# Forecasting Hot Water Consumption Demand for Residential Dwellings Using Hybrid Regression Technique

Ibrahim Ali Kachalla, Christian Ghiaus

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Ibrahim Ali Kachalla, Christian Ghiaus. Forecasting Hot Water Consumption Demand for Residential Dwellings Using Hybrid Regression Technique. 15th IEEE International Conference on Green Energy and Smart Systems (GESS 2024), IEEE, Nov 2024, Long Beach, CA, United States. pp.1-6, 10.1109/GESS63533.2024.10784974. hal-04838039v2

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# Forecasting Hot Water Consumption Demand for Residential Dwellings Using Hybrid Regression Technique

1st Ibrahim Ali Kachalla

Centre d'Energétique et de Thermique de Lyon
CETHIL UMR5008, INSA Lyon, Université de Lyon
F-69621 Villeurbanne, France
ibrahim-ali.kachalla@insa-lyon.fr

2nd Christian Ghiaus

Centre d'Energétique et de Thermique de Lyon
CETHIL UMR5008, INSA Lyon, Université de Lyon
F-69621 Villeurbanne, France
christian.ghiaus@insa-lyon.fr

**Abstract**—Residential buildings contribute approximately 30% of global greenhouse gas emissions, with electric water boilers accounting for around 20% of total energy consumption. The development of a smart renewable energy system and control requires adequate and accurate forecasting models to mitigate both short-term and long-term energy demand. Accurate forecasting of hot water consumption is crucial for optimizing load demand scheduling and grid energy management in residential dwellings. This study develops hybrid forecasting models by combining a seasonal auto-regressive model (SARIMA) with machine learning models, specifically Support Vector Regression (SVR) and Artificial Neural Network (ANN). The study uses six months of hot water consumption data from residential electric boilers, categorized into hourly and daily scenarios. The models are evaluated based on performance metrics, including Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). Results obtain, indicate that the SARIMA-ANN model outperforms the SARIMA-SVR model in terms of both predictive accuracy and computational efficiency. The SARIMA-ANN model's superior feature mapping, in both long- and short-time frames, makes it optimal and robust for Model Predictive Control (MPC) applications and real-time use, especially in renewable energy grid integration. It offers a more scalable solution compared to the hyperplane-dependent SARIMA-SVR model.

**Index Terms**—Energy consumption, Electric water boilers, Hybrid machine learning model, Hot water consumption, Residential buildings.

## I. INTRODUCTION

With the rise in global warming, transitioning to green energy sources like PV systems has become essential. This shift is crucial, especially given the projected 50% increase in energy demand due to industrial and residential activities, with the residential sector accounting for 20% of this increase. A significant portion of residential energy consumption comes from hot water use, including showering, kitchen activities, and bathing, which contributes to energy demand fluctuations. Electric water boilers alone account for 45.8% of home energy consumption [1]. Implementing energy-saving measures in this sector can significantly reduce overall energy usage, lower greenhouse gas emissions, and

support a more sustainable energy system. The development of robust forecasting models that can accurately predict hot water usage based on hourly and daily consumption can help mitigate this challenge [2], [3]. These hot water consumption patterns span across the year and include various end-use activities such as showering, kitchen use, bathtub reheating, and bathtub filling.

Accurate models are crucial for enhancing Model Predictive Control (MPC) strategies for demand side response management. However, developing these models presents challenges, particularly in handling the complexities of time series data, regression analysis, and the non-linearity of user pattern and behavior. This non-linearity is especially evident in the hourly, daily, and seasonal variations in hot water usage. Load demand models have evolved from traditional statistical methods to advanced machine learning and hybrid techniques [4]–[7]. Time series models like ARIMA are widely used for capturing seasonal trends, stochastic behaviours, and temporal dynamics in hot water consumption data [6], [8]–[12].

Aurore Lomet et al. [13] developed an ARIMA model to forecast daily domestic hot water (DHW) consumption, accounting for weekly periodicity, prior-day consumption, and random fluctuations, demonstrating its potential. Traditional regression analysis, such as linear regression, remains important for modeling the relationship between hot water and energy consumption, considering factors like ambient temperature and usage behaviour over time [14], [15]. Techniques like Support Vector Regression (SVR) are also effective for handling non-linearity and are recognized as powerful tools in machine learning, complementing classical methods like ARIMA, exponential smoothing, and ARMAX [16]–[18].

