# Performance Meta-analysis for Big-Data Univariate Auto-Imputation in the Building Sector

Aliki Stefanopoulou, Iakovos Michailidis, Asimina Dimara, Stelios Krinidis, Elias B. Kosmatopoulos, Christos-Nikolaos Anagnostopoulos, Dimitrios Tzovaras

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Aliki Stefanopoulou, Iakovos Michailidis, Asimina Dimara, Stelios Krinidis, Elias B. Kosmatopoulos, et al.. Performance Meta-analysis for Big-Data Univariate Auto-Imputation in the Building Sector. 18th IFIP International Conference on Artificial Intelligence Applications and Innovations (AIAI), Jun 2022, Hersonissos, Greece. pp.276-288, 10.1007/978-3-031-08341-9_23. hal-05335653

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# Performance Meta-analysis for Big-Data
Univariate Auto-Imputation
in the Building Sector

Aliki Stefanopoulou<fnref n="1" /> Ⓓ, Iakovos Michailidis<fnref n="1" />,<fnref n="2" /> Ⓓ, Asimina Dimara<fnref n="1" />,<fnref n="4" />(✉) Ⓓ, Stelios Krinidis<fnref n="1" />,<fnref n="3" /> Ⓓ, Elias B. Kosmatopoulos<fnref n="1" />,<fnref n="2" /> Ⓓ, Christos-Nikolaos Anagnostopoulos<fnref n="4" /> Ⓓ, and Dimitrios Tzovaras<fnref n="1" /> Ⓓ

**Abstract.** Filtering refers to the process of defining, detecting and correcting errors in a given dataset, to achieve system reliability and minimize the impact of errors in data analysis. Automated and accurate tools for data filtering and healing are crucial to ensure reliability of the system. This study aims to investigate statistical and machine-learning-based methodologies for data gaps healing and missing values imputation. In total, five models are being investigated individually, the well known ARIMA model, Linear and Polynomial Interpolation, General Regression and Facebook Prophet. The raw data that are used to evaluate these methods are simulated, and artificial data gaps are imposed randomly within the dataset to evaluate the univariate imputation performance of the aforementioned models based on Mean Squared Error and Mean Absolute Error. As expected the evaluation results illustrate the efficiency of highly elaborate machine-learning Facebook Prophet against more simple statistic ARIMA in expense of time and computational efforts. However, for Big Data univariate imputation applications the study findings suggest that a combination of ARIMA and Facebook Prophet, depending on the data gap size, could balance out the required computational resources while maintaining highly accurate imputation results.

**Keywords:** Big data · Building application · Simulation data · Hybrid auto-imputation

<footnote n="1">¹ Information Technologies Institute, Centre for Research and Technology Hellas,
57001 Thessaloniki, Greece
adimara@iti.gr</footnote>

<footnote n="2">² Electrical and Computer Engineering Department,
Democritus University of Thrace, 67000 Xanthi, Greece</footnote>

<footnote n="3">³ Management Science and Technology Department, International Hellenic
University (IHU), Kavala, Greece</footnote>

<footnote n="4">⁴ Department of Cultural Technology and Communication, Intelligent Systems Lab,
University of the Aegean, Mytilene, Greece</footnote>
# 1 Introduction

During 2020 almost 2.5 quintillion data bytes were created daily [1]. All these data are mostly unstructured and of low-density. Data streams of sensor-enabled devices, equipment and infrastructure generate tens of terabytes of information. Moreover, all this volume of data is transferred and received in fast rate while requiring real-time processing, action and evaluation [2]. Additionally, big data comes in a semi-structured or unstructured way while demanding an additional process to reinforce metadata [3]. As a result, handling, processing, saving, exploiting and development of big data is a thorny task that demands perplexing processes and methods.

One of the major problems when starting to assess big data is the missing values that generate lost sequences of valuable information [4]. This lack of information is crucial especially during the training process of machine learning models affecting the models' accuracy [5]. Specifically, even in small data-sets containing enormous gaps, missing data imputation may increase the algorithm's accuracy by at least 50% [4]. Furthermore, in numerous cases data are time-dependent as a result, forecasting the missing values is the one and only solution [6] to fit the time-series model to predict.

