# Non-intrusive Diagnostics for Legacy Heat-Pump Performance Degradation

Iakovos Michailidis, Georgios Vougiatzis, Aliki Stefanopoulou, Asimina Dimara, Christos Korkas, Stelios Krinidis, Elias B. Kosmatopoulos, Dimosthenis Ioannidis, Christos-Nikolaos Anagnostopoulos, Dimitrios Tzovaras

► To cite this version:

Iakovos Michailidis, Georgios Vougiatzis, Aliki Stefanopoulou, Asimina Dimara, Christos Korkas, et al.. Non-intrusive Diagnostics for Legacy Heat-Pump Performance Degradation. 18th IFIP International Conference on Artificial Intelligence Applications and Innovations (AIAI), Jun 2022, Herissos, Greece. pp.265-275, 10.1007/978-3-031-08341-9_22. hal-05335619

HAL Id: hal-05335619

https://inria.hal.science/hal-05335619v1

Submitted on 28 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

ifip

International Federation for Information Processing

This document is the original author manuscript of a paper submitted to an IFIP
conference proceedings or other IFIP publication by Springer Nature. As such, there
may be some differences in the official published version of the paper. Such
differences, if any, are usually due to reformatting during preparation for publication or
minor corrections made by the author(s) during final proofreading of the publication
manuscript.
# Non-intrusive Diagnostics for Legacy Heat-Pump Performance Degradation

Iakovos Michailidis¹,²✉, Georgios Vougiatzis¹✉, Aliki Stefanopoulou¹✉,
Asimina Dimara¹,⁴✉, Christos D. Korkas¹,²✉, Stelios Krinidis¹,³✉,
Elias B. Kosmatopoulos¹,²✉, Dimosthenis Ioannidis¹✉,
Christos-Nikolaos Anagnostopoulos⁴✉, and Dimitrios Tzovaras¹✉

¹ Information Technologies Institute, Centre for Research and Technology Hellas,
57001 Thessaloniki, Greece

adimara@iti.gr

² Electrical and Computer Engineering Department,
Democritus University of Thrace, 67000 Xanthi, Greece

³ Management Science and Technology Department, International Hellenic
University (IHU), Kavala, Greece

⁴ Department of Cultural Technology and Communication, Intelligent Systems Lab,
University of the Aegean, Mytilene, Greece

**Abstract.** Diagnosing abnormal behavior of different severity and convenience effects in a real-time manner is of paramount importance for energy-intensive building appliances. Both industrial and residential sectors suffer from post-incident maintenance where undetected faults occur for several days until the total breakdown of the equipment. To generate the necessary data set, a simulative test bed from Energym initiative was considered, exploiting an already validated residential environment. In this work, a Convolutional Neural Network (CNN) model was considered for classifying non-intrusive, low-cost temperature sensor embeddings in 3 categories with different abnormal heat pump severity levels. The features considered available derived from indoor zones temperatures and the outdoor/ambient temperature of the building; omitting intentionally readings from more elaborate sensors e.g., power analyzers or energy meters. The trained CNN model was eventually able to achieve very high accuracy i.e., around 95%; ensuring its high operational reliability by consuming real-time 15 min sequential temperature embeddings.

**Keywords:** Heat-Pump maintenance · Performance degradation
diagnostics · Simulation data · Non-Intrusive malfunction classification

## 1 Introduction

Systems that heat and/or cool a space are used by the occupants to manage all temperatures, weather fluctuations, and seasons changing, while assessing a comfortable indoor environment. Almost 43% of the total energy consumption
is used for heating and cooling, while there is also an increasing of heating and cooling energy consumption by 32% during the last decade [1]. A proper heating and/or cooling system is really beneficiary for the occupants as it helps them deal with extreme weather conditions while regulating a convenient Indoor Environmental Quality (IEQ). Energy expenses, especially nowadays, are one of the biggest expenses for the occupants. As a result, heating and/or cooling systems that do not operate smoothly and perpetually may greatly increase energy costs [2].

A suitable heating system will preserve the desired thermal comfort levels during a short period of time. Nonetheless, malfunctions in the heating system have an enormous effect on exergy and energy efficiency [3]. Error and problems in the operation of heat pumps could result significant energy losses during the heating period [3]. Consequently, tools and applications that have the ability to predict and alert the occupants for upcoming heat pump faults, malfunctions or unusual behaviour are of utmost importance. On time notifications of potential faulty heat pump operation will ensure non delayed healing actions while reducing maintenance and repairing costs of a total system breakdown [4].

