the city of Larissa (0.9846) while the LSTM implementation for the city of Athens (0.9644) and the ANN for the city of Trikala (0.699). For the worst-case scenario, the city of Agioi Theodoroi, has consistently obtained the worst accuracies, with the DNN (0.5748) achieving significant higher accuracy, even though still not so good, compared to the LSTM (0.3848) and ANN (0.1440) implementation. The dataset of Agioi Theodoroi is the smallest compared to the rest, being one reason for achieving these low accuracies. It ca be argued that the size of the city (<5000 habitants) is another important reason, since the consumption trends are sparser due its low population.

^{2}values. This can be derived from several facts. The more important is that since the dataset is finite, the further ahead in time the prediction is, the less training data the model is left with to “learn” from. Machine learning models are highly dependent on data, and their performance is highly correlated to the data quality and quantity. Particularly for the ANN approach, it’s simplistic implementation cannot capture the complexity that is required for the long-term forecasting, even if in general ANNs are powerful. Another reason is that the scale of the energy prediction units is large (in absolute numbers), thus the worse the prediction is, the larger is the penalty for it. Additionally, since the forecasting timescale increases for additionally 1, 2, and 3 years, the ill-fitted models produce large errors in predictions which are accumulated, because the forecasting time is 1, 2, and 3 times larger, respectively. The R

^{2}metric is based on the MSE, and is scale-dependent, while MAPE is not, therefore it is useful for understanding the performance of the models. It is considered that R

^{2}is still probably the best metric for forecasts [62], however, MAPE can still be used because the percentage of error makes sense and there are no zero values in our dataset.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix

**Figure A1.**Correlation of the energy demand and the mean temperature for the training set and the test set for all the examined cities.

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**Figure 1.**Natural gas energy consumption [MWh] for Athens, Thessaloniki, and Larissa over the years.

**Figure 2.**Natural gas energy consumption [MWh] for Alexandroupoli, Drama, Karditsa, and Trikala over the years.

**Figure 3.**Correlation of the energy demand and the mean temperature for the training set (

**a**) and the test set (

**b**) for the city of Athens.

**Figure 6.**Forecasts of (

**a**) one-, (

**b**) two-, (

**c**) three-, and (

**d**) four-year ahead of natural gas demand with the use of ANN.

**Figure 10.**Forecasts of (

**a**) one-, (

**b**) two-, (

**c**) three-, and (

**d**) four-year ahead of natural gas demand with the use of DNN.

**Figure 11.**Partial Dependence Plots for the dataset of Athens on the mean daily temperature for the ANN (

**a**) and the DNN (

**b**) models, and the energy consumption values of 1-day (

**c**) and 2-days (

**d**) prior.

**Table 1.**Variables that are used as output and input for each implementation of the neural network variants. ANN: Artificial neural network; LSTM: Long Short-Term Memory; DNN: Deep neural network.

Output | Inputs | ||||||
---|---|---|---|---|---|---|---|

Energy Current Day (MJ) | Daily Mean Temperature (°C) | Energy 1 Previous Day (MJ) | Energy 2 Previous Days (MJ) | Month (Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec) | Day of the Week (Mon, Tue, Wen, Thu, Fri, Sat, Sun) | Bank Holiday (Yes, No) | |

ANN | × | × | |||||

LSTM | × | ||||||

DNN | × | × | × | × | × | × | × |

City | Start Date | Ratio of Training/Testing |
---|---|---|

Agioi Theodoroi | 07/06/2014 | 3.41 |

Alexandroupoli | 02/02/2013 | 4.78 |

Athens | 01/03/2010 | 7.68 |

Drama | 07/09/2011 | 6.15 |

Karditsa | 01/05/2014 | 3.51 |

Kilkis | 01/03/2010 | 7.68 |

Lamia | 01/02/2013 | 4.75 |

Larissa | 01/03/2010 | 7.68 |

Laurio | 01/03/2010 | 7.68 |

Markopoulo | 01/03/2010 | 7.68 |

Serres | 01/06/2013 | 4.42 |

Thessaloniki | 01/03/2012 | 5.67 |

Trikala | 12/09/2012 | 5.14 |

Volos | 01/03/2010 | 7.68 |

Xanthi | 01/03/2010 | 7.68 |

**Table 3.**Performance metrics of the selected ANN architecture. MSE: Mean square error; MAE: Mean absolute error; MAPE: Mean absolute percentage error; R

^{2}: Coefficient of determination.

