# A COP Prediction Model of Hybrid Geothermal Heat Pump Systems based on ANN and SVM with Hyper-Parameters Optimization

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Analysis

#### 2.1. Hyper-Parameter

#### 2.2. COP Prediction Model Based on Machine Learning

## 3. Methodology

#### 3.1. Data Collection and Pre-Processing

- r: Pearson correlation coefficient
- $\mathrm{n}$: Number of data
- ${\mathrm{X}}_{\mathrm{i}}$: Input data
- $\overline{\mathrm{X}}$: Average of input data
- ${\mathrm{Y}}_{\mathrm{i}}$: Output data
- $\overline{\mathrm{X}}$: Average of output data

#### 3.2. Accuracy Metrics

- $P$: Predicted value
- $M$: Measured value (or simulation value)
- $n$: Number of measured data
- $\overline{P}$: Average of predicted value

## 4. COP Prediction Model Development with Hyper-Parameter Optimization

#### 4.1. Initial COP Prediction Model Development

#### 4.2. Hyper-Parameter Optimization

#### 4.2.1. ANN Hyper-Parameter Optimization

#### 4.2.2. SVM Hyper-Parameter Optimization

## 5. COP Prediction Model Accuracy Analysis with Hyper-Parameter Optimization

## 6. Conclusions

- (1)
- The data of the target building where the actual geothermal system was installed and operated were collected to develop a predictive model for the coefficient of performance of the hybrid geothermal heat pump system. The data were measured at the test bed installed with equipment that simulated a geothermal system. The learning data comprised one set of outdoor air temperature, a heat source side inlet/outlet temperature, load side inlet/outlet temperature, wattage, and COP.
- (2)
- The input variables were selected by quantitatively evaluating the relationship between the Pearson correlation coefficient and the performance coefficient to be predicted using the Pearson correlation coefficient and the determination coefficient for the collected learning data. The outlet temperature of the heat source had the highest correlation among the input variables with a Pearson correlation coefficient of −0.76 and a coefficient of determination of 0.58, and the outdoor temperature showed a relatively small relationship among the input variables with a Pearson correlation coefficient of 0.32 and a coefficient of determination of 0.10.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Kelly, J.A.; Fu, M.; Clinch, J.P. Residential home heating: The potential for air source heat pump technologies as an alternative to solid and liquid fuels. Energy Policy
**2016**, 98, 431–442. [Google Scholar] [CrossRef] [Green Version] - Kang, E.C.; Riederer, P.; Yoo, S.Y.; Lee, E.J. New approach to evaluate the seasonal performance of building integrated geothermal heat pump system. Renew. Energy
**2013**, 54, 51–54. [Google Scholar] [CrossRef] - Fischer, D.; Madani, H. On heat pumps in smart grids: A review. Renew. Sustain. Energy Rev.
**2017**, 70, 342–357. [Google Scholar] [CrossRef] [Green Version] - Zhou, C.H.; Ni, L.; Wang, J.; Yao, Y. Investigation on the performance of ASHP heating system using frequency-conversion technique based on a temperature and hydraulic-balance control strategy. Renew. Energy
**2020**, 141, 141–154. [Google Scholar] [CrossRef] - Kazjonovs, J.; Sipkevics, A.; Jakovics, A.; Dancigs, A.; Bajare, D.; Dancigs, L. Performance analysis of air-to-water heat pump in Latvian climate conditions. Environ. Clim. Technol.
**2014**, 14, 18–22. [Google Scholar] [CrossRef] [Green Version] - Szreder, M. Economical and technical aspects of using air source heat pumps for hot water. In Proceedings of the E3S Web of Conferences, Sanya, China, 19–21 November 2018; 46, p. 00014. [Google Scholar]
- Zhou, C.; Ni, L.; Li, J.; Lin, Z.; Wang, J.; Fu, X.; Yao, Y. Air-source heat pump heating system with a new temperature and hydraulic-balance control strategy: A field experiment in a teaching building. Renew. Energy