Literature points out that enormous performance losses occur in heat pumps in the building sector. Specifically, almost 20–50% of heat pumps operate with a lowest efficiency of at least 70–80% compared to their design efficiency [5]. Moreover, this faulty heat pump operation contributes in an increase of 40% in the energy consumption [5]. Nevertheless, there is lack of machine learning models and applications in the literature for early-diagnosis of heat pump errors, especially for the residential sector [6].

The current study is structured as follows:

- In Sect. 1, basic information about the energy efficiency of heating systems and the contribution of the study is addressed.

- In Sect. 2, the simulation test bed, the dataset synthesis and the fault diagnosis model are presented.

- In Sect. 3, the experimental results are given along with an evaluation.

- In Sect. 4, conclusions are drawn.

## 1.1 Contributions of the Study

Operational malfunctions and abnormal behaviors may result significant energy losses or even devastating breakdowns, since such dynamics may stay undetected for several days. Modern smart appliances are usually equipped with elaborate micro-sensorial and on-board processing capabilities [7], having the ability to detect and report errors and faults by using simplistic rule based engines for raising alerts. However, legacy conventional appliances usually do not have such capability [8]. Moreover, installing additional OEMS sensory equipment may conflict with the appliance guarantee; while in other non-intrusive approaches, quite elaborate sensors (e.g., power analyzers) may be a quite expensive solution surpassing the value of the appliance itself; especially in domestic or small-scale industrial use-cases. As a result low-cost non-intrusive approaches are often
required in order to be able to monitor, detect, diagnose and even predict abnormal behaviour of the appliances themselves [9].

The current study exploits the performance of a supervised machine-learning approach for the accurate and early detection of heat pump performance degradation effects at different severity levels. The goal is to train such a model utilizing data from non-intrusive low-cost sensors [10] which are commonly used in building automation applications. For this reason, the current study considers the indoor zone temperatures of a simulative building plant - from Energym [11] initiative - and the ambient/outdoor temperature as the only available features (for more details see Sect. 2.1 and Sect. 2.2); such sensory readings can derive by cheap and easy to install (even wireless) sensors, enabling the application across different building types and use cases. It is important to note the current study focuses on one of the most energy-intensive end-use sectors with very high disruption potential (very important for occupants convenience) in buildings which is climating [12].

# 2 Experimental Setup

## 2.1 Simulation Testbed

The building where the simulation was applied consists of four floors, each of which is an apartment and has two thermal zones on each storey (in total 8 thermal zones). The building is located in Spain, specifically in Tarragona. The area of surface of building is 417.12 m² and total volume is 1042.83 m³. Apartments thermal system consists of a centralized water-to-water geothermal heat pump (HP) system, which extracts heat from the ground through a vertical ground heat exchanger, and provides hot water for the indoor fan coil units (two units per apartment) and the Domestic Hot Water (DHW)<fnref n="1" />. The DHW system is composed by four storage systems, one for each household, and consist in a four node-stratified tank (see footnote 1). Heating loop circuit from the heat pump is connected to the bottom half part of the tanks and electrical heaters are placed on the top part acting as auxiliary systems (see footnote 1). Regarding the electrical part, apartments system includes a PV array, a community battery and an electric vehicle (EV) and in the thermal scenario, community battery and electric vehicle charging are disregarded (see footnote 1).

"ApartmentsThermal-v0" is a EnergyPlus model [13]. A description of the model's inputs and outputs is provided in Table 1 and Table 2 respectively. More information regarding inputs and outputs can be found in https://bsl546.github.io/energym-pages/sources/apt.html. It is noted that the evaluation process is carried out under predetermined weather conditions and for a specific period of time. The weather instantiation (i.e., outdoor temperature) considers conditions occurring between January and April. The main controllable inputs for the "ApartmentsThermal-v0" model are listed in Table 3.