ANN | Architecture Selection | ||||
---|---|---|---|---|---|

Layers | Nodes | MSE (MJ^{2}) | MAE (MJ^{2}) | MAPE (%) | R^{2} |

1 | 8 | 7.70 × 10^{–3} | 7.01 × 10^{–2} | 16.41 | 0.87 |

1 Layer/ 8 Nodes | Dropout Comparison | |||
---|---|---|---|---|

Dropout | MSE (MJ^{2}) | MAE (MJ^{2}) | MAPE (%) | R^{2} |

0 | 7.70 × 10^{−3} | 7.01 × 10^{−2} | 16.41 | 0.87 |

0.25 | 8.20 × 10^{−3} | 6.94 × 10^{−2} | 30.30 | 0.86 |

0.50 | 9.00 × 10^{−3} | 7.41 × 10^{−2} | 52.74 | 0.84 |

0.75 | 1.25 × 10^{−2} | 8.66 × 10^{−2} | 73.02 | 0.78 |

1 Layer/ 8 Nodes | Forecasting Comparison | |||
---|---|---|---|---|

Years ahead | MSE (MJ^{2}) | MAE (MJ^{2}) | MAPE (%) | R^{2} |

1 | 7.70 × 10^{−3} | 7.01 × 10^{−2} | 16.41 | 0.87 |

2 | 1.08 × 10^{−1} | 3.07 × 10^{−1} | 48.61 | −1.39 |

3 | 9.28 × 10^{−2} | 2.83 × 10^{−1} | 52.46 | −1.31 |

4 | 1.42 × 10^{−1} | 3.53 × 10^{−1} | 49.73 | −2.57 |

LSTM | Architecture Selection | ||||
---|---|---|---|---|---|

Layers | Units | MSE (MJ^{2}) | MAE (MJ^{2}) | MAPE (%) | R^{2} |

1 | 200 | 2.20 × 10^{−3} | 2.95 × 10^{−2} | 11.07 | 0.96 |

1 Layer/ 200 Units | Dropout Comparison | |||
---|---|---|---|---|

Dropout | MSE (MJ^{2}) | MAE (MJ^{2}) | MAPE (%) | R^{2} |

0 | 2.20 × 10^{−3} | 2.95 × 10^{−2} | 11.07 | 0.96 |

0.25 | 2.40 × 10^{−3} | 3.31 × 10^{−2} | 20.94 | 0.96 |

0.50 | 2.20 × 10^{−3} | 3.10 × 10^{−2} | 18.50 | 0.96 |

0.75 | 2.10 × 10^{−3} | 2.92 × 10^{−2} | 9.77 | 0.96 |

1 Layer/ 8 Nodes | Forecasting Comparison | |||
---|---|---|---|---|

Years ahead | MSE (MJ^{2}) | MAE (MJ^{2}) | MAPE (%) | R^{2} |

1 | 2.10 × 10^{−3} | 2.92 × 10^{−2} | 9.77 | 0.96 |

2 | 6.30 × 10^{−3} | 5.90 × 10^{−2} | 15.00 | 0.86 |

3 | 5.26 × 10^{−2} | 2.06 × 10^{−1} | 59.06 | −0.31 |

4 | 8.73 × 10^{−2} | 2.44 × 10^{−1} | 80.87 | −1.20 |

DNN | Architecture Selection | ||||
---|---|---|---|---|---|

Layers | Nodes | MSE (MJ^{2}) | MAE (MJ^{2}) | MAPE (%) | R^{2} |

4 | 32 | 1.70 × 10^{−3} | 2.75 × 10^{−2} | 7.53 | 0.97 |

4 Layer/ 32 Nodes | Dropout Comparison | |||
---|---|---|---|---|

Dropout | MSE (MJ^{2}) | MAE (MJ^{2}) | MAPE (%) | R^{2} |

0 | 1.70 × 10^{−3} | 2.75 × 10^{−2} | 7.53 | 0.97 |

0.25 | 2.20 × 10^{−3} | 3.11 × 10^{−2} | 10.98 | 0.96 |

0.50 | 2.90 × 10^{−3} | 4.32 × 10^{−2} | 26.45 | 0.95 |

0.75 | 3.00 × 10^{−3} | 3.82 × 10^{−2} | 48.61 | 0.95 |

4 Layer/ 32 Nodes | Forecasting Comparison | |||
---|---|---|---|---|

Years ahead | MSE (MJ^{2}) | MAE (MJ^{2}) | MAPE (%) | R^{2} |

1 | 1.70 × 10^{−3} | 2.75 × 10^{−2} | 7.53 | 0.97 |

2 | 1.50 × 10^{−3} | 2.76 × 10^{−2} | 8.98 | 0.97 |

3 | 1.30 × 10^{−3} | 2.06 × 10^{−2} | 8.68 | 0.97 |

4 | 1.70 × 10^{−3} | 3.22 × 10^{−2} | 9.40 | 0.96 |

ANN | Cities Comparison | ||||
---|---|---|---|---|---|

Cities | MSE (MJ^{2}) | MAE (MJ^{2}) | MAPE (%) | R^{2} | CI |

Agioi Theodoroi | 4.96 × 10^{−2} | 1.70 × 10^{−1} | 58.29 | 0.14 | [92,246–101,257] |