**2019**, 141, 148–161. [Google Scholar] [CrossRef] - Lazzarin, R.; Noro, M. Lessons learned from long term monitoring of a multisource heat pump system. Energy Build.
**2018**, 174, 335–346. [Google Scholar] [CrossRef] - Cho, S.H.; Kim, W.T.; Tae, C.S.; Zaheeruddin, M. Effect of length of measurement period on accuracy of predicted annual heating energy consumption of buildings. Energy Convers. Manag.
**2004**, 45, 2867–2879. [Google Scholar] [CrossRef] - Bourdeau, M.; Zhai, X.Q.; Nefzaoui, E.; Guo, X.; Chatellier, P. Modeling and forecasting building energy consumption: A review of data-driven techniques. Sustain. Cities Soc.
**2019**, 48, 101533. [Google Scholar] [CrossRef] - Alobaidi, M.H.; Chebana, F.; Meguid, M.A. Robust ensemble learning framework for day-ahead forecasting of household based energy consumption. Appl. Energy
**2018**, 212, 997–1012. [Google Scholar] [CrossRef] [Green Version] - Asaee, S.R.; Ugursal, V.I.; Beausoleil-Morrison, I. Techno-economic feasibility evaluation of air to water heat pump retrofit in the Canadian housing stock. Appl. Therm. Eng.
**2017**, 111, 936–949. [Google Scholar] [CrossRef] [Green Version] - Akhlaghi, Y.G.; Ma, X.; Zhao, X.; Shittu, S.; Li, J. A statistical model for dew point air cooler based on the multiple polynomial regression approach. Energy
**2019**, 181, 868–881. [Google Scholar] [CrossRef] [Green Version] - Park, S.K.; Moon, H.J.; Min, K.C.; Hwang, C.; Kim, S. Application of a multiple linear regression and an artificial neural network model for the heating performance analysis and hourly prediction of a large-scale ground source heat pump system. Energy Build.
**2018**, 165, 206–215. [Google Scholar] [CrossRef] - Dai, B.; Qi, H.; Liu, S.; Ma, M.; Zhong, Z.; Li, H.; Song, M.; Sun, Z. Evaluation of transcritical CO
_{2}heat pump system integrated with mechanical subcooling by utilizing energy, exergy and economic methodologies for residential heating. Energy Convers. Manag.**2019**, 192, 202–220. [Google Scholar] [CrossRef] - Yan, L.; Hu, P.; Li, C.; Yao, Y.; Xing, L.; Lei, F.; Zhu, N. The performance prediction of ground source heat pump system based on monitoring data and data mining technology. Energy Build.
**2016**, 127, 1085–1095. [Google Scholar] [CrossRef] - Kim, J.; Nam, Y.J. A Numerical Study on System Performance of Groundwater Heat Pumps. Eneriges
**2016**, 9, 4. [Google Scholar] [CrossRef] [Green Version] - Esen, H.; Inalli, M.; Sengur, A.; Esen, M. Forecasting of a ground-coupled heat pump performance using neural networks with statistical data weighting pre-processing. Int. J. Therm. Sci.
**2008**, 47, 431–441. [Google Scholar] [CrossRef] - Sayegh, M.A.; Danielewicz, J.; Nannou, T.; Miniewicz, M.; Jadwiszczak, P.; Piekarska, K. Trends of European research and development in district heating technologies. Renew. Sustain. Energy Rev.
**2017**, 68, 1183–1192. [Google Scholar] [CrossRef] [Green Version] - Rivière, P.; Adnot, J.; Marchio, D.; Pérez-Lombard, L.; Ortiz, J.A. A method to reduce European chiller hourly load curves to a few points. In Proceedings of the Climamed 2005–2nd Mediterranean Congress of Climatization, Madrid, Spain, 24–25 February 2005. [Google Scholar]
- Eberhart, R.C.; Dobbins, R.W. Neural Network PC Tools: A Practical Guide; Academic Press: San Diego, CA, USA, 1990. [Google Scholar]
- Zurada, J.M. Introduction to Artificial Neural Systems; West Publishing Company: St. Paul, MN, USA, 1992. [Google Scholar]
- Fausett, L.V. Fundamentals Neural Networks: Architecture, Algorithms, and Applications; Prentice-Hall: Hoboken, NJ, USA, 1994. [Google Scholar]
- Hassoun, M.H. Fundamentals of Artificial Neural Networks; MIT Press: Cambridge, MA, USA, 1995. [Google Scholar]

**Figure 9.**Comparison of prediction performance of prediction model with hyper-parameter optimization.

**Figure 10.**Comparison of measured performance and prediction performance through an ANN model with optimal hyper-parameter.