<footnote n="1">¹ https://bsl546.github.io/energym-pages/sources/apt.html.</footnote>
<table><caption>**Table 1.** Heat pump available information</caption><thead><tr><th>Variable name</th><th>Type</th><th>Lower bound</th><th>Upper bound</th><th># States</th><th>Description</th></tr></thead><tbody><tr><td colspan="6"><strong>Inputs</strong></td></tr><tr><td>P1_T_Thermolat_sp ...<br>P4_T_Thermolat_sp</td><td>Scalar</td><td>16</td><td>26</td><td></td><td>Floor 1 Thermostat Setpoint<br>(°C) ... Floor 4 Thermostat<br>Setpoint (°C)</td></tr><tr><td>Bd_T_HP_sp</td><td>Scalar</td><td>35</td><td>55</td><td></td><td>Heat Pump Temperature<br>Setpoint (°C)</td></tr><tr><td>P1_T_Tank_sp ...<br>P4_T_Tank_sp</td><td>Scalar</td><td>30</td><td>70</td><td></td><td>Floor 1 Tank Temperature<br>(°C) ... Floor 4 Tank<br>Temperature (°C)</td></tr><tr><td>HVAC_onoff_HP_sp</td><td>Discrete</td><td>0</td><td>1</td><td>2</td><td>Heat Pump on/off Setpoint</td></tr><tr><td>Bd_Pw_Bat_sp</td><td>Scalar</td><td>-1</td><td>1</td><td></td><td>Battery<br>Charging/Discharging<br>Setpoint Rate</td></tr><tr><td>Bd_Ch_EVBat_sp</td><td>Scalar</td><td>0</td><td>1</td><td></td><td>EV Battery Charging Setpoint<br>Rate</td></tr></tbody></table>

## 2.2 Dataset Synthesis

As already mentioned above, the dataset considers synthetically generated data from a simulative test bed. The energy consuming assets consider existing domestic appliances and a heat pump coupled with dedicated fan coils in different climate zones. In order to decouple the observed thermal dynamics of the building from the control strategy applied, the fan coil control thermostats were set constantly to 22 °C in order to preserve indoor thermal comfort between acceptable bounds.

The main goal was to simulate abnormal dynamics and behaviours during different realization conditions (external conditions) that would enable sampling and annotating accordingly. The application considered annotating/classifying different degradation effects imposed in the heating capacity of the heat pump during operation, considering only the indoor and outdoor temperature readings. The degradation effects were imposed by lowering the temperature set point of the heat pump (see Table 1).

The nominal behavior of the heat pump was acquired by setting the heat pump temperature (i.e., Bd_T_HP_sp in Table 1) to its maximum value, i.e., 55 °C. To generate enough data, the simulation tests considered two different degradation severity levels for the heat pump temperature: a) 35 °C, b) 45 °C. These two different events/incidents were simulated during three different

<table><caption>**Table 2.** Indicative outputs</caption><thead><tr><th>Variable name</th><th>Type</th><th>Lower bound</th><th>Upper bound</th><th>Description</th></tr></thead><tbody><tr><td colspan="5"><strong>Outputs</strong></td></tr><tr><td>Ext_T</td><td>Scalar</td><td>-10</td><td>40</td><td>Outdoor Temperature (°C)</td></tr><tr><td>HVAC_Pw_HP</td><td>Scalar</td><td>0</td><td>120000.0</td><td>Heat Pump Power (W)</td></tr><tr><td>Z01_T ... Z08_T</td><td>Scalar</td><td>10</td><td>40</td><td>Zone 1 Temperature (°C) ...<br>Zone 8 Temperature (°C)</td></tr><tr><td>P1_T_Thermostat_sp_out ...<br>P4_T_Thermostat_sp_out</td><td>Scalar</td><td>16</td><td>26</td><td>Floor 1 Thermostat Setpoint<br>(°C) ... Floor 4 Thermostat<br>Setpoint (°C)</td></tr></tbody></table>
simulation days between January and April, while the degradation events were inserted at four different timeslots: early morning (4 p.m.), morning (9 p.m.), noon (14 a.m.), afternoon (18 p.m.).

The considered dataset presented a sampling rate of 180 s i.e., 480 samples per day. The indoor (i.e., 8 thermal zones) and outdoor temperature timeseries were hashed into slices of 5 consecutive timesteps i.e., 5 × 180 s = 15 min, lagged by 1 (stride) i.e., 1 × 180 s = 3 min; and annotated with three different labels:

- Nominal operation, considering Heat Pump temperature = 55°C was annotated with 0,

- Operation with severe fault, considering Heat Pump temperature = 35°C was annotated with 1,

- Operation with mild fault, considering Heat Pump temperature = 45°C was annotated with 2,

Evidently, the abnormal heat pump behavior (vertical green line) is not easily detectable by visualizing the indoor temperature evolution as shown in Fig. 1.