In recent years, machine learning technologies such as Artificial Neural Networks (ANNs) have become popular for modeling hot water consumption due to their ability to manage the complexities of non-linear end-user consumption [19]–[21]. Sheng Cao et al., [22] proposed using a
support vector machine (SVM) to predict occupants' show-
ering behaviors, achieving a 33% reduction in hot water
demand compared to traditional control methods. Similarly,
techniques like SVR and ensemble methods have shown
exceptional performance in managing high-dimensional and
non-linear data [4], [6], [23]. Christopher Bennett et al., [19],
developed an ANN-based model for residential water end-use
demand forecasting. Combining classical regression methods
with machine learning has paved the way for more accurate
and hybrid load demand models, particularly in scenarios
involving complex stochastic user behaviour in residential
building applications for grid demand response management
[24]. These hybrid models leverage the strengths and com-
pensate for the weaknesses of each approach to obtain a more
accurate hot water consumption profile [25].

Our study highlights the need for a comparative analy-
sis of hybrid models (SARIMA-ANN and SARIMA-SVR)
specifically for hot water consumption in residential building
applications, an area that has received limited attention.
Such a study could help identify the most suitable modeling
technique based on forecasting accuracy and computational
efficiency. Table I summarizes related literature on hot water
consumption in residential dwellings, focusing on research
methods, forecast horizons, data scenarios, and gaps in hybrid
model comparisons. This study combines classical regression
(SARIMA) with two machine learning techniques (SVR
and ANN) to develop SARIMA-ANN and SARIMA-SVR
models. The focus is on forecasting hot water consump-
tion in residential buildings and comparing the accuracy of
these models in both short-term and long-term forecasting
horizons using various performance metrics. The article is
structured as follows: first, the methodology for developing
the forecasting models; followed by results and discussion;
a comparative analysis of the models; and concluding with
recommendations for future research.

II. METHODOLOGY

The research methodology employed in this study aims
to compare two hybrid forecasting models that integrate
time series and regression techniques (SARIMA) with ma-
chine learning methods (SVR and ANN). These integrations
yield two hybrid models: SARIMA-SVR and SARIMA-
ANN, which are developed through empirical evaluation
and a structured methodology. The primary objectives are
to compare the prediction and forecast accuracy of these
models across two different scenarios for domestic hot water
boiler consumption, as detailed in Table II. The models’ per-
formance is evaluated using RMSE and MAE performance
metrics. This section outlines the detailed model development
and research methodology framework, as illustrated in Figure
1.

A. Data description and processing

The hot water consumption data for this case study was
obtained from 67 apartments. Data were collected from

<figure><img src="image_2.png" /><figcaption>Fig. 1. Research methodology framework</figcaption></figure>

December 1, 2020, to June 11, 2021. The data were used
to evaluate forecasts, categorizing the consumption into two
distinct scenarios, as detailed in Table II. The statistical
description of the training period data-set is presented in
Figure 2 and Figure 3.

The daily consumption scenario (Fig. 3) shows more
significant variability and higher average usage compared
to the hourly scenario (Fig. 2), indicating more consistent
daily consumption patterns with distinct peaks, especially
in apartments 4, 5, and 10. Furthermore, the models were
trained using 80% of the data, with the remaining 20%
serving as the test set. Furthermore, Table II, outlines the
different scenarios used for evaluating the forecasting models,
detailing the time-step, training period, and forecast length
for each scenario.

B. Hybrid model development

In this study, the hybridization of seasonal learning regres-
sion (SARIMA) with machine learning techniques (ANN and
SVR) is modeled using a two-stage prediction and forecasting
approach. In the first stage, the SARIMA model is employed
to capture the seasonal linear components within a 24hour
seasonality. The residuals obtained from the SARIMA model,
along with the hourly and daily data, are then used as features
in the second stage prediction using the machine learning
models.
<table><caption>TABLE I
COMPARISON OF VARIOUS RESEARCH METHODS AND DATA SCENARIOS</caption><thead><tr><th rowspan="2">Authors</th><th colspan="3">Research Methods</th><th rowspan="2">Forecast horizon</th><th rowspan="2">Data Scenarios</th><th rowspan="2">Research disparity</th></tr><tr><th>Regression</th><th>Machine Learning</th><th>Hybrid</th></tr></thead><tbody><tr><td>Fargallo et al. [26]</td><td>✓<sup>a</sup></td><td></td><td></td><td>—<sup>b</sup></td><td>98 apartments, 2015 to 2021</td><td>failed to compare hybrid techniques</td></tr><tr><td>Louis-Gabriel et al. [27]</td><td></td><td>✓</td><td></td><td>—</td><td>40-unit residential building located in Quebec City (Canada)</td><td>failed to compare Hybrid techniques</td></tr><tr><td>Ferrantelli et al. [28]</td><td>✓</td><td></td><td></td><td>—</td><td>Finland dwellings, November &amp; August</td><td>failed to compare Hybrid techniques</td></tr><tr><td>Juan de Santiago et al. [29]</td><td>✓</td><td></td><td></td><td>—</td><td>401 per person in swiss dwelling</td><td>failed to compare Hybrid techniques</td></tr><tr><td>Azar Nilsson et al. [20]</td><td></td><td>✓</td><td></td><td>monthly</td><td>Yazd, Iran, from 2011 to 2020</td><td>Did not consider Hybrid techniques</td></tr><tr><td>Xin Zhou et al. [25]</td><td></td><td>✓</td><td>✓</td><td>—</td><td>Female hostel university in Xi'an, China, 1 March to 30 Nov. 2022</td><td>Did not consider various periods or scenarios</td></tr><tr><td>Gelazan et al. [30]</td><td>✓</td><td></td><td></td><td>hourly</td><td>1hour, 2hours, 3hours for 2006 EWB</td><td>failed to compare hybrid models</td></tr><tr><td>Lomet et al. [31]</td><td>✓</td><td></td><td></td><td>daily</td><td>8 residents EWBs in France, 2009 to 2011, 10 Liters timesteps</td><td>failed to compare hybrid models</td></tr><tr><td>Barteczko et al. [32]</td><td>✓</td><td></td><td></td><td>—</td><td>130L EWB 47 data</td><td>failed to compare hybrid models</td></tr><tr><td>Denis et al. [14]</td><td>✓</td><td></td><td></td><td>yearly</td><td>USA dwelling hot water consumption</td><td>failed to compare hybrid models</td></tr><tr><td>Xu et al. [7]</td><td></td><td>✓</td><td></td><td>daily</td><td>150 EWB hot water consumption</td><td>failed to compare hybrid models</td></tr><tr><td>Bennett et al. [19]</td><td>✓</td><td></td><td></td><td>liter/person</td><td>Southeast queen land residential end-user study (SEWREUS)</td><td>failed to compare hybrid models</td></tr><tr><td>S. Cao et al. [22]</td><td>✓</td><td></td><td></td><td>—</td><td>7 occupants, 8.33L/mins daily and hour consumption</td><td>failed to compare hybrid models</td></tr><tr><td>Aki et al. [4]</td><td>✓</td><td></td><td></td><td>—</td><td>Osaka Japan, April 2007 to March 2010</td><td>failed to compare hybrid models</td></tr><tr><td>D. Kim et al. [33]</td><td>✓</td><td></td><td></td><td>—</td><td>2017 to 2022, data of apartment complex in Seongnam-si, Korea</td><td>failed to compare hybrid models</td></tr><tr><td>Rzeznik et al. [34]</td><td>✓</td><td></td><td></td><td>daily</td><td>2021 Grudziadz, in Central Poland</td><td>Neglected to consider hybrid models</td></tr></tbody></table>

<table><caption>TABLE II
SCENARIOS (TIME-STEP) DATA FOR FORECASTING MODEL EVALUATION</caption><thead><tr><th>Scenarios</th><th>Time-step</th><th>Training period</th><th>Forecast length</th></tr></thead><tbody><tr><td>Hourly</td><td>hourly</td><td>7 days</td><td>24 hours</td></tr><tr><td>Daily</td><td>24 hours</td><td>6 months</td><td>30 days</td></tr></tbody></table>

The SARIMA residuals, representing the significant non-linear relationships between the actual time series data and the SARIMA-predicted values, are input into the machine learning models (ANN and SVR) to address the non-linear complexities that the SARIMA model could not capture. The final prediction is obtained by combining the weighted outputs from both the SARIMA model and the machine learning models. The novel hybrid models developed in

this research, SARIMA-ANN and SARIMA-SVR, aim to enhance prediction accuracy by leveraging the strengths of both regression and machine learning techniques.

### C. SARIMA-ANN Model Development

The Auto ARIMA algorithm searches for the optimal combination of *p*, *d*, *q*, *P*, *D*, *Q*, and *s* parameters to find the best-fitting SARIMA model based on the Akaike Information Criterion (AIC). The best-fit SARIMA configuration, ((1, 0, 1), (1, 0, 1, 24)), was selected for hybridization with machine learning models (ANN and SVR) from empirical analysis. By analyzing 24-hourly hot water consumption data with *s* = 24 representing the daily cycle, the model captures both regular daily consumption patterns and non-linear variations. This configuration enables accurate predictions for both short-term (hourly) and long-term (daily) forecasts. The

<footnote>a Method considered by author</footnote>

<footnote>b Demand not considered by author</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 2. Hot water hourly consumption scenario</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3. Hot water daily consumption scenario</figcaption></figure>

hot water forecasting model uses the entire dataset to predict future consumption levels:

$$ \hat{x}_{t+1} = \zeta + \phi_1 \Delta x_t + \phi_2 \Delta x_{t-1} + \phi_3 \Delta x_{t-2} + \theta_1 \epsilon_t \quad (1) $$

where $\hat{x}_{t+1}$ is the forecast at time $t+1$, $\zeta$ is a constant, and $\theta_1$ models the error as a linear combination of past errors up to the $q$-th lag. The residual error of the SARIMA forecast is used as input to the machine learning models to capture the non-linear components that the SARIMA model cannot address. Forecast errors are computed as the difference between the actual observed values in the test set and the forecasted values produced by the SARIMA model:

$$ f_t = y_t - \hat{y}_t \quad (2) $$

where $y_t$ is the actual observed value at time $t$ and $\hat{y}_t$ is the forecasted value at time $t$. The forecast error $f_t$ reflects the discrepancies between the actual outcomes and the model's

forecasts. Both $e_t$ (residuals) and $f_t$ (forecast errors) are used as inputs to the ANN, which aims to learn from these errors to correct similar mistakes in future predictions and capture the non-linear patterns that the linear model (SARIMA) might miss. The hybrid forecasts subsequently combine the SARIMA forecasts $\hat{y}_{f,t}$ with the ANN-forecasted $\hat{z}_{\text{fore},t}$ using a weighted sum, yielding the final forecasts of the hybridized model:

$$ \hat{y}_{f,\text{adj},t} = w_1 \cdot \hat{y}_{f,t} + w_2 \cdot \hat{z}_{\text{fore},t} \quad (3) $$

where $\hat{y}_{f,\text{adj},t}$ is the final hybrid forecast at time $t$, and $w_1$ and $w_2$ are the respective weights for the SARIMA and ANN forecast contributions.

## D. SARIMA-SVR Model Development

Similar to the SARIMA-ANN implementation, the SARIMA model in the SARIMA-SVR design calculates residuals $e_t$ as follows:

$$ e_t = X_t - \hat{y}_t \quad (4) $$

where $e_t$ represents the residual at time $t$, $X_t$ is the actual observed value at time $t$, and $\hat{y}_t$ is the value predicted by the SARIMA model at time $t$.

The forecast $\hat{y}_{t+k}$ for a future time $t+k$ is given as:

$$ \hat{y}_{t+k} = \text{SAR}(X_t) \quad (5) $$

where $\hat{y}_{t+k}$ is the forecasted value $k$ periods ahead of the last observed time $t$. The forecast from the SARIMA model for future time $t+k$ is denoted as $\hat{f}_{t+k}^{\text{SAR}}$, while $\hat{f}_{t+k}^{\text{SVR}}$ is the corresponding forecast from the SVR model for the same future time $t+k$.

The hybrid forecasts $\hat{f}_{t+k}^{\text{hyb}}$ for future time $t+k$ are computed as:

$$ \hat{f}_{t+k}^{\text{hyb}} = w_1 \cdot \hat{f}_{t+k}^{\text{SAR}} + w_2 \cdot \hat{f}_{t+k}^{\text{SVR}} \quad (6) $$

where $w_1$ and $w_2$ are the weights assigned to the SARIMA and SVR predictions, respectively, and $\hat{f}_{t+k}^{\text{SAR}}$ and $\hat{f}_{t+k}^{\text{SVR}}$ represent the individual model forecasts at time $t+k$.

