# A Data-Driven Multi-Regime Approach for Predicting Energy Consumption

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## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Contribution

## 2. Related Work

_{2}emissions, which have a significant impact on climate change [30]. An artificial neural network (ANN) was implemented based on the principal physical method to estimate the building energy consumption [31]. Hamzacebi demonstrated the power of the ANN for the prediction of the seasonal time series [32]. A novel method named pattern sequence-based forecasting (PSF) was developed by Alvarez et al. First, a clustering method was applied to cluster the time series data. Second, the sequence of labeled groups was calculated to predict the next day group, which increased the model performance for the specified group of the time series [33]. Hill et al. compared the traditional statistical method and the neural network method on the time series forecasting [14]. Similarly, Tso et al. showed that the decision tree and the neural network outperformed the regression method for the Hong Kong energy-consumption prediction [34]. Kankal et al. used four independent variables, gross domestic product, population, and the amount of import and export, and implemented an ANN to forecast energy demand [38]. A genetic algorithm and ANN were integrated by Azadeh et al. to forecast electricity demand for agricultural activities by using stochastic procedures [39]. Wang et al. developed a method to select secondary variables data from the cooling energy consumption dataset, and the model discovered periodicity over the time series. As a result, the model could predict energy consumption more precisely compared to the conventional methods [40].

## 3. Methodology

## 4. Experiments

#### 4.1. Dataset

#### 4.2. Experimental Results

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

ANN | Artificial neural network |

$\beta $ | Bias |

C | Chunk no |

CO_{2} | Carbon dioxide |

dB | Decibel |

DNN | Deep neural network |

Err | Error rate |

E | Error rate of the neural network |

f | activation function |

h | The number of hidden nodes |

kWh | Kilowatt-hour |

M | Model no |

MAE | Mean absolute error |

MAPE | Mean absolute percentage error |

MRA | Multi-Regime approach |

n | The number of input nodes |

NC | Total number of chunks |

NM | Number of models |

psi | Pounds per square inch |

PSF | Pattern sequence-based forecasting |

ReLU | Rectified linear unit |

RF | Random forest |

RMSE | Root mean square error |

SAG | Semi-autonomous grinding mill |

SME | Subject matter expert |

SVR | Support vector regression |

${S}_{OV}$ | The sum of the output variable |

t | Time index |

tanh | Hyperbolic tangent function |

Th | Threshold value |

TPH | Ton per hour |

${O}_{V}$ | Mill energy consumption values |

${W}_{b}$,${W}_{j}$,${W}_{bj}$,${W}_{ij}$ | The weights for the neural network connections |

Wt | Window timing |

${y}_{t}$ | The output variable |

${y}_{t-i}$ | Input variables |

## Appendix A

Chunk No. | RMSE (kW) | MAE (kW) | MAPE | Model No. | Data Size | DNN Model Details |
---|---|---|---|---|---|---|

Chunk-1 | 558.606 | 399.851 | 4.07% | 1 | 884 | 4 layers each with 50 neurons, 80% training, 20% testing |

Chunk-2 | 369.197 | 277.147 | 2.75% | 2 | 1134 | 3 layers each with 50 neurons, 80% training, 20% testing |

Chunk-3 | 374.185 | 289.057 | 2.96% | 3 | 1006 | 3 layers each with 100 neurons, 80% training, 20% testing |

Chunk-4 | 286.719 | 234.354 | 2.27% | 4 | 918 | 5 layers each with 50 neurons, 80% training, 20% testing |

Chunk-5 | 251.755 | 191.603 | 1.85% | 5 | 449 | 4 layers each with 50 neurons, 70% training, 30% testing |

Chunk-6 | 391.644 | 305.965 | 3.17% | 6 | 2338 | 5 layers each with 50 neurons, 80% training, 20% testing |

Chunk-7 | 434.867 | 290.972 | 3.05% | 7 | 381 | 4 layers each with 100 neurons, 70% training, 30% testing |

Chunk-8 | 374.29 | 270.084 | 2.86% | 8 | 535 | 4 layers each with 150 neurons, 70% training, 30% testing |

Chunk-9 | 455.702 | 338.252 | 3.61% | 9 | 919 | 4 layers each with 50 neurons, 80% training, 20% testing |

Chunk-10 | 293.248 | 235.917 | 2.48% | 10 | 624 | 4 layers each with 50 neurons, 70% training, 30% testing |

Chunk-11 | 471.422 | 354.039 | 3.87% | 11 | 435 | 3 layers each with 50 neurons, 70% training, 30% testing |

Chunk-12 | 336.583 | 261.434 | 2.74% | 12 | 306 | 3 layers each with 100 neurons, 70% training, 30% testing |

Chunk-13 | 372.154 | 266.002 | 2.68% | 13 | 906 | 5 layers each with 50 neurons, 80% training, 20% testing |

