# Comparison of Heat Demand Prediction Using Wavelet Analysis and Neural Network for a District Heating Network

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work and Theoretical Basis

#### 2.1. Wavelet Theory and Multiresolution Analysis

#### 2.2. Artificial Neural Networks

#### 2.2.1. Scaled Conjugate Gradient

#### 2.2.2. Levenberg‒Marquardt

#### 2.2.3. BFGS Quasi-Newton Backpropagation

## 3. Dataset Overview

_{−1}and P

_{+1}values. Data normalization is a necessary step to avoid node saturation, which could negatively affect the training phase. For data normalization, we used Z score normalization:

## 4. ANN and WANN Modeling

#### 4.1. Mother Wavelet Selection Criteria

- Maximum Energy Criteria

- 2.
- Minimum Shannon Entropy

_{i}is the energy probability distribution of the wavelet coefficients, defined as

- 3.
- Energy-to-Shannon Entropy ratio

_{energy}and E

_{entropy}are calculated using (Equations (8) and (9)).

#### 4.2. Decomposition Level Selection

_{2}(N), where N is the series length, to determine the decomposition level [64]. In our case, it would be 14 levels. The difference between the raw heat load series and decomposed series is clearly visible after approximation at level 11. We set the maximum decomposition level to 11; this decomposition level also involves all possible mother wavelet candidates [65]:

#### 4.3. Building WANN and ANN Models

- Hour—To capture the cyclical behavior of the series, the hour variable was encoded via sine and cosine transform:

_{−144}. Because of small differences in temperature, the average temperature at t

_{−1}and t

_{−2}is used. Lagged load L(t)—Autocorrelation analysis was used to select the most relevant historical consumption. A window of length 1008 (one week) was considered for selection. Selected lags are listed in Table 3.

- Load input raw data;
- Decompose load data using DWT into N subseries of details and approximations;
- Perform feature selection—autocorrelation, correlation analysis;
- Normalize data using mapstd function;
- Create an input matrix from selected features;
- Divide the processed data into training and testing sets;
- Create WANN models
- Compute the number of hidden neurons (2/3 of inputs)
- Train and test until error starts to increase, then stop training;
- Reconstruct predicted outputs and reconstruct signal X
_{rec}= D_{1+},…,+ D_{n}+ A_{n}; - Denormalize outputs using reverse mapstd function;
- Validate proposed models on a new dataset.

## 5. Results and Discussion

#### 5.1. Evaluation Metrics

_{i}—actual value, $\overline{{Y}_{i}}$—predicted value. The smaller results represent better prediction accuracy.

#### 5.2. WANN and ANN Prediction Comparison

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Parameter | Min | Max | Mean | Std |
---|---|---|---|---|

Temperature (°C) | −8.93 | 18.47 | 5.27 | 4.52 |

Load (MW) | 0 | 74.04 | 32.34 | 8.92 |

Input Number | Input Name | Value | Calculation |
---|---|---|---|

1. | Hour | 0–23 | Timestamp |

2. | Weekend | 0–1 | |

3. | Day of the week | 1–7 | |

4. | Temperature | Various | Exogenous |

5. | Lagged load | Various | Endogenous + timestamp |

Number | Selected Lags | Model Structure (I × h × o) | ||
---|---|---|---|---|

L(t) | T(t) | |||

D1 | 1–5 | – | 10 × h × 1 | |

D2 | 1–4, 6 | – | 10 ×h × 1 | |

D3 | 1,2,4,5,6 | – | 10 × h × 1 | |

D4 | 1–3,10–12 | – | 11 × h × 1 | |

D5 | 1–4,20–24 | – | 14 × h × 1 | |

D6 | 1–5, 39–42 | ✓ | 18 × h × 1 | |

D7 | 1–5, 79–81 | – | 13 × h × 1 | |

D8 | 1–5, 172–174 | – | 13 × h × 1 | |

D9 | 1–5, 319–321 | ✓ | 17 × h × 1 | |

A9 | 1–5 | ✓ | 14 × h × 1 | |

A6 | 1–5 | ✓ | 14 × h × 1 |

Model | Parameter | Value |
---|---|---|

BPNN and WANN | Number of hidden layers | 1 |

Number of neurons in hidden layer | 21 for ANN models Various for WANN; see Table 3 | |

Number of output neurons | 1 | |

Hidden layer activation function | tansig | |

Output layer activation function | purelin | |

Data set division train/test | random 80/20 (%) | |

Epochs | 1000 | |

Data normalization | mapstd; see (Equation (7)) | |

Training algorithms | trainlm, trainscg, trainbfg | |

Learning rate | 0.001 | |

WANN | Decomposition level | 6 and 9 |

Mother wavelet | db5 |

Models | ANN | WANN | |||||||
---|---|---|---|---|---|---|---|---|---|

Parameters | Dec. Level 6 | Dec. Level 9 | |||||||

BFG | LM | SCG | BFG | LM | SCG | BFG | LM | SCG | |

MAPE (%) | 1.91 | 1.75 | 1.83 | 0.58 | 0.36 | 0.51 | 0.98 | 0.36 | 1.51 |

RMSE (MW) | 0.88 | 0.85 | 0.89 | 0.28 | 0.16 | 0.25 | 0.39 | 0.16 | 0.56 |

MAE (MW) | 0.66 | 0.61 | 0.64 | 0.20 | 0.12 | 0.18 | 0.33 | 0.12 | 0.51 |

Improvement percentage | WANN | |||||
---|---|---|---|---|---|---|

Dec. level 6 | Dec. level 9 | |||||

BFG | LM | SCG | BFG | LM | SCG | |

MAPE | 69% | 79% | 72% | 48% | 79% | 17% |

RMSE | 68% | 81% | 71% | 55% | 81% | 37% |

MAE | 81% | 80% | 71% | 50% | 80% | 20% |

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**MDPI and ACS Style**

Kováč, S.; Micha’čonok, G.; Halenár, I.; Važan, P.
Comparison of Heat Demand Prediction Using Wavelet Analysis and Neural Network for a District Heating Network. *Energies* **2021**, *14*, 1545.
https://doi.org/10.3390/en14061545

**AMA Style**

Kováč S, Micha’čonok G, Halenár I, Važan P.
Comparison of Heat Demand Prediction Using Wavelet Analysis and Neural Network for a District Heating Network. *Energies*. 2021; 14(6):1545.
https://doi.org/10.3390/en14061545

**Chicago/Turabian Style**

Kováč, Szabolcs, German Micha’čonok, Igor Halenár, and Pavel Važan.
2021. "Comparison of Heat Demand Prediction Using Wavelet Analysis and Neural Network for a District Heating Network" *Energies* 14, no. 6: 1545.
https://doi.org/10.3390/en14061545