## III. RESULTS AND DISCUSSION

The SARIMA-ANN shows superior accuracy, particularly in short-term forecasting (1-hour), where it achieves an $R^2$ of 0.9766 and an RMSE of 0.0223. However, SARIMA-SVR is significantly computationally expensive, making SARIMA-ANN a more efficient model for real-time forecasting in both short and long-term scenarios.

The computational efficiency was evaluated by comparing computation times under identical simulation parameters across different scenarios. The models were developed using the Python programming language and tested on a system equipped with an 8th Gen Intel Core i5-8265U CPU @ 1.60GHz, 1.80GHz, and 16.0 GB RAM. Comparative results
<table><caption>TABLE III
SUMMARY OF FORECAST PERFORMANCE METRICS FOR SARIMA-SVR AND SARIMA-ANN MODELS</caption><thead><tr><th>Scenario (Timestep)</th><th>Algorithms Model</th><th>Computation Time</th><th>R<sup>2</sup></th><th>RMSE</th><th>MAE</th><th>MSE</th></tr></thead><tbody><tr><td rowspan="2">1 hour</td><td>SARIMA-SVR</td><td>3 mins 44.2 s</td><td>0.5080</td><td>0.0862</td><td>0.0692</td><td>0.0074</td></tr><tr><td>SARIMA-ANN</td><td>0.7802 s</td><td>0.9766</td><td>0.0223</td><td>0.0074</td><td>0.0005</td></tr><tr><td rowspan="2">24 hours</td><td>SARIMA-SVR</td><td>3 mins 13.0 s</td><td>0.2678</td><td>0.0616</td><td>0.0466</td><td>0.0038</td></tr><tr><td>SARIMA-ANN</td><td>0.6949 s</td><td>0.4051</td><td>0.1229</td><td>0.1032</td><td>0.0152</td></tr></tbody></table>

for the prediction and forecasting capabilities are presented in Table III. The SARIMA-ANN model demonstrated low computation times in both scenarios, while the SARIMA-SVR model was the most computationally expensive, taking 3 minutes and 44 seconds in scenario one (hourly).

<figure><img src="image_5.png" /><figcaption>Fig. 4. Prediction & forecasting for hourly Scenario</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5. Prediction & forecasting daily Scenario</figcaption></figure>

The results in these figures 4 and 5, show a clear pattern in how the SARIMA-ANN and SARIMA-SVR models fit to time series hot water boiler consumption data. In both hourly and daily scenarios, the SARIMA-ANN model (black line) aligns more closely with the actual data (green line), capturing both short-term fluctuations and long-term trends more accurately than the SARIMA-SVR model (red line), which exhibits greater deviations. The forecasted areas further emphasize SARIMA-ANN's superior ability to model hot water boiler consumption patterns, maintaining better consistency in both trends and forecasted values, whereas

SARIMA-SVR struggles, especially during peak consumption periods, making SARIMA-ANN a better choice for hot water boiler consumption forecasting.

## IV. CONCLUSION

To accurately address demand response with the integration of green energy systems in residential dwellings, it is crucial to develop accurate and robust models for hot water consumption, which this research aims to achieve. The novelty lies in incorporating daily and time-of-day features into the ANN model, along with the non-linear residuals that SARIMA could not capture in the second-stage prediction. These feature inputs enhance the hybrid model's accuracy and robustness in capturing stochastic user behavior. SARIMA-ANN has demonstrated optimal performance in both short-term and long-term predictions, which is significant for real-time kWh deployment, smart meter management, and mini-grid integration for demand response applications.

The SARIMA-ANN model proved more effective in mapping features than the SARIMA-SVR model, which relies on hyperplanes and incurs higher computational costs as the feature space and scalability increase. The hidden layers of the ANN effectively learned and captured the high dimensional feature space. Future work should explore the use of 1D Convolutional Neural Networks (CNN) or transformer models to better forecast intrinsic variations, further improving forecasting accuracy and computational efficiency.

## ACKNOWLEDGMENT

The authors would like to thank the Institut National des Sciences Appliquées de Lyon and the Centre d'Energétique et de Thermique de Lyon for providing the necessary resources and facilities to conduct this research. We are grateful to the Petroleum Technology Development Fund (PTDF), Nigeria, and Immobilier Rhône Alpes-Groupe 3 F for their financial support and data, which made this study possible. Lastly, we extend our gratitude to our families and friends for their continuous encouragement and understanding.

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