Energy Consumption Forecasting in Commercial Buildings during the COVID-19 Pandemic: A Multivariate Multilayered Long-Short Term Memory Time-Series Model with Knowledge Injection

: The COVID-19 pandemic and the subsequent implementation of lockdown measures have signiﬁcantly impacted global electricity consumption, necessitating accurate energy consumption forecasts for optimal energy generation and distribution during a pandemic. In this paper, we propose a new forecasting model called the multivariate multilayered long short-term memory (LSTM) with COVID-19 case injection ( mv-M-LSTM-CI ) for improved energy forecast during the next occurrence of a similar pandemic. We utilized data from commercial buildings in Melbourne, Australia, during the COVID-19 pandemic to predict energy consumption and evaluate the model’s performance against commonly used methods such as LSTM, bidirectional LSTM, linear regression, support vector machine, and multilayered LSTM (M-LSTM). The proposed forecasting model was analyzed using the following metrics: mean percent absolute error (MPAE), normalized root mean square error (NRMSE), and R 2 score values. The model mv-M-LSTM-CI demonstrated superior performance, achieving the lowest mean percentage absolute error values of 0.061, 0.093, and 0.158 for DatasetS1 , DatasetS2 , and DatasetS3 , respectively. Our results highlight the improved precision and accuracy of the model, providing valuable information for energy management and decision making during the challenges posed by the occurrence of a pandemic like COVID-19 in the future.


Introduction 1.Background
Electricity plays a key role in sustaining industrialization in all economies.Over time, the global demand for energy and electricity usage continue to rise.Given the substantial electrical consumption of commercial and residential buildings, the need for efficient prediction and management of smart electrical energy is becoming increasingly important.Accurate load forecasting directly influences the control and planning of power system operation, emphasizing the significance of this aspect.
Nevertheless, global consumption patterns have been profoundly impacted by the coronavirus pandemic.As demonstrated [1][2][3], the closure of nonessential businesses and the implementation of stay-at-home directives resulted in a substantial decrease in power demand and significant alterations in daily consumption patterns.Due to the effects of unusual circumstances such as the COVID-19 pandemic, finding novel approaches to better predict the load demand during these troubling times is of paramount importance.Although we acknowledge the specific context of the COVID-19 pandemic as a use case, the proposed energy consumption forecasting model aims to provide a generic framework that can be adapted to future pandemic scenarios and other comparable crisis situations.
The COVID-19 pandemic has had unprecedented global impacts, leading to widespread lockdown measures, travel restrictions, and changes in social and economic activities.These measures have resulted in dramatic shifts in energy consumption patterns across many sectors.For example, Australia witnessed a substantial decrease in energy consumption of 3.6% during the 2020-2021 fiscal year, which was 5790 petajoules.These record declines in the last two years, driven primarily by the pandemic, have pushed energy consumption levels below those recorded a decade ago (5910 petajoules).In particular, the transport sector experienced the most significant reduction, with an 11% decline in energy consumption.Air transport operated at approximately one-third of the energy use levels observed two years earlier [4].Considering the breakdown of electricity end users in selected industries, as depicted in Figure 1, based on the data from the Australian Bureau of Statistics, energy forecasting evidently plays a vital role in managing and planning energy resources.Among the selected industries, transport, storage, and services saw a notable decline in energy usage of 24.1%, reaching 465 petajoules.Manufacturing saw a modest increase of 1.1%, reaching 909 petajoules, while mining experienced a slight decrease of 0.9%, reaching 564 petajoules [4].These variations in energy consumption in industries emphasize the need for accurate energy forecasting to optimize resource allocation, enable effective energy management, and support decisionmaking processes.By forecasting energy consumption levels, stakeholders can adapt their strategies and policies to the changing landscape and make informed decisions about energy generation, distribution, and utilization.
The implementation of global lockdown policies in response to the COVID-19 pandemic has had a notable impact on worldwide electricity consumption.Recognizing the crucial role of electricity supply security in safeguarding people's livelihoods during the pandemic, many countries have emphasized the importance of the accurate prediction of the electricity demand.Although there have been numerous studies on electricity forecasting, some studies [5][6][7] have addressed prediction during the COVID-19 pandemic.Moreover, these studies have generally overlooked the unique challenges presented by the pandemic, particularly in the context of specific commercial buildings, with limited emphasis on capturing detailed consumption patterns in 15 min intervals.