Alexandroupoli | 8.30 × 10^{−3} | 6.72 × 10^{−2} | 13.43 | 0.89 | [80,527–88,566] |

Athens | 2.40 × 10^{−3} | 3.53 × 10^{−2} | 10.94 | 0.96 | [7,710,057–9,006,556] |

Drama | 8.50 × 10^{−3} | 6.77 × 10^{−2} | 6.42 | 0.78 | [736,302–764,636] |

Karditsa | 2.60 × 10^{−3} | 3.54 × 10^{−2} | 28.66 | 0.97 | [234,893–293,622] |

Kilkis | 2.87 × 10^{−2} | 1.23 × 10^{−1} | 20.16 | 0.43 | [1,023,806–1,088,807] |

Lamia | 3.96 × 10^{−2} | 1.62 × 10^{−1} | 33.76 | 0.20 | [125,129–135,568] |

Larissa | 2.60 × 10^{−3} | 3.43 × 10^{−2} | 14.18 | 0.96 | [1,329,088–1,609,373] |

Laurio | 1.32 × 10^{−2} | 7.59 × 10^{−2} | 86,605.00 | 0.74 | [6,004,693–7,432,331] |

Markopoulo | 3.06 × 10^{−2} | 1.38 × 10^{−1} | 19.38 | 0.27 | [250,400–264,171] |

Serres | 3.60 × 10^{−3} | 4.52 × 10^{−2} | 11.69 | 0.96 | [400,111–467,284] |

Thessaloniki | 3.40 × 10^{−3} | 4.52 × 10^{−2} | 16.80 | 0.95 | [6,283,167–7,449,531] |

Trikala | 2.40 × 10^{−3} | 2.76 × 10^{−2} | 25.62 | 0.97 | [213,058–266,020] |

Volos | 3.90 × 10^{−3} | 4.92 × 10^{−2} | 11.41 | 0.91 | [1,662,841–1,845,579] |

Xanthi | 2.94 × 10^{−2} | 1.33 × 10^{−1} | 36.12 | 0.17 | [153,935–168,218] |

LSTM | Cities Comparison | ||||
---|---|---|---|---|---|

Cities | MSE (MJ^{2}) | MAE (MJ^{2}) | MAPE (%) | R^{2} | CI |

Agioi Theodoroi | 3.56 × 10^{−2} | 1.50 × 10^{−1} | 59.68 | 0.38 | [86,688–94,424] |

Alexandroupoli | 4.20 × 10^{−3} | 4.60 × 10^{−2} | 8.29 | 0.94 | [86,103–95,178] |

Athens | 2.10 × 10^{−3} | 2.92 × 10^{−2} | 9.77 | 0.96 | [7,634,555–8,986,641] |

Drama | 1.06 × 10^{−2} | 7.82 × 10^{−2} | 9.86 | 0.72 | [765,187–790,777] |

Karditsa | 8.40 × 10^{−3} | 7.61 × 10^{−2} | 72.99 | 0.89 | [290,871–357,268] |

Kilkis | 1.15 × 10^{−2} | 8.17 × 10^{−2} | 10.97 | 0.77 | [1,008,757–1,071,517] |

Lamia | 1.86 × 10^{−2} | 1.11 × 10^{−1} | 32.19 | 0.62 | [157,729–167,902] |

Larissa | 3.30 × 10^{−3} | 4.43 × 10^{−2} | 17.39 | 0.95 | [1,377,457–1,661,699] |

Laurio | 2.45 × 10^{−2} | 1.30 × 10^{−1} | 78,544.00 | 0.53 | [8,712,884–10,054,310] |

Markopoulo | 8.00 × 10^{−3} | 6.79 × 10^{−2} | 9.70 | 0.81 | [258,990–272,945] |

Serres | 4.00 × 10^{−3} | 4.85 × 10^{−2} | 15.78 | 0.96 | [375,137–443,421] |

Thessaloniki | 3.90 × 10^{−3} | 4.79 × 10^{−2} | 19.54 | 0.94 | [6,268,458–7,571,520] |

Trikala | 4.60 × 10^{−3} | 5.41 × 10^{−2} | 32.77 | 0.94 | [256,379–318,363] |

Volos | 4.80 × 10^{−3} | 5.21 × 10^{−2} | 13.18 | 0.89 | [1,480,596–1,649,836] |

Xanthi | 9.80 × 10^{−3} | 7.60 × 10^{−2} | 24.43 | 0.72 | [169,605–180,582] |

DNN | Cities Comparison | ||||
---|---|---|---|---|---|

Cities | MSE (MJ^{2}) | MAE (MJ^{2}) | MAPE (%) | R^{2} | CI |

Agioi Theodoroi | 2.46 × 10^{−2} | 1.19 × 10^{−1} | 38.70 | 0.57 | [89,946–98,778] |