Chunk-14 | 527.264 | 389.147 | 3.90% | 14 | 689 | 4 layers each with 150 neurons, 70% training, 30% testing |

Chunk-15 | 397.105 | 310.283 | 3.06% | 15 | 1138 | 4 layers each with 50 neurons, 80% training, 20% testing |

Chunk-16 | 405.892 | 310.186 | 3.19% | 16 | 2871 | 4 layers each with 50 neurons, 70% training, 30% testing |

Chunk-17 | 488.183 | 339.273 | 3.51% | 17 | 1711 | 3 layers each with 100 neurons, 70% training, 30% testing |

Chunk-18 | 450.178 | 331.914 | 3.70% | 18 | 1272 | 4 layers each with 100 neurons, 70% training, 30% testing |

Chunk-19 | 334.007 | 253.484 | 2.75% | 19 | 406 | 4 layers each with 50 neurons, 70% training, 30% testing |

Chunk-20 | 465.403 | 345.34 | 3.99% | 20 | 1719 | 4 layers each with 100 neurons, 70% training, 30% testing |

Chunk-21 | 283.137 | 227.15 | 2.53% | 21 | 462 | 5 layers each with 100 neurons, 70% training, 30% testing |

Chunk-22 | 596.904 | 407.922 | 4.48% | 22 | 959 | 5 layers each with 100 neurons, 70% training, 30% testing |

Chunk-23 | 272.855 | 209.01 | 1.83% | 23 | 228 | 3 layers each with 100 neurons, 70% training, 30% testing |

**Figure A1.**Prediction performance for static Model-1 (Traditional Approach), where the x-axes represent the time and the y-axes reflect the value.

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**Figure 1.**SAG Mill inputs and output, where the x-axes represent the time and the y-axes reflect the value.

**Figure 5.**The distribution of the feature variables, where the x-axes represent the actual value, and the y-axes reflect the frequency.

**Figure 6.**The daily cumulative SAG mill energy consumption values over three years, where the x-axes represent the time, and the y-axes reflect the value.

**Figure 7.**Prediction performance for the MRA method over the distinctive chunks, where the x-axes represent the time, and the y-axes reflect the value.

**Figure 8.**Comparison of the traditional approach and the MRA method, where the x-axes represent the time and the y-axes reflect the value.

Feed Particular Size (cm) | Mill Density (%) | Fresh Feed Amount (TPH) | Mill Sound (dB) | Mill Pressure (psi) | Mill Energy Consumption (kWh) | |
---|---|---|---|---|---|---|

Mean | 3.47 | 80.65 | 1069.23 | 30.26 | 895.61 | 9756.94 |

Standard Deviation | 1.09 | 3.10 | 372.78 | 11.6 | 66.09 | 780.95 |

Minimum | 0.28 | 60.02 | 0 | 7.04 | 240.895 | 492.60 |

Maximum | 16.54 | 98.11 | 2196.72 | 99.1 | 1054.39 | 13,009.76 |

Chunk No. | RMSE (kW) | MAE (kW) | MAPE | General MAPE Moving Average | Data Size |
---|---|---|---|---|---|