Numerous methodologies and technologies are exploited for missing data imputation in time-series data sets [7]. Some of these methods are of low complexity like averaging technique [8] or backward filling technique [9]. While others use more complicated methodologies like artificial neural networks [9]. To sum up, models of low complexity are of low accuracy but they are easy-to-use models and require low execution time and may be used for real-time applications [10]. Contrariwise, perplexing models offer higher accuracy and better results but they require longer execution time and further processing for big data [10].

## 1.1 Contributions of the Study

Based on the aforementioned discussion, the current study attempts to create an automated framework for big series data filtering. The study emphasizes on univariate imputation problems, which is a common issue in large data warehouses where continuous and reliable monitoring for long periods of time is not usual [11, 12]. Reasonably, data warehouses usually present data gaps where data samples are missing, replaced with *NaN*, *Null* or even constant/frozen values instead. The root-cause and the size of such a problem may differ, depending on: the type of IoT/sensing infrastructure, the transmission channel bandwidth, power supply quality (constant supply or battery-based devices), the gateways operational reliability (freezing due to overloading and poor cooling), the protocol security (vulnerability to external cyber-attacks) and the data-storage management quality. Therefore, as data gaps may occur due to a large variety of causes; addressing such a problem usually suggests healing data gaps after their migration in the database/data-warehouse instead of trying to fix any or all aforementioned issues.
Several statistical approaches such as general regression (Gaussian mix imputation), linear interpolation, moving average (MA), auto-regressive MA (ARMA) and even ARIMA; have been proven capable of performing imputation in a quite robust manner [13, 14], however their accuracy is gradually becoming poorer as the size of the data gap increases, where such lightweight mechanisms are called to impute large sequences of missing data. The main reason for such a performance degradation is their locally-driven nature [15], utilizing only neighboring data entries of the time-series which cannot replicate adequately the wide-scale trends and seasonalities of the entire time-series.

On the other hand, deep machine learning techniques, e.g., Convolutional Neural Networks (CNNs), Generative Adversarial Networks (GANs), Self Organizing Maps (SOMs); and applications have emerged over the recent past years due to the rapid emergence of cloud as well as distributed computational platforms (GPUs) providing adequate capacity to train such complex data-processing structures in a reasonable expense [16]. The usual approach for such mechanisms is to effectively fit a uni-variate forecasting deep-learning regression tool which can reliably impute missing values. Such complex mechanisms are trained over the entire available dataset in order to be able to generalize and adequately mimic the dynamic of the underlying time-series.

The current study utilizes simulative ground truth data and randomly generated data missing gaps in different time-series (see Sect. 3). Simulative data can provide a ground truth baseline which could support the performance assessment of the tested mechanisms. The data gaps imposed are of different sizes and were randomly applied at different time slots across the same series. The study investigates the performance of individually applied univariate imputation mechanisms of diverse complexity in order to assess their behavior in terms of accuracy (with respect to the ground truth data series) and in terms of computational/time expenses. Ultimately, the goal of the study is to identify an inventory of the most appropriate - both in terms of accuracy and time/complexity - big data imputation techniques to build an auto-imputation univariate engine based on automatically selected imputation mechanisms that depend on the size of the missing data sequences.

## 1.2 Study Structure

The current study is structured as follows:

- Section 1 includes a description of the objectives of this study, its possible application and contributions to the scientific community as well as a brief description of the approaches that are currently used for timeseries analysis and prediction.

- In Sect. 2, the investigated models are thoroughly described.

- In Sect. 3, the dataset synthesis is presented in depth.

- Section 4 includes the experimental ARIMA, Linear Interpolation, General Regression and Facebook Prophet results that are compared in detail in their overall performance with each other, in various cases of missing data gaps.
Finally, a hybrid model that makes use of both ARIMA and Facebook Prophet models is presented and evaluated as well.

- In Sect. 5, the final conclusions of this study are drawn.

# 2 Investigated Approaches

## 2.1 ARIMA

One of the most widely used statistical methods for times series forecasting is the AutoRegressive Integrated Moving Average (ARIMA model). The key aspects of ARIMA model are:

- **AR:** *AutoRegression*. This model uses the dependent relationship between an observation and a predefined number of lagged observations in the time series.

- **I:** *Integrated*. It describes the differencing of observations that are used to make the time series stationary. If the time series is already stationary, this parameter is set to zero.