Alexandroupoli | 3.00 × 10^{−3} | 4.01 × 10^{−2} | 7.57 | 0.96 | [80,268–88,430] |

Athens | 1.70 × 10^{−3} | 2.75 × 10^{−2} | 7.53 | 0.97 | [7,571,538–8,863,422] |

Drama | 1.03 × 10^{−2} | 7.69 × 10^{−2} | 7.32 | 0.73 | [729,057–757,898] |

Karditsa | 3.50 × 10^{−3} | 4.84 × 10^{−2} | 25.10 | 0.95 | [230,724–290,272] |

Kilkis | 8.20 × 10^{−3} | 6.73 × 10^{−2} | 10.36 | 0.84 | [984,497–1,049,268] |

Lamia | 1.41 × 10^{−2} | 9.71 × 10^{−2} | 21.23 | 0.71 | [126,988–137,111] |

Larissa | 1.10 × 10^{−3} | 2.40 × 10^{−2} | 9.95 | 0.98 | [1,413,437–1,698,290] |

Laurio | 2.03 × 10^{−2} | 1.17 × 10^{−1} | 78,518.00 | 0.61 | [6,822,570–8,233,887] |

Markopoulo | 6.80 × 10^{−3} | 6.29 × 10^{−2} | 10.10 | 0.84 | [245,857–259,800] |

Serres | 4.50 × 10^{−3} | 5.21 × 10^{−2} | 17.46 | 0.95 | [396,910–466,370] |

Thessaloniki | 1.60 × 10^{−3} | 2.72 × 10^{−2} | 10.25 | 0.98 | [6,289,857–7,456,553] |

Trikala | 4.40 × 10^{−3} | 5.04 × 10^{−2} | 22.98 | 0.95 | [222,492–276,310] |

Volos | 5.10 × 10^{−3} | 5.70 × 10^{−2} | 11.73 | 0.89 | [1,644,087–1,825,076] |

Xanthi | 1.02 × 10^{−2} | 7.44 × 10^{−2} | 26.04 | 0.71 | [165,997–179,896] |

**Table 15.**Comparison of results between machine learning and soft computing methods for three benchmark cities.

Cities | ||||||
---|---|---|---|---|---|---|

Athens | Thessaloniki | Larissa | ||||

Methods | MSE (MJ^{2}) | MAE (MJ^{2}) | MSE (MJ^{2}) | MAE (MJ^{2}) | MSE (MJ^{2}) | MAE (MJ^{2}) |

ANN | 7.70 × 10^{−3} | 7.01 × 10^{−2} | 3.40 × 10^{−3} | 4.52 × 10^{−2} | 2.60 × 10^{−3} | 3.43 × 10^{−2} |

LSTM | 2.10 × 10^{−3} | 2.92 × 10^{−2} | 3.90 × 10^{−3} | 4.79 × 10^{−2} | 3.30 × 10^{−3} | 4.43 × 10^{−2} |

Hybrid FCM | 3.20 × 10^{−3} | 3.28 × 10^{−2} | 3.30 × 10^{−3} | 3.81 × 10^{−2} | 4.10 × 10^{−3} | 4.17 × 10^{−2} |

Ensemble (EB) | 3.10 × 10^{−3} | 3.28 × 10^{−2} | 3.10 × 10^{−3} | 3.69 × 10^{−2} | 4.00 × 10^{−3} | 4.17 × 10^{−2} |

Proposed DNN | 1.70× 10^{−3} | 2.75× 10^{−2} | 1.60× 10^{−3} | 2.72× 10^{−2} | 1.10× 10^{−3} | 2.40× 10^{−2} |

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**MDPI and ACS Style**

Anagnostis, A.; Papageorgiou, E.; Bochtis, D.
Application of Artificial Neural Networks for Natural Gas Consumption Forecasting. *Sustainability* **2020**, *12*, 6409.
https://doi.org/10.3390/su12166409

**AMA Style**

Anagnostis A, Papageorgiou E, Bochtis D.
Application of Artificial Neural Networks for Natural Gas Consumption Forecasting. *Sustainability*. 2020; 12(16):6409.
https://doi.org/10.3390/su12166409

**Chicago/Turabian Style**

Anagnostis, Athanasios, Elpiniki Papageorgiou, and Dionysis Bochtis.
2020. "Application of Artificial Neural Networks for Natural Gas Consumption Forecasting" *Sustainability* 12, no. 16: 6409.
https://doi.org/10.3390/su12166409