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Indoor temperature readings (red) and thermostat (blue dashed) from Zone01 during nominal operation, severe and mild heat pump malfunction. The vertical green line indicates the exact moment when the malfunction is imposed. (Color figure online)</figcaption></figure>
The problem becomes even more complicated when the available temperature readings reduce to only one i.e., consider the case where the only available thermal zone temperature was from “Zone 1”. Moreover, the severity of the heat pump malfunction is even more difficult to be determined visually only by considering the indoor temperature readings; facts which both suggest the adoption of an intelligent data-driven approach for this purpose.

The data set generated eventually was consisted of X-Y tuples, where the feature matrix X was formed by 9-by-5 = 45 features resulted by flattening the aforementioned hashed slices of length 5 and the annotation (label) matrix Y was formed by 0, 1 and 2 labels as already discussed.

In order to further reduce the intrusiveness of the approach and the number of features used, the same data set was reduced significantly omitting all indoor temperature readings but one; zone 1 (ground floor) in specific. As a result the reduced data set was consisted of X-Y tuples, where the feature matrix X was formed by 2-by-5 = 10 features resulted by flattening the aforementioned hashed slices of length 5 and the annotation (label) matrix Y was formed by the exact same 0, 1 and 2 labels with the extended data set case.

<table><caption>**Table 3.** Control inputs</caption><thead><tr><td>Variable Name</td><td>Value</td><td>Description</td></tr></thead><tbody><tr><td>P1_T_Tank_sp ...<br/>P4_T_Tank_sp</td><td>70</td><td>Floor 1 Tank Temperature Setpoint (°C) ... Floor 4 Tank Temperature Setpoint (°C)</td></tr><tr><td>Bd_Ch_EVBat_sp</td><td>1</td><td>EV Battery Charging Setpoint Rate</td></tr><tr><td>Bd_Disch_EVBat_sp</td><td>0</td><td>Heat Pump Power (W)</td></tr><tr><td>HVAC_onoff HP_sp</td><td>1</td><td>Heat Pump Setpoint</td></tr><tr><td>Bd_T HP_sp</td><td>55</td><td>Heat Pump Temperature (°C)</td></tr><tr><td>P1_T_Thermostat_sp ...<br/>P4_T_Thermostat_sp</td><td>22</td><td>Floor 1 Thermostat Setpoint (°C) ...<br/>Floor 4 Thermostat Setpoint (°C)</td></tr></tbody></table>

# 3 Results and Evaluation

## 3.1 Fault Diagnosis Model

The aforementioned dataset was used to train a Convolutional Neural Network, whose main goal was to predict whether data sample refers to a nominal or faulty sensor operation. The dataset was split into train and test data with percentage 70% and 30% respectively. The neural network defined was sequential and consisted of five layers in total:

i An Input layer for $9 - by - 5$ (extended) or $2 - by - 5$ (reduced) temperature embeddings;

ii A Convolution layer with “relu” activation functions
iii A Max Pooling layer;

iv A Fully Connected layer;

v An Output Layer implementing a “softmax” activation function of size 1 determining the class of the input embedding.

The convolution layer is the layer that a filter is applied to the data sample, to extract its features. For this layers we used 16 filters of size (3, 3), and “relu” as the activation function. After the Convolution layer, a Pooling layer was used to reduce the dimensions of the feature map, in order to preserve its important information and reduce computation time. The Max Pooling layer used was of size (2, 2) with a stride of 1. The next layer used was a fully connected layer of size 100 and activation function “relu”, whose goal was to classify the input data into labels. This layer was fully connected to the output layer, aiming to classify the input data according to their type. The three different output types was “0”, for a nominal sensor operation, “1” for an operation with mild fault and “2” for an operation with severe fault. The output layer’s activation function was “softmax”. For the compilation of the described model, “Adam” was used as an optimizer, “sparse categorical crossentropy” as a loss function and “accuracy” as a validation metrics function over the training set. Lastly, ten epochs were used in total to fit the model; enough to reach a very high training accuracy and avoid exhaustive optimization.

## 3.2 Model Inference Performance

**Extended Model Case: 9-by-5 Input Size.** The results of the model are depicted in Table 4. It is apparent that the model successfully diagnoses the type of error in the heat pump. The training accuracy of the model increases

<table><caption>**Table 4.** Training performance: extended model</caption><thead><tr><th>Epochs</th><th>Data loss</th><th>Accuracy</th></tr></thead><tbody><tr><td>1/10</td><td>0.2487</td><td>0.9332</td></tr><tr><td>2/10</td><td>0.2233</td><td>0.9407</td></tr><tr><td>3/10</td><td>0.2109</td><td>0.9443</td></tr><tr><td>4/10</td><td>0.1984</td><td>0.9478</td></tr><tr><td>5/10</td><td>0.1850</td><td>0.9515</td></tr><tr><td>6/10</td><td>0.1761</td><td>0.9541</td></tr><tr><td>7/10</td><td>0.1725</td><td>0.9555</td></tr><tr><td>8/10</td><td>0.1683</td><td>0.9564</td></tr><tr><td>9/10</td><td>0.1657</td><td>0.9570</td></tr><tr><td>10/10</td><td>0.1644</td><td>0.9576</td></tr></tbody><tfoot><tr><td colspan="3">Test loss: 0.1546788364648819<br>Test accuracy: 0.9591668844223022</td></tr></tfoot></table>
with each epoch from 93.32% (Epoch 1) to 95.76% (Epoch 10). Data loss during training decreases consecutively, specifically from 24.87% to 16.44%. Focusing on the inference results on unknown data from the test set used, it can be observed that the performance results are comparable enabling the model to reach accuracy of 95.91% and reduce categorical cross entropy loss to 15.46%. In Figs. 2a and 2b the evolution of the aforementioned results is depicted across the different training epochs.

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** (a) Training (blue) and Validation (red) Accuracy of the Extended Model (b) Training (blue) and Validation (red) Accuracy of the Extended Model (Color figure online)</figcaption></figure>

**Reduced Model Case: 2-by-5 Input Size.** The results of the reduced model are depicted in Table 5. Evidently the reduced version of the model i.e., considering only one out of the eight indoor zone temperatures in the features matrix; was able to achieve comparable performance both on training and test sets. The training accuracy of the reduced model increased every epoch from 92.55% (Epoch 1) to 94.43% (Epoch 10). As expected the data loss during the training process descended, in specific from 30.85% to 21.86%. Focusing on the inference results on unknown data from the test set used, it can be observed that the performance results are comparable enabling the model to reach accuracy of 94.49% and reduce categorical cross entropy loss to 20.57%.

As expected the overall performance of the model both at training and inferring evaluation stages is slightly worse than the one achieved when considering the extended data set case. However, the feasibility and practical value of such a reduced model surpasses the minor efficiency difference, since it utilizes one indoor temperature sensor instead of eight. In Figs. 3a and 3b the evolution of the aforementioned results is depicted across the different training epochs.
<table><caption>**Table 5.** Training performance: reduced model</caption><thead><tr><th>Epochs</th><th>Data loss</th><th>Accuracy</th></tr></thead><tbody><tr><td>1/10</td><td>0.3085</td><td>0.9255</td></tr><tr><td>2/10</td><td>0.2987</td><td>0.9255</td></tr><tr><td>3/10</td><td>0.2892</td><td>0.9255</td></tr><tr><td>4/10</td><td>0.2594</td><td>0.9333</td></tr><tr><td>5/10</td><td>0.2371</td><td>0.9400</td></tr><tr><td>6/10</td><td>0.2317</td><td>0.9418</td></tr><tr><td>7/10</td><td>0.2264</td><td>0.9427</td></tr><tr><td>8/10</td><td>0.2249</td><td>0.9425</td></tr><tr><td>9/10</td><td>0.2216</td><td>0.9437</td></tr><tr><td>10/10</td><td>0.2186</td><td>0.9443</td></tr></tbody><tfoot><tr><td colspan="3">Test loss: 0.2057267129421234<br>Test accuracy: 0.9449745416641235</td></tr></tfoot></table>

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** (a) Training (blue) and Validation (red) Accuracy of the Reduced Model (b) Training (blue) and Validation (red) Loss of the Reduced Model (Color figure online)</figcaption></figure>