- **MA:** *Moving Average*. This model uses the dependent relationship between an observation and a residual error from a moving average model that is applied to lagged observations of the original time series.

The aforementioned components are specified in the model as parameters (p, d, q). These parameters are defined as follows:

- **p**: This parameter is mentioned as lag order and it defines the number of lagged observations that are used for the model.

- **d**: This parameter is mentioned as degree of differencing and it defines the number of times that the time series if differenced, in order for it to become stationary, to remove trend and seasonality.

- **q**: This parameter is mentioned as order of moving average and it defines the size of the moving average window.

For each of the elements, a value of 0 can be used to indicate that this element will not be used for the model, constructing a simpler model. In case that a value of 0 is used for the d parameter, the model performs the function of an ARMA model.

## 2.2 Linear Interpolation

Linear Interpolation is a method of curve fitting. According to this method, linear polynomials are used to construct new data points within the time series, to substitute possible missing values. Below is the algorithm for estimation of a value between two points of data, using linear interpolation.

- **Given Data X:** Independent variable for which the dependent variable is to be estimated.
- **Wanted Data Y<sub>e</sub>:** Estimated dependent value for an independent given value X.

**Linear Interpolation followed procedure:**

1. Find the independent data in the records, with the highest value that is less than X. This will be **X<sub>1</sub>**. X<sub>1</sub> will give **Y<sub>1</sub>**, since they are associated in the time series.

2. Find the independent data in records, with the lowest value that is more than X. This will be **X<sub>2</sub>**. X<sub>2</sub> will give **Y<sub>2</sub>**, since they are associated in the time series.

3. These four values will give **Y<sub>e</sub>** using the formula:

$$Y_e = Y_1 + \frac{(X - X_1)(Y_2 - Y_1)}{(X_2 - X_1)} \quad (1)$$

This method can be used for all missing values in between known data points in a time series.

## 2.3 General Regression

General regression is a method of statistical curve fitting. This method makes use of historical data for filling in the missing data and modeling. The aim of this method is to try to estimate a missing value Q<sub>e</sub>, for a given value V, which denotes time, with the use of stored records:

$$ \begin{gathered} Z_1, Z_2, Z_3, \dots, Z_n, \dots, Z_N \\ \Downarrow \\ (V_1, Q_1), (V_2, Q_2), (V_3, Q_3), \dots, (V_n, Q_n), \dots, (V_N, Q_N) \end{gathered} \quad (2) $$

General Regression assumes that the closer V is to the given attributes of a stored record in the time series, V<sub>n</sub>, the more similar the missing value Q<sub>e</sub> will be, to the missing attribute of the same record in the time series Q<sub>n</sub>. This means that the closer V is to V<sub>n</sub>, the more the contribution of Q<sub>n</sub> to Q<sub>e</sub> will be (Eq. (3)).

$$Q_e = G(V) = \frac{\sum_{n=1}^{N} Q_n g(V - V_n, \sigma)}{\sum_{k=1}^{N} g(V - V_n, \sigma)}, \quad (3)$$

where g is the Gaussian window function:

$$G(V - V_n, \sigma) = \frac{1}{(\sqrt{2\pi\sigma})^2} e^{-\frac{(V - V_n)^2}{2\sigma^2}}, \quad (4)$$

where σ is the standard deviation of the distribution.
## 2.4 Facebook Prophet

Facebook prophet is an open-source algorithm that makes for time series models generation. Facebook prophet model includes three main components, trend, seasonality and holidays. These components are combined to form the model's equation:

$$y(t) = g(t) + s(t) + h(t) + \epsilon_t, \quad (5)$$

where $g(t)$ is the piecewise linear or logistic growth curve for modeling non-periodic changes in a time series, $s(t)$ refers to the seasonality of the timeseries, $h(t)$ refers to the effect of holidays with irregular schedules and $\epsilon_t$ is the error term that describes any unusual changes that are not described in the model. Prophet's goal is to fit linear and non-linear functions of time as components, using time as a regressor.

## 3 Dataset Synthesis

As mentioned above, the dataset considers synthetically generated data from a simulative test bed. The simulative test bed comprises a commercial medium scale (3-thermal zone) building, equipped with indoor sensors for temperature, relative humidity, and energy consumption. The energy consumption relates to two different highly energy-intensive appliances, an electric heat pump for кли- mating purposes coupled with DHW component. The control of the DHW and heat pump was undertaken by a simplified rule-based approach so as to maintain indoor thermal comfort between acceptable bounds. The considered dataset pre- sented a sampling rate of one hour incorporating data from 12 months in total; for simplicity purposes only the available measurements from the first thermal zone were taken into account. To emulate missing values incidents, different data gaps were randomly imposed across timeseries with different descriptive statis- tical characteristics (e.g., minimum, maximum, mean value, variance): indoor temperature [°C], relative humidity [%], heating load [kWh] and DHWs [kWh]. Initially only one short or one long data gap was imposed in order to individu- ally evaluate the performance of the different imputation approaches mentioned above. Secondly both short and long incidents were randomly imposed in the con- sidered timeseries evaluating again the performance of each individual univariate imputation technique. Eventually a hybrid approach, considering combinations of such techniques in order to exploit their different advantages/properties: light- ness, complexity, data intensity, time required, accuracy achieved.

## 4 Evaluation of Results

All aforementioned methods where used in the datasets to impute the missing values. The models were evaluated using Mean Absolute Error, Mean Squared Error and Execution Time as metrics. They were evaluated in the data sets
mentioned in Sect. 3, with a small number of consecutive missing values, in the same data sets with a large number of consecutive of missing values, and lastly in the same data sets with both a small number and a large number of consecutive missing values. The Results are presented below.

## 4.1 Two (2) Consecutive Missing Values

<table><caption>**Table 1.** Two missing values</caption><thead><tr><th>Model</th><th>MSE</th><th>MAE</th><th>Execution Time (seconds)</th></tr></thead><tbody><tr><td colspan="4"><em>Indoor Temperature</em></td></tr><tr><td>ARIMA</td><td>0,00447</td><td>0,0659</td><td>26,8601</td></tr><tr><td>Linear Interpolation</td><td>0,0002</td><td>0,0116</td><td>0,0441</td></tr><tr><td>General Regression</td><td>0,00255</td><td>0,0424</td><td>19,6569</td></tr><tr><td>Facebook Prophet</td><td>0,1229</td><td>0,3395</td><td>29,7903</td></tr><tr><td colspan="4"><em>Indoor Relative Humidity</em></td></tr><tr><td>ARIMA</td><td>0,176</td><td>0,3805</td><td>20,878</td></tr><tr><td>Linear Interpolation</td><td>0,1094</td><td>0,325</td><td>0,0437</td></tr><tr><td>General Regression</td><td>0,1227</td><td>0,3459</td><td>20,0882</td></tr><tr><td>Facebook Prophet</td><td>1,8674</td><td>1,3665</td><td>22,8563</td></tr><tr><td colspan="4"><em>Heating Load</em></td></tr><tr><td>ARIMA</td><td>0</td><td>0,272</td><td>14,26</td></tr><tr><td>Linear Interpolation</td><td>0</td><td>0</td><td>0,0434</td></tr><tr><td>General Regression</td><td>1,046e-07</td><td>0,0002</td><td>19,96</td></tr><tr><td>Facebook Prophet</td><td>2,282</td><td>1,51</td><td>19,68</td></tr><tr><td colspan="4"><em>Cooling Load</em></td></tr><tr><td>ARIMA</td><td>10</td><td>3,02</td><td>19,66</td></tr><tr><td>Linear Interpolation</td><td>3,2</td><td>1,79</td><td>0,0456</td></tr><tr><td>General Regression</td><td>6,61</td><td>2,18</td><td>20,436</td></tr><tr><td>Facebook Prophet</td><td>621,454</td><td>24,718</td><td>20,456</td></tr></tbody></table>

As illustrated in Table 1, in cases the data gap is comparatively small, linear interpolation manages to achieve the most accurate results, in and its execution time is significantly smaller than the execution time of the other investigated methods. However, as the data gap increases, it is evident that linear interpolation is unable to produce accurate results, because its predicted values depend only on the last value acquired right before the error and the first value acquired right after the error, and occasional trends are not considered.
## 4.2 Forty-eight (48) Consecutive Missing Values

As illustrated in Table 2, in cases the data gap is large, Facebook Prophet is able to achieve the most accurate results, in most of the datasets, however it is computationally expensive. ARIMA also manages to achieve notable results, and it is not as computationally expensive. General Regression does not manage to achieve accurate results in any of the studied datasets.

<table><caption>**Table 2.** Forty-eight consecutive missing values</caption><thead><tr><th>Model</th><th>MSE</th><th>MAE</th><th>Execution Time (seconds)</th></tr></thead><tbody><tr><td colspan="4"><em>Indoor Temperature</em></td></tr><tr><td>ARIMA</td><td>0,3173</td><td>0,5113</td><td>25,255</td></tr><tr><td>Linear Interpolation</td><td>0,4832</td><td>0,5513</td><td>0,0671</td></tr><tr><td>General Regression</td><td>0,5046</td><td>0,5602</td><td>26,2536</td></tr><tr><td>Facebook Prophet</td><td>0,2762</td><td>0,461</td><td>28,6181</td></tr><tr><td colspan="4"><em>Indoor Relative Humidity</em></td></tr><tr><td>ARIMA</td><td>2,4543</td><td>1,2754</td><td>23,1787</td></tr><tr><td>Linear Interpolation</td><td>1,6711</td><td>0,9774</td><td>0,0702</td></tr><tr><td>General Regression</td><td>14,6187</td><td>3,0567</td><td>27,1273</td></tr><tr><td>Facebook Prophet</td><td>101,512</td><td>9,8752</td><td>24,7457</td></tr><tr><td colspan="4"><em>Heating Load</em></td></tr><tr><td>ARIMA</td><td>1,519</td><td>1,019</td><td>25,439</td></tr><tr><td>Linear Interpolation</td><td>6,554</td><td>2,109</td><td>0,065</td></tr><tr><td>General Regression</td><td>16,7</td><td>3,756</td><td>25,853</td></tr><tr><td>Facebook Prophet</td><td>0,348</td><td>0,436</td><td>20,183</td></tr><tr><td colspan="4"><em>Cooling Load</em></td></tr><tr><td>ARIMA</td><td>4144,877</td><td>54,493</td><td>20,562</td></tr><tr><td>Linear Interpolation</td><td>9185,682</td><td>84,73</td><td>0,0693</td></tr><tr><td>General Regression</td><td>16124,449</td><td>90,898</td><td>25,895</td></tr><tr><td>Facebook Prophet</td><td>2829,142</td><td>48,661</td><td>21,772</td></tr></tbody></table>
4.3 Multiple Consecutive Missing Values

After investigating the accuracy of the previously mentioned models in small and large data gaps, a hybrid model that uses ARIMA model in comparatively small data gaps and Facebook Prophet in large data gaps was considered. We used an auto-detection gap technique to identify the gaps in the timeseries and then, we used ARIMA model for gaps that are of size fifteen at most, and Facebook Prophet for larger gaps. The Results are illustrated at Table 3 and Figs. 1, 2, 3 and 4.