Related Work
Several studies have been conducted on energy consumption forecasting during the COVID-19 pandemic.Some studies have explored the relationships between electricity demand and its influencers.Various factors, including COVID-19 measures, have an impact on national electricity demand, but quantifying these impacts is challenging.For example, Sinden [8] investigated the correlation between wind power generation and electricity demand by analyzing 66 offshore weather measuring sites in the U.K. The study revealed that the supply of wind power tends to increase during periods of high electricity demand.Rosenberg et al. [9] used the modeling of the energy system to project the long-term Norwegian energy demand, suggesting that the fraction of renewable energy would increase if the energy demand decreases.Klemes et al. [10] investigated the additional energy and resource demands during the implementation of COVID-19 containment measures.Norouzi et al. [11] studied the impact of COVID-19 on electricity demand in China using a neural network model, revealing that the historical trends in electricity demand becsme blurred during the global pandemic.The neural network model incorporated a range of variables, encompassing historical GDP growth rate, oil demand, electricity demand, epidemic control index, daily infected individuals, daily manufacturing activity, export income, foreign investment, and the stock market index.Bedi et al. [12] proposed a deep-learning-based approach using LSTM to forecast the electricity demand within a user-defined time interval, and the approach outperformed other algorithms, like recurrent neural network (RNN), support vector machine (SVM), and artificial neural network (ANN).Hongfang et al. [13] developed a hybrid system for daily electricity demand prediction, considering the impacts of the pandemic.The accuracy and stability of the proposed models were tested using an example based in the U.S. The model incorporated variables such as historical electricity demand, daily infection cases, daily mortality figures, and the Government Response Stringency Index (GRSI).Santiago et al. [5] presented a detailed analysis of how confinement measures to prevent the spread of COVID-19 have modified the electricity consumption in Spain.The analysis involved utilizing daily records of both anticipated and actual electricity demand to comprehend the alterations caused by the pandemic-related restrictions.Alasali et al. [6] developed a rolling stochastic ARIMAX forecast model aimed at enhancing prediction accuracy by accommodating the irregular nature of electrical demand.Their approach involved generating multiple future electrical demand scenarios to bolster the predictive model.The probabilistic forecast models were tailored to predict electrical demand at different intervals (half-hourly, daily, weekly, and monthly) based on historical data spanning five years, including the pandemic-affected year of 2020.Zhong et al. [7] conducted a comprehensive review of the impacts that the pandemic has caused on the electricity sector.These studies offere predictive insights and an overview of electricity dynamics during the COVID-19 pandemic.Table 1 is a summary of different forecasting models for load forecasting in commercial buildings.Moreover, these studies have generally overlooked the distinctive challenges posed by the pandemic, particularly within the context of specific commercial buildings.To the best of the our knowledge, no existing studies quantitatively examined how lockdown restrictions specifically influenced the national electricity system, despite its importance for ensuring safe and normal operations.

Contribution
In this research, we introduced a novel forecasting model called multivariate multilayered long short-term memory (LSTM) with COVID-19 case Injection (mv-M-LSTM-CI).The model aims to accurately predict energy consumption in specific commercial buildings, such as the Hawthorn Campus-ATC Building, the Hawthorn Campus-AMDC Building, and the Wantirna Campus-KIOSC Building in Australia, with the granularity of 15 min intervals.Through experimentation, we observed that the proposed models, accompanied by the employed data-processing techniques, consistently outperformed baseline models, such as LSTM, bidirectional LSTM (Bi-LSTM), linear regression, and support vector machine, in terms of key evaluation metrics, including the mean absolute percentage error (MAPE), the normalized root mean square error (NRMSE), and the R 2 score.The results highlight the effectiveness of our approach in achieving highly reliable and precise energy consumption forecasts, providing valuable insights for energy management and decision-making processes not just specifically during the pandemic but also for other crisis situations of equal magnitude to make commercial buildings smarter and energy-efficient.

Paper Organization
The remaining sections of this paper are structured as follows.In Section 2, we present the energy consumption data obtained from commercial buildings, together with the daily COVID-19 case records in the respective areas.The methodology used in this study, including the proposed models and the data preprocessing techniques, is described in detail in Section 3. Section 4 presents the experimental results, showcasing the effectiveness of the models.Finally, Section 5 concludes this paper.

Daily COVID-19 Cases in Victoria
In addition to incorporating data from three commercial buildings in a 15 min interval, we integrated the daily COVID-19 case data from the state of Victoria, Australia, to improve the accuracy of our predictions.During COVID-19, the state of Victoria experienced multiple periods of strict lockdowns and restrictions.The timeline of COVID-19 restrictions is shown in Figure 2 [24], and Figure 3 shows the trend in the daily number of COVID-19 cases from February 2020 to January 2021.On 16 March 2020, Victoria declared a state of emergency, implementing social distancing measures, work-from-home policies, and restrictions on nonessential activities and travel [25].Stricter Stage 3 restrictions were introduced on 31 March 2020, which were gradually eased on 13 May 2020, and further relaxed on 1 June 2020.
However, due to a significant rise in COVID-19 cases and breaches in hotel quarantine, Stage 3 restrictions were reintroduced in Metropolitan Melbourne and Mitchell Shire.The second lockdown, known as Vic lockdown 2, was announced on 7 July 2020, and was scheduled to last for six weeