# District Heating Load Prediction Algorithm Based on Feature Fusion LSTM Model

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Feature Analysis and Selection of Heating Load in SDHS

- (1)
- Internal factors:
- Historical heat load (GJ)
- Secondary supply temperature (supply temp for short) (°C)
- Secondary return temperature (return temp for short) (°C)
- Instantaneous flow rate (flow rate for short) (m
^{3}/h)

- (2)
- External factors:
- Outdoor temperature (outdoor temp for short) (°C)

## 3. Methodology and Analysis

#### 3.1. The Architecture of the Proposed FFLSTM

#### 3.2. The Mathmatical Model of FFLSTM

_{1}indicates a predictive model of the proximity data;

_{2}indicates a predictive model of periodic data;

_{3}indicates a predictive model of trend data;

- ${\mathit{x}}_{h-i}$ represents the input vector composed of the outdoor temperature, heat consumption, secondary supply temperature, secondary return temperature, and instantaneous flow rate in the (h-i)th hour. The hours factor p = (1,2,…,24) represents the interval from the predicted time of the proximity input data, ranging from 1 to 24 h.
- ${\mathit{x}}_{h-24j}$ represents the input vectors such as the outdoor temperature, heat consumption, secondary supply temperature, secondary return temperature, and instantaneous flow in the (h-24j)th hour. The days factor q = (1,2,…,7) represents the interval from the predicted time of the periodic input data, ranging from 1 to 7 days.
- ${\mathit{x}}_{h-24\times 7k}$ represents the input vector of the outdoor temperature, heat consumption, secondary water supply temperature, secondary water return temperature, and instantaneous flow in the (h-24×7k)th hour. The weeks factor r = (1, 2, 3, 4) represents the interval from the predicted time of the trend input data, ranging from 1 to 4 weeks.

^{o}), heat load (Q), secondary supply temperature (T

^{S}), secondary return temperature (T

^{R}), and instantaneous flow (F) are considered to build the predictive model for the purpose of achieving a more accurate prediction performance.

_{h,i}denotes the ith instantaneous flow rate measurement value at the hth hour; and

_{h}denotes the average instantaneous flow rate value at the hth hour; and

_{h}denotes the average heat load value at the hth hour.

#### 3.3. Evaluation Criteria

_{i}and P

_{i}represent the true value and predicted value of the heat load, respectively, and n represents the total number of the test samples.

## 4. Experiments and Discussion

#### 4.1. System Background and Data Description

#### 4.2. Time Delay Factors Selection and Different Time-Scale Models

_{i}and y

_{i}represent two different variables, $\overline{x}$ represents the mean of x

_{i}, $\overline{y}$ represents the mean of y

_{i}, and corr represents the correlation between variables x

_{i}and y

_{i}.

#### 4.3. Parameter Selection and Performance Evaluation

#### 4.4. Compared with the Base LSTM Models

#### 4.5. Compared with Other Algorithms

#### 4.6. System Verification and Energy Saving Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

ANFIS | adaptive neuro-fuzzy inferences system |

ANN | artificial neural networks |

BP | back propagation |

DHS | district heating system |

DL | deep learning |

ELM | extreme learning machines |

ETR | extra trees regression |

FFA | firefly algorithm |

FFLSTM | feature fusion long short-term memory |

GA | genetic algorithm |

GA–SVR | genetic algorithm–support vector regression |

GBR | gradient boosting regression |

IA | immune algorithm |

IoT | Internet of Things |

LSTM | long short-term memory |

MAE | mean absolute error |

MAPE | mean absolute percentage error |

MVA | multivariate autoregressive |

N-LSTM | proximity LSTM |

PLS | Partial Least Square |

P-LSTM | periodic LSTM |

PM10 | particulate matter 10 |

PSO | particle swarm optimization |

RBF | radial kernel function |

RFR | random forest regression |

RMSE | root-mean-square error |

RNN | recurrent neural networks |

RT | regression tree |

SCADA | supervisory control and data acquisition |

SDHS | smart district heating system |

SVM | support vector machine |

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**Figure 2.**Correlation of heat load versus each of the influencing factors. (

**a**) Historical heat load, (

**b**) outdoor temperature, (

**c**) second supply temperature, (

**d**) second return temperature, and (

**e**) instantaneous flow rate.

**Figure 3.**The overall architecture of the prediction based on the fusion algorithm of time feature extraction.

**Figure 4.**Evaluation of the results of the root-mean-square error (RMSE) for station A and B, respectively.

**Figure 5.**Evaluation of the results of the mean absolute error (MAE) for station A and B, respectively.

**Figure 6.**Evaluation of the results of the mean absolute percentage error (MAPE) for station A and B, respectively.

**Figure 7.**The operation process of the FFLSTM prediction algorithm in a smart district heating system (SDHS).

Literature | Algorithm | Influencing Factors |
---|---|---|

[3] | ARMA | outdoor temperature, heat load, behavior of the consumers |

[11] | PSO–SVR | outdoor temperature, supply water temperature, supply water pressure, circular flow, heat load |

[12] | SVM–FFA | time lagged heat load, outdoor temperature, primary return temperatures |

[14] | SVR, PLS, RT | forward temperature, return temperature, flow rate, heat load |

[15] | ELM | outdoor temperature, primary supply temperature, primary return temperature, flow on primary side |

[18] | ANFIS | outdoor temperature, primary supply temperature, primary return temperature, secondary supply temperature, secondary return temperature, flow on primary side |

Time intervals | Historical Heat load | Outdoor Temp | Supply Temp | Return Temp | Flow Rate |
---|---|---|---|---|---|

p = 1 h | 0.913 | −0.339 | 0.767 | 0.710 | 0.783 |

p = 2 h | 0.729 | −0.301 | 0.577 | 0.538 | 0.549 |

p = 3 h | 0.553 | −0.275 | 0.379 | 0.360 | 0.320 |

p = 4 h | 0.408 | 0.271 | 0.206 | 0.208 | 0.124 |

p = 5 h | 0.291 | 0.294 | 0.090 | 0.123 | 0.027 |

q =1 d | 0.765 | −0.224 | 0.768 | 0.717 | 0.693 |

q = 2 d | 0.626 | −0.219 | 0.579 | 0.396 | 0.524 |

q = 3 d | 0.151 | −0.157 | 0.045 | −0.086 | 0.140 |

q = 4 d | −0.128 | −0.117 | −0.189 | −0.283 | 0.069 |

r = 1 w | −0.529 | 0.257 | −0.545 | −0.578 | 0.390 |

r = 2 w | 0.395 | −0.126 | 0.726 | 0.691 | 0.377 |

Model | Proximity Factor (p) | Periodic Factor (q) | Trend Factor (r) |
---|---|---|---|

model 1 | 1 h | 1 d | 1 w |

model 2 | 2 h | 1 d | 1 w |

model 3 | 3 h | 1 d | 1 w |

model 4 | 1 h | 2 d | 1 w |

model 5 | 2 h | 2 d | 1 w |

model 6 | 3 h | 2 d | 1 w |

Parameters | Value | Description |
---|---|---|

hide_unit | 20 | the number of hidden cells |

learn_rate | 0.006 | the value of the learning rate |

time_step | 5 | the value of the time step |

batch_size | 20 | the value of the batch size |

iter_count | 200 | the number of iterations |

Parameters Set | Turning Parameter | Value | Train | Test | ||||
---|---|---|---|---|---|---|---|---|

RMSE | MAE | MAPE | RMSE | MAE | MAPE | |||

hide_unit = 20 time_step = 5 batch_size = 20 iter_count = 200 | learn_rate | 0.0006 | 0.027 | 0.020 | 0.007 | 0.049 | 0.039 | 0.014 |

0.0001 | 0.043 | 0.034 | 0.011 | 0.053 | 0.044 | 0.016 | ||

0.003 | 0.021 | 0.014 | 0.005 | 0.048 | 0.039 | 0.014 | ||

0.001 | 0.027 | 0.019 | 0.006 | 0.048 | 0.040 | 0.014 | ||

0.002 | 0.022 | 0.014 | 0.005 | 0.044 | 0.035 | 0.013 | ||

learn_rate = 0.002 hide_unit = 20 time_step = 5 iter_count = 200 | batch_size | 5 | 0.187 | 0.013 | 0.004 | 0.045 | 0.036 | 0.013 |

10 | 0.025 | 0.019 | 0.006 | 0.052 | 0.041 | 0.015 | ||

12 | 0.021 | 0.015 | 0.005 | 0.051 | 0.042 | 0.015 | ||

15 | 0.022 | 0.015 | 0.004 | 0.046 | 0.038 | 0.013 | ||

20 | 0.022 | 0.014 | 0.005 | 0.044 | 0.035 | 0.013 | ||

learn_rate = 0.002 hide_unit = 20 batch_size = 20 iter_count = 200 | time_step | 7 | 0.020 | 0.013 | 0.004 | 0.051 | 0.044 | 0.016 |

10 | 0.021 | 0.016 | 0.005 | 0.051 | 0.042 | 0.015 | ||

12 | 0.021 | 0.015 | 0.005 | 0.038 | 0.029 | 0.011 | ||

15 | 0.019 | 0.013 | 0.004 | 0.054 | 0.042 | 0.015 | ||

20 | 0.019 | 0.014 | 0.005 | 0.045 | 0.037 | 0.013 | ||

learn_rate = 0.002 batch_size = 20 time_step = 12 iter_count = 200 | hide_unit | 5 | 0.033 | 0.025 | 0.009 | 0.031 | 0.026 | 0.009 |

7 | 0.029 | 0.023 | 0.008 | 0.041 | 0.034 | 0.012 | ||

10 | 0.023 | 0.017 | 0.006 | 0.035 | 0.031 | 0.011 | ||

12 | 0.022 | 0.017 | 0.006 | 0.046 | 0.034 | 0.012 | ||

15 | 0.019 | 0.014 | 0.005 | 0.044 | 0.035 | 0.013 |

Parameters | Value | Description |
---|---|---|

hide_unit | 5 | the number of hidden cells |

learn_rate | 0.002 | the value of the learning rate |

time_step | 12 | the value of the time step |

batch_size | 20 | the value of the batch size |

iter_count | 200 | the number of iterations with early stopping |

Algorithm | Model | Station A | Station B | ||||
---|---|---|---|---|---|---|---|

RMSE | MAE | MAPE | RMSE | MAE | MAPE | ||

FFLSTM | model 1 | 0.043 | 0.035 | 0.012 | 0.624 | 0.491 | 0.064 |

N-LSTM | 0.050 | 0.039 | 0.014 | 0.707 | 0.575 | 0.074 | |

P-LSTM | 0.099 | 0.087 | 0.031 | 1.205 | 0.953 | 0.128 | |

T-LSTM | 0.129 | 0.113 | 0.040 | 1.061 | 0.883 | 0.118 | |

FFLSTM | model 2 | 0.044 | 0.040 | 0.014 | 0.518 | 0.414 | 0.055 |

N-LSTM | 0.045 | 0.034 | 0.012 | 0.694 | 0.593 | 0.079 | |

P-LSTM | 0.104 | 0.089 | 0.031 | 1.468 | 1.086 | 0.149 | |

T-LSTM | 0.131 | 0.107 | 0.038 | 1.038 | 0.882 | 0.117 | |

FFLSTM | model 3 | 0.039 | 0.028 | 0.010 | 0.589 | 0.453 | 0.060 |

N-LSTM | 0.039 | 0.029 | 0.010 | 0.920 | 0.699 | 0.093 | |

P-LSTM | 0.106 | 0.095 | 0.033 | 1.325 | 0.955 | 0.128 | |

T-LSTM | 0.136 | 0.105 | 0.037 | 1.223 | 1.010 | 0.131 | |

FFLSTM | model 4 | 0.048 | 0.035 | 0.012 | 0.512 | 0.422 | 0.056 |

N-LSTM | 0.048 | 0.035 | 0.013 | 0.834 | 0.597 | 0.081 | |

P-LSTM | 0.072 | 0.063 | 0.022 | 1.448 | 1.129 | 0.153 | |

T-LSTM | 0.097 | 0.081 | 0.029 | 1.511 | 1.130 | 0.157 | |

FFLSTM | model 5 | 0.065 | 0.050 | 0.018 | 0.428 | 0.335 | 0.044 |

N-LSTM | 0.066 | 0.055 | 0.020 | 0.763 | 0.614 | 0.084 | |

P-LSTM | 0.088 | 0.076 | 0.027 | 0.964 | 0.760 | 0.102 | |

T-LSTM | 0.133 | 0.101 | 0.035 | 0.999 | 0.798 | 0.109 | |

FFLSTM | model 6 | 0.042 | 0.032 | 0.012 | 0.485 | 0.381 | 0.049 |

N-LSTM | 0.045 | 0.035 | 0.013 | 0.699 | 0.579 | 0.078 | |

P-LSTM | 0.090 | 0.074 | 0.026 | 1.071 | 0.878 | 0.115 | |

T-LSTM | 0.097 | 0.078 | 0.028 | 1.232 | 1.014 | 0.136 |

Algorithm | Model | Station A | Station B | ||||
---|---|---|---|---|---|---|---|

RMSE | MAE | MAPE | RMSE | MAE | MAPE | ||

FFLSTM | model1 | 0.043 | 0.035 | 0.012 | 0.707 | 0.575 | 0.074 |

LSTM | 0.070 | 0.056 | 0.020 | 1.109 | 0.850 | 0.112 | |

BP | 0.077 | 0.065 | 0.023 | 0.750 | 0.549 | 0.073 | |

SVR(RBF) | 0.124 | 0.100 | 0.036 | 1.121 | 0.930 | 0.122 | |

RT | 0.133 | 0.106 | 0.038 | 1.216 | 0.994 | 0.131 | |

RFR | 0.133 | 0.107 | 0.038 | 1.172 | 0.957 | 0.126 | |

GBR | 0.127 | 0.103 | 0.037 | 1.201 | 0.980 | 0.128 | |

ETR | 0.139 | 0.111 | 0.040 | 1.155 | 0.947 | 0.124 | |

FFLSTM | model2 | 0.044 | 0.040 | 0.014 | 0.518 | 0.414 | 0.055 |

LSTM | 0.071 | 0.056 | 0.020 | 0.766 | 0.590 | 0.077 | |

BP | 0.060 | 0.047 | 0.017 | 1.191 | 0.966 | 0.137 | |

SVR(RBF) | 0.123 | 0.100 | 0.036 | 1.109 | 0.921 | 0.122 | |

RT | 0.140 | 0.110 | 0.039 | 1.282 | 1.042 | 0.140 | |

RFR | 0.137 | 0.111 | 0.040 | 1.210 | 0.983 | 0.128 | |

GBR | 0.133 | 0.107 | 0.039 | 1.176 | 0.960 | 0.126 | |

ETR | 0.133 | 0.108 | 0.039 | 1.157 | 0.948 | 0.124 | |

FFLSTM | model3 | 0.039 | 0.028 | 0.010 | 0.589 | 0.453 | 0.060 |

LSTM | 0.050 | 0.042 | 0.015 | 1.279 | 1.041 | 0.141 | |

BP | 0.058 | 0.046 | 0.016 | 1.191 | 0.966 | 0.137 | |

SVR(RBF) | 0.122 | 0.122 | 0.036 | 1.096 | 0.912 | 0.121 | |

RT | 0.144 | 0.114 | 0.041 | 1.393 | 1.143 | 0.150 | |

RFR | 0.131 | 0.105 | 0.038 | 1.170 | 0.964 | 0.127 | |

GBR | 0.132 | 0.107 | 0.038 | 1.173 | 0.960 | 0.127 | |

ETR | 0.132 | 0.107 | 0.038 | 1.189 | 0.972 | 0.127 | |

FFLSTM | model4 | 0.033 | 0.027 | 0.010 | 0.556 | 0.445 | 0.058 |

LSTM | 0.090 | 0.068 | 0.025 | 1.059 | 0.832 | 0.108 | |

BP | 0.066 | 0.050 | 0.018 | 1.191 | 0.966 | 0.137 | |

SVR(RBF) | 0.123 | 0.100 | 0.036 | 1.110 | 0.923 | 0.120 | |

RT | 0.133 | 0.106 | 0.038 | 1.234 | 1.006 | 0.132 | |

RFR | 0.122 | 0.098 | 0.035 | 1.210 | 0.982 | 0.128 | |

GBR | 0.142 | 0.116 | 0.041 | 1.174 | 0.963 | 0.125 | |

ETR | 0.130 | 0.106 | 0.038 | 1.167 | 0.962 | 0.126 | |

FFLSTM | model5 | 0.055 | 0.037 | 0.013 | 0.572 | 0.414 | 0.056 |

LSTM | 0.105 | 0.075 | 0.027 | 1.169 | 0.969 | 0.129 | |

BP | 0.068 | 0.051 | 0.018 | 1.191 | 0.966 | 0.137 | |

SVR(RBF) | 0.122 | 0.099 | 0.036 | 1.093 | 0.913 | 0.119 | |

RT | 0.136 | 0.107 | 0.039 | 1.283 | 1.051 | 0.139 | |

RFR | 0.131 | 0.105 | 0.038 | 1.169 | 0.962 | 0.126 | |

GBR | 0.141 | 0.115 | 0.041 | 1.149 | 0.944 | 0.123 | |

ETR | 0.129 | 0.104 | 0.038 | 1.106 | 0.918 | 0.119 | |

FFLSTM | model6 | 0.030 | 0.026 | 0.009 | 0.535 | 0.404 | 0.055 |

LSTM | 0.068 | 0.054 | 0.019 | 1.540 | 1.193 | 0.166 | |

BP | 0.066 | 0.052 | 0.019 | 1.191 | 0.966 | 0.137 | |

SVR(RBF) | 0.122 | 0.098 | 0.035 | 1.086 | 0.909 | 0.119 | |

RT | 0.134 | 0.106 | 0.038 | 1.467 | 1.162 | 0.154 | |

RFR | 0.128 | 0.103 | 0.037 | 1.173 | 0.961 | 0.127 | |

GBR | 0.140 | 0.114 | 0.041 | 1.150 | 0.944 | 0.124 | |

ETR | 0.125 | 0.101 | 0.036 | 1.123 | 0.933 | 0.122 |

Algorithm | Station A | Station B |
---|---|---|

Accuracy (%) | Accuracy (%) | |

FFLSTM | 98.87 | 94.03 |

LSTM | 97.9 | 87.78 |

BP | 98.15 | 87.37 |

SVR(RBF) | 96.42 | 87.95 |

RT | 96.12 | 85.9 |

RFR | 96.87 | 87.3 |

GBR | 96.05 | 87.45 |

ETR | 96.18 | 87.63 |

Year | Heat Consumption (GJ) | |
---|---|---|

Station A | Station B | |

2017 | 10,762 | 31,601 |

2018 | 9711 | 29,010 |

Energy saving rate | 9.7% | 8.2% |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xue, G.; Pan, Y.; Lin, T.; Song, J.; Qi, C.; Wang, Z.
District Heating Load Prediction Algorithm Based on Feature Fusion LSTM Model. *Energies* **2019**, *12*, 2122.
https://doi.org/10.3390/en12112122

**AMA Style**

Xue G, Pan Y, Lin T, Song J, Qi C, Wang Z.
District Heating Load Prediction Algorithm Based on Feature Fusion LSTM Model. *Energies*. 2019; 12(11):2122.
https://doi.org/10.3390/en12112122

**Chicago/Turabian Style**

Xue, Guixiang, Yu Pan, Tao Lin, Jiancai Song, Chengying Qi, and Zhipan Wang.
2019. "District Heating Load Prediction Algorithm Based on Feature Fusion LSTM Model" *Energies* 12, no. 11: 2122.
https://doi.org/10.3390/en12112122