# 4 Conclusions

In this work, a Convolutional Neural Network (CNN) model was considered for classifying non-intrusive, low-cost sensor embeddings as nominal or faulty. The features considered were derived from indoor zones temperatures and the outdoor/ambient temperature of the building: a) extended case: all 8 indoor temperature sensor readings are considered in the feature matrix; b) reduced case: only 1 indoor temperature sensor readings are considered in the feature matrix. In both data set cases, it was observed that such a CNN model was capable to classify unknown (test set) embeddings with very high accuracy i.e., around 95%; without any power or energy meter readings from the heat pump itself.
As a result, the CNN model once trained could be utilized in real-time inference applications where real-time 15 min sequential temperature embeddings (either from all or even one thermal zone) could be used to detect and diagnose the severity of the heat pump abnormal behavior; reducing excessive exergy, energy and capital expenditures as well as reducing the risk of total heat pump break-down due to undetected incidents.

Indicative future research work topics have already been identified by the authors including: imposing heat pump faults in much higher granularity (i.e., create more annotated classes) as well as impose other types of malfunctions in the heat pump tanks to complicate the classification problem furthermore.

**Acknowledgements.** The research leading to these results was partially funded by the European Commission “LC-EEB-07-2020 - Smart Operation of Proactive Residential Buildings” - PRECEPT H2020 project (Grant agreement ID: 958284) https://www.precept-project.eu/, accessed on 8 March 2022; and “LC-SC3-B4E-3-2020 Upgrading smartness of existing buildings through innovations for legacy equipment” - Smart2B H2020 project (Grant agreement ID: 101023666) https://www.smart2b-project.eu/, accessed on 2 March 2022.

## References

1. Frayssinet, L., et al.: Modeling the heating and cooling energy demand of urban buildings at city scale. Renew. Sustain. Energy Rev. 81, 2318-2327 (2018)

2. Bye, B., Fæhn, T., Rosnes, O.: Residential energy efficiency policies: costs, emissions and rebound effects. Energy 143, 191-201 (2018)

3. Ceylan, İ., et al.: The effect of malfunctions in air handling units on energy and exergy efficiency. Heat Transf. Res. 51(11) (2020)

4. Han, Z., et al.: Study on design error of ground source heat pump system and its influencing factors. Appl. Therm. Eng. 144, 1030-1036 (2018)

5. Narayanaswamy, B., Balaji, B., Gupta, R., Agarwal, Y.: Data driven investigation of faults in HVAC systems with model, cluster and compare (MCC). In: Proceedings of the 1st ACM Conference on Embedded Systems for Energy-Efficient Buildings, Memphis, TN, USA (2014)

6. A review of the fault behavior of heat pumps and measurements, detection and diagnosis methods including virtual sensors

7. Elmenreich, W., Egarter, D.: Design guidelines for smart appliances. In: Proceedings of the 10th International Workshop on Intelligent Solutions in Embedded Systems, pp. 76-82 (2012)

8. Egarter, D., Monacchi, A., Khatib, T., Elmenreich, W.: Integration of legacy appliances into home energy management systems. J. Ambient Intell. Humaniz. Comput. 7(2), 171-185 (2015). https://doi.org/10.1007/s12652-015-0312-9

9. Gardner, G.T., Stern, P.C.: The short list: the most effective actions U.S. households can take to curb climate change. Environ. Sci. Policy Sustain. Dev. 50(5), 12-25 (2008). https://doi.org/10.3200/ENVT.50.5.12-25

10. Meijer, G.C., Wang, G., Heidary, A.: Smart temperature sensors and temperature sensor systems (2018). https://doi.org/10.1016/B978-0-08-102055-5.00003-6

11. Scharnhorst, P., et al.: Energym: a building model library for controller benchmarking. Appl. Sci. 11, 3518 (2021)
12. Carlson, D.R., Matthews, H.S., Berges, M.: One size does not fit all: averaged data on household electricity is inadequate for residential energypolicy and decisions. Energy Build. **64**, 132–144 (2013)

13. Crawley, D.B., Pedersen, C.O., Lawrie, L.K., Winkelmann, F.C.: EnergyPlus: energy simulation program. ASHRAE J. **42**, 49–56 (2000)