Hyper-Parameter | Contents |
---|---|

Learning rate | A variable that determines how fast it will move in the gradient direction |

Cost function | A function that estimates the difference between the expected value and the actual value according to the input |

Regularization parameter | Using regularization method to avoid and solve overfitting problems |

Mini-batch size | Splitting the entire training data to perform a batch set |

Training loop | Variables that determine early termination of learning |

Hidden unit | Learning Optimization Determinants on Training Data |

Weight initialization | A determinant of performance |

Category | Methods | Input | Author |
---|---|---|---|

Mathematical method | Polynomial | 7 point (Heating load, etc.) | Nam et al. |

Machine learning | Random Forest | 9 point (Power consumption, etc.) | Cho |

Recurrent Neural Networks | 12 point (Environmental variable, etc.) | Sun et al. | |

ANN | 5 point (Power consumption, etc.) | Benli | |

SVM | 8 points (Heating capacity, etc.) | Esen et al. | |

Adaptive neuro fuzzy inference system | 8 points (Heating capacity, etc.) | Kecman | |

ANN | 7 point (Power consumption, etc.) | Yilmaz | |

K-NN | 8 points (Water flow rate, etc.) | Akhlaghi | |

Random Forest | 12 point (Power consumption, etc.) | Swider | |

ANN | 29 point (Power consumption, etc.) | Park et al. | |

ANN | 5 point (Ground temperature, etc) | Esen et al. | |

ANN | 3 point (Ground temperature, etc) | Esen et al. | |

Back-propagation Neural Network | 23 point (Water flow rate, etc) | Yan et al. | |

Random Forest and Back propagation Neural Network | 16 point (Power consumption, etc.) | Lu et al. |

Category | Contents | |
---|---|---|

Building | Use | Office |

Total floor area | 21,492 m^{2} | |

Size | B1/F9 | |

Geothermal system | Type | Vertical closed-loop |

EA | 7 | |

Capacity (Cooling) | 105.6 kW | |

Capacity (Heating) | 101.4 kW | |

Number of borehole | 70 | |

Interval of borehole | 5 m | |

Period of data collection | 2014.02.05~2019.08.31 |

Classification | Cooling | Heating |
---|---|---|

Capacity (kW) | 190.61 | 178.93 |

Power (W) | 38.03 | 44.52 |

Flow rate (LPM) | 600 | 600 |

COP | 5.01 | 4.02 |

Classification | Spec. | Contents |
---|---|---|

Heat source tank | 18.7 ton | Circulation flow rate on heat source side: 5~10 Ton |

Load tank | 18.7 ton | Circulation flow rate on load side: 5~100 Ton |

Auxiliary heat source | 10 HP | Air-cooled heat pump |

Category | Building | Test-Bed |
---|---|---|

Data collection period | 1 January 2018~31 December 2018 | 25 August 2019~ 27 August 2019 |

Data collection cycle | 3 h | 1 min |

Data collection method | BAS | Measurement |

Temperature range (cooling) | 24~43 °C | 20~49 °C |

Temperature range (heating) | 11~24 °C | 8.1~26.8 °C |

Measurement Device | Specific Information | Ranges | Accuracy |
---|---|---|---|

Temperature sensor (°C) | RTD (OMEGA) | −50~200 | ±0.15% |

HOBO U12 (ONSET) | −20~70 | ±0.35% | |

Flow meter (m^{3}/h) | FMAG 5000 (SIEMENS) | 0~400 | ±0.4% |

Power meter | CW240 (YOKOGAWA) | 0~3000 | ±0.6% |

Category | Unit | Symbol |
---|---|---|

Outdoor air temperature | °C | ${T}_{OA}$ |

Source side inlet temperature | °C | ${T}_{S,i}$ |

Source side outlet temperature | °C | ${T}_{S,o}$ |

Load side inlet temperature | °C | ${T}_{L,i}$ |

Load side outlet temperature | °C | ${T}_{L,o}$ |

Heat pump power | kW | ${W}_{HP}$ |

COP | - | $COP$ |

Pump power | kW | ${W}_{P}$ |

Category | Uncertainty (%) |
---|---|

Temperature | 0.2 |

Flow rate | 0.26~0.32 |

Category | $\mathit{r}$ | ${\mathit{r}}^{2}$ |
---|---|---|

Outdoor air temperature | −0.72 | 0.52 |

Source side inlet temperature | −0.76 | 0.58 |

Source side outlet temperature | 0.59 | 0.35 |

Load side inlet temperature | 0.60 | 0.39 |

Load side outlet temperature | 0.32 | 0.10 |

Variables | Statistical Parameters | ||||
---|---|---|---|---|---|

Means | Standard Deviation | Minimum | Maximum | ||

COP | Training | 2.90 | 0.71 | 1.17 | 5.46 |

Testing | 2.76 | 0.55 | 1.22 | 3.77 | |

Load side inlet temperature | Training | 17.29 | 1.71 | 11.60 | 25.00 |

Testing | 17.30 | 1.75 | 12.10 | 24.20 | |

Load side outlet temperature | Training | 16.02 | 2.12 | 9.00 | 24.40 |

Testing | 15.99 | 2.16 | 9.10 | 23.60 | |

Source side inlet temperature | Training | 33.52 | 3.81 | 24.20 | 43.50 |

Testing | 33.56 | 3.74 | 24.60 | 43.00 | |

Source side outlet temperature | Training | 37.52 | 3.81 | 28.20 | 47.50 |

Testing | 37.56 | 3.74 | 28.60 | 47.00 | |

Outside temperature | Training | 25.43 | 2.21 | 22.90 | 33.70 |

Testing | 2530 | 2.22 | 23.00 | 33.10 |

Variables | Statistical Parameters | ||||
---|---|---|---|---|---|

Means | Standard Deviation | Minimum | Maximum | ||

COP | Training | 2.90 | 0.71 | 1.17 | 5.46 |

Testing | 2.76 | 0.55 | 1.22 | 3.77 | |

Load side inlet temperature | Training | 17.29 | 1.71 | 11.60 | 25.00 |

Testing | 17.30 | 1.75 | 12.10 | 24.20 | |

Load side outlet temperature | Training | 16.02 | 2.12 | 9.00 | 24.40 |

Testing | 15.99 | 2.16 | 9.10 | 23.60 | |

Source side inlet temperature | Training | 33.52 | 3.81 | 24.20 | 43.50 |

Testing | 33.56 | 3.74 | 24.60 | 43.00 | |

Source side outlet temperature | Training | 37.52 | 3.81 | 28.20 | 47.50 |

Testing | 37.56 | 3.74 | 28.60 | 47.00 | |

Outside temperature | Training | 25.43 | 2.21 | 22.90 | 33.70 |

Testing | 2530 | 2.22 | 23.00 | 33.10 |

Category | Contents | ||
---|---|---|---|

Function | Activation | Sigmoid | |

Loss | Mean squared error | ||

Optimization algorithm | Adam | ||

Epoch | 5000 | ||

Structure | Input layer | Number of layer | 1 |

Number of neuron | 5 | ||

Hidden layer | Number of layer | 1 | |

Number of neuron | 2 | ||

Output layer | Number of layer | 1 | |

Number of neuron | 1 |

Category | Contents |
---|---|

Type | Eps-regression |

Kernel | Polynomial |

Epsilon | 0.1 |

Cost | 1 |

Gamma | 1 |

Category | Accuracy | ||
---|---|---|---|

R^{2} | CvRMSE | Error | |

ANN | 0.89 | 17.8 | −12~11 |

SVM | 0.65 | 15.9 | −14~16 |

Category | Normalization | Train Time (s) |
---|---|---|

ANN | Min-Max | 1.43 |

Standardization | 0.83 | |

SVM | Min-Max | 2.63 |

Standardization | 6.64 |

Machine Learning Model | Hyper Parameter | Optimization Method |
---|---|---|

ANN | Training iterations | Grid search |

Number of hidden layer | Bayesian optimization | |

Number of hidden node | Bayesian optimization | |

SVM | Kernel | Grid search |

Number of gamma | Random search | |

Number of cost | Random search |

Category | Parameters |
---|---|

ANN | 1, 2, 3, 4 |

SVM | 1~17 |

Category | Parameters |
---|---|

Kernel | Radial, Linear, Polynomial, Sigmoid |

Cost | 1, 2, 4, 8, 16 |

Gamma | 0.00001, 0.0001, 0.001, 0.01, 0.1, 0 |

Category | Cost | ||||
---|---|---|---|---|---|

Gamma | 1 | 2 | 4 | 8 | 16 |

0.00001 | 49.6 | 47.0 | 43.9 | 41.4 | 39.6 |

0.0001 | 39.3 | 38.5 | 37.9 | 37.7 | 36.5 |

0.001 | 36.5 | 34.1 | 29.7 | 26.5 | 24.7 |

0.01 | 20.4 | 12.3 | 5 | 2.6 | 1.7 |

0.1 | 3.2 | 4.4 | 1.9 | 2.4 | 2.5 |

0 | 5.2 | 3.1 | 2.5 | 1.2 | 0.8 |

Category | Cost | ||||
---|---|---|---|---|---|

Gamma | 1 | 2 | 4 | 8 | 16 |

0.00001 | 2.334 | 2.334 | 2.313 | 2.310 | 2.310 |

0.0001 | 2.334 | 2.334 | 2.313 | 2.310 | 2.310 |

0.001 | 2.334 | 2.334 | 2.313 | 2.310 | 2.310 |

0.01 | 2.334 | 2.334 | 2.313 | 2.310 | 2.310 |

0.1 | 2.334 | 2.334 | 2.313 | 2.310 | 2.310 |

0 | 2.334 | 2.334 | 2.313 | 2.310 | 2.310 |

Category | Cost | ||||
---|---|---|---|---|---|

Gamma | 1 | 2 | 4 | 8 | 16 |

0.00001 | 51.21 | 47.00 | 50.05 | 51.05 | 53.05 |

0.0001 | 40.70 | 39.20 | 38.30 | 49.60 | 47.00 |

0.001 | 50.47 | 49.69 | 48.22 | 46.50 | 44.63 |

0.01 | 52.99 | 52.94 | 52.85 | 53.03 | 53.02 |

0.1 | 15.31 | 20.84 | 18.38 | 16.38 | 14.95 |

0 | 11.52 | 13.52 | 13.41 | 20.28 | 15.31 |

Category | Cost | ||||
---|---|---|---|---|---|

Gamma | 1 | 2 | 4 | 8 | 16 |

0.00001 | 51.21 | 49.55 | 47.00 | 43.92 | 41.41 |

0.0001 | 43.07 | 40.78 | 39.25 | 38.46 | 37.89 |

0.001 | 24.70 | 20.84 | 32.85 | 33.78 | 26.47 |

0.01 | 38.27 | 37.65 | 36.12 | 46.72 | 53.05 |

Category | Contents | ||
---|---|---|---|

Function | Activation | Sigmoid | |

Loss | Mean squared error | ||

Optimization algorithm | Adam | ||

Epoch | 5000 | ||

Structure | Input layer | Number of layer | 1 |

Number of neuron | 4 | ||

Hidden layer | Number of layer | 2 | |

Number of neuron | 11 | ||

Output layer | Number of layer | 1 | |

Number of neuron | 1 |

Category | Contents |
---|---|

Type | Eps-regression |

Kernel | Radial |

Epsilon | 16 |

Cost | 0 |

Gamma | 0.1 |

Number of support vector | 1116 |

Category | Accuracy | |||
---|---|---|---|---|

MBE | RMSE | CvRMSE | R^{2} | |

ANN | −3.6% | 15.96% | 5.4% | 0.953 |

SVM | −9.8% | 43.96% | 8.10% | 0.962 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Shin, J.; Lee, J.; Cho, Y.
A COP Prediction Model of Hybrid Geothermal Heat Pump Systems based on ANN and SVM with Hyper-Parameters Optimization. *Appl. Sci.* **2023**, *13*, 7771.
https://doi.org/10.3390/app13137771

**AMA Style**

Shin J, Lee J, Cho Y.
A COP Prediction Model of Hybrid Geothermal Heat Pump Systems based on ANN and SVM with Hyper-Parameters Optimization. *Applied Sciences*. 2023; 13(13):7771.
https://doi.org/10.3390/app13137771

**Chicago/Turabian Style**

Shin, Jihyun, Jinhyun Lee, and Younghum Cho.
2023. "A COP Prediction Model of Hybrid Geothermal Heat Pump Systems based on ANN and SVM with Hyper-Parameters Optimization" *Applied Sciences* 13, no. 13: 7771.
https://doi.org/10.3390/app13137771