Chunk-1 | 558.606 | 399.851 | 4.07% | 4.07% | 884 |

Chunk-2 | 482.829 | 377.286 | 3.76% | 3.92% | 1134 |

Chunk-3 | 619.539 | 508.141 | 5.27% | 4.37% | 1006 |

Chunk-4 | 636.746 | 478.183 | 6.72% | 4.96% | 918 |

Chunk-5 | 471.063 | 385.239 | 3.77% | 4.72% | 449 |

Chunk-6 | 599.276 | 477.449 | 5.03% | 4.77% | 2338 |

Chunk-7 | 501.044 | 383.753 | 3.91% | 4.65% | 381 |

Chunk-8 | 927.837 | 723.436 | 8.02% | 5.07% | 535 |

Chunk-9 | 855.624 | 701.537 | 7.74% | 5.37% | 919 |

Chunk-10 | 857.830 | 672.027 | 7.28% | 5.56% | 624 |

Chunk-11 | 891.772 | 704.841 | 8.07% | 5.79% | 435 |

Chunk-12 | 531.324 | 421.940 | 4.46% | 5.68% | 306 |

Chunk-13 | 510.956 | 387.609 | 3.99% | 5.55% | 906 |

Chunk-14 | 700.204 | 544.330 | 5.22% | 5.52% | 689 |

Chunk-15 | 496.442 | 385.021 | 3.84% | 5.41% | 1138 |

Chunk-16 | 957.800 | 811.572 | 8.63% | 5.61% | 2871 |

Chunk-17 | 685.724 | 501.897 | 5.27% | 5.59% | 1711 |

Chunk-18 | 1644.924 | 1464.499 | 16.67% | 6.21% | 1272 |

Chunk-19 | 1647.166 | 1537.029 | 17.76% | 6.81% | 406 |

Chunk-20 | 1771.213 | 1556.966 | 18.42% | 7.40% | 1719 |

Chunk-21 | 1718.737 | 1616.370 | 18.36% | 7.92% | 462 |

Chunk-22 | 1767.231 | 1628.439 | 18.43% | 8.40% | 959 |

Chunk-23 | 1053.187 | 811.229 | 7.33% | 8.35% | 228 |

Chunk No. | RMSE (kW) | MAE (kW) | MAPE < Threshold (10%) | General MAPE Moving Average | Data Size | Regime-Model No. | Are There Any Old Models? |
---|---|---|---|---|---|---|---|

Chunk-1 | 558.606 | 399.851 | 4.07% | 4.07% | 884 | 1 | No |

Chunk-2 | 482.829 | 377.286 | 3.76% | 3.92% | 1134 | 1 | No |

Chunk-3 | 619.539 | 508.141 | 5.27% | 4.37% | 1006 | 1 | No |

Chunk-4 | 636.746 | 478.183 | 6.72% | 4.96% | 918 | 1 | No |

Chunk-5 | 471.063 | 385.239 | 3.77% | 4.72% | 449 | 1 | No |

Chunk-6 | 599.276 | 477.449 | 5.03% | 4.77% | 2338 | 1 | No |

Chunk-7 | 501.044 | 383.753 | 3.91% | 4.65% | 381 | 1 | No |

Chunk-8 | 927.837 | 723.436 | 8.02% | 5.07% | 535 | 1 | No |

Chunk-9 | 855.624 | 701.537 | 7.74% | 5.37% | 919 | 1 | No |

Chunk-10 | 857.830 | 672.027 | 7.28% | 5.56% | 624 | 1 | No |

Chunk-11 | 891.772 | 704.841 | 8.07% | 5.79% | 435 | 1 | No |

Chunk-12 | 531.324 | 421.940 | 4.46% | 5.68% | 306 | 1 | No |

Chunk-13 | 510.956 | 387.609 | 3.99% | 5.55% | 906 | 1 | No |

Chunk-14 | 700.204 | 544.330 | 5.22% | 5.52% | 689 | 1 | No |

Chunk-15 | 496.442 | 385.021 | 3.84% | 5.41% | 1138 | 1 | No |

Chunk-16 | 957.800 | 811.572 | 8.63% | 5.61% | 2871 | 1 | No |

Chunk-17 | 685.724 | 501.897 | 5.27% | 5.59% | 1711 | 1 | No |

Chunk-18 | 1644.924 | 1464.499 | 16.67% | 6.21% | 1272 | 1 | No |

Chunk-18 | 450.178 | 331.914 | 3.70% | 5.49% | 1272 | 2 | Yes |

Chunk-19 | 387.165 | 287.935 | 3.17% | 5.36% | 406 | 2 | Yes |

Chunk-20 | 1172.610 | 981.431 | 10.67% | 5.63% | 1719 | 2 | Yes |

Chunk-20 | 1771.213 | 1556.966 | 18.42% | 6.02% | 1719 | 1 | No |

Chunk-20 | 465.403 | 345.34 | 3.99% | 5.30% | 1719 | 3 | Yes |

Chunk-21 | 623.416 | 525.236 | 5.74% | 5.32% | 462 | 3 | Yes |

Chunk-22 | 1125.931 | 784.768 | 8.20% | 5.45% | 959 | 3 | Yes |

Chunk-23 | 2354.083 | 2272.379 | 20.14% | 6.09% | 228 | 3 | Yes |

Chunk-23 | 1053.187 | 811.229 | 7.33% | 5.53% | 228 | 1 | Yes |

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## Share and Cite

**MDPI and ACS Style**

Kahraman, A.; Kantardzic, M.; Kahraman, M.M.; Kotan, M. A Data-Driven Multi-Regime Approach for Predicting Energy Consumption. *Energies* **2021**, *14*, 6763.
https://doi.org/10.3390/en14206763

**AMA Style**

Kahraman A, Kantardzic M, Kahraman MM, Kotan M. A Data-Driven Multi-Regime Approach for Predicting Energy Consumption. *Energies*. 2021; 14(20):6763.
https://doi.org/10.3390/en14206763

**Chicago/Turabian Style**

Kahraman, Abdulgani, Mehmed Kantardzic, Muhammet Mustafa Kahraman, and Muhammed Kotan. 2021. "A Data-Driven Multi-Regime Approach for Predicting Energy Consumption" *Energies* 14, no. 20: 6763.
https://doi.org/10.3390/en14206763