<table><caption>Table 3. Multiple consecutive missing values</caption><thead><tr><th>Model</th><th>MSE</th><th>MAE</th><th>Execution Time (seconds)</th></tr></thead><tbody><tr><td><em>Indoor Temperature</em></td><td></td><td></td><td></td></tr><tr><td>ARIMA</td><td>0,0066</td><td>0,0058</td><td>24,8823</td></tr><tr><td>Linear Interpolation</td><td>0,0047</td><td>0,0049</td><td>0,0775</td></tr><tr><td>General Regression</td><td>0,0057</td><td>0,0054</td><td>28,1362</td></tr><tr><td>Facebook Prophet</td><td>0,0032</td><td>0,0042</td><td>31,1767</td></tr><tr><td>ARIMA and Facebook Prophet</td><td>0,0043</td><td>0,0044</td><td>30,604</td></tr><tr><td><em>Indoor Relative Humidity</em></td><td></td><td></td><td></td></tr><tr><td>ARIMA</td><td>0,3912</td><td>0,041</td><td>22,3956</td></tr><tr><td>Linear Interpolation</td><td>0,09133</td><td>0,01944</td><td>0,0789</td></tr><tr><td>General Regression</td><td>0,3132</td><td>0,0375</td><td>28,8337</td></tr><tr><td>Facebook Prophet</td><td>0,3029</td><td>0,04352</td><td>33,9757</td></tr><tr><td>ARIMA and Facebook Prophet</td><td>0,14733</td><td>0,0276</td><td>30,4774</td></tr><tr><td><em>Heating Load</em></td><td></td><td></td><td></td></tr><tr><td>ARIMA</td><td>0,0543</td><td>0,0159</td><td>13,9703</td></tr><tr><td>Linear Interpolation</td><td>0,04414</td><td>0,0137</td><td>0,0776</td></tr><tr><td>General Regression</td><td>0,0485</td><td>0,01422</td><td>28,821</td></tr><tr><td>Facebook Prophet</td><td>0,0066</td><td>0,0054</td><td>18,7469</td></tr><tr><td>ARIMA and Facebook Prophet</td><td>0,0187</td><td>0,0082</td><td>18,5313</td></tr><tr><td><em>Cooling Load</em></td><td></td><td></td><td></td></tr><tr><td>ARIMA</td><td>17,1138</td><td>0,2761</td><td>17,2349</td></tr><tr><td>Linear Interpolation</td><td>9,7903</td><td>0,1966</td><td>0,0777</td></tr><tr><td>General Regression</td><td>9,9738</td><td>0,1998</td><td>28,2922</td></tr><tr><td>Facebook Prophet</td><td>7,1788</td><td>0,2014</td><td>20,4320</td></tr><tr><td>ARIMA and Facebook Prophet</td><td>13,1541</td><td>0,2571</td><td>19,0174</td></tr></tbody></table>
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** (a) Raw Indoor Temperature Data with multiple missing values. (b) Indoor Temperature Data Univariate Imputation using ARIMA. (c) Indoor Temperature Data Univariate Imputation using Facebook Prophet. (d) Indoor Temperature Data Univariate Imputation using ARIMA on small gaps and Facebook Prophet on large gaps.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** (a) Raw Indoor Relative Humidity Data with multiple missing values. (b) Indoor Relative Humidity Data Univariate Imputation using ARIMA. (c) Indoor Relative Humidity Data Univariate Imputation using Facebook Prophet. (d) Indoor Relative Humidity Data Univariate Imputation using ARIMA on small gaps and Facebook Prophet on large gaps.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** (a) Raw Heating Load Data with multiple missing values. (b) Heating Load Data Univariate Imputation using ARIMA. (c) Heating Load Data Univariate Imputation using Facebook Prophet. (d) Heating Load Data Univariate Imputation using ARIMA on small gaps and Facebook Prophet on large gaps.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** (a) Raw Cooling Load Data with multiple missing values. (b) Cooling Load Data Univariate Imputation using ARIMA. (c) Cooling Load Data Univariate Imputation using Facebook Prophet. (d) Cooling Load Data Univariate Imputation using ARIMA on small gaps and Facebook Prophet on large gaps.</figcaption></figure>

# 5 Conclusions

As indicated in Sect. 4 of this article, the longer the gap in the time-series, the more difficult it is for the models to accurately predict the missing values. In case the data gap is comparatively small, Linear Interpolation method predicts the missing values more accurately, outperforming all the other methods,
especially when its execution time is taken under consideration. General Regression and ARIMA models are precise when the data gap is small, but their execution times are notably larger than the Linear Interpolation method's execution time. Facebook Prophet on the other hand is imprecise in small data gaps and its execution time is comparatively large as well. As the data gap increases, Linear Interpolation method's accuracy deteriorates, although its execution time remains significantly smaller than the execution time of the other methods. In large data gaps, Facebook Prophet tends to be the most accurate between all the aforementioned methods, however, its execution time is considerably large. To accommodate for that, we used a hybrid approach, using an auto-detection gap technique and we made use of the ARIMA model for the imputation of small data gaps, to take advantage of its accuracy and small execution time in such cases, and Facebook Prophet for the comparatively larger gaps, to take advantage of its high accuracy in such cases. The resulting model outperforms the ARIMA model when it comes to aggregated accuracy, and its execution time is slightly smaller than the execution time of Facebook Prophet model, in the same data sets.

**Acknowledgements.** The research leading to these results was partially funded by the European Commission “EEB-07-2017 Integration of energy harvesting at building and district level” - PLUG-N-HARVEST H2020 project (Grant agreement ID: 768735) https://www.plug-n-harvest.eu/, accessed on 22 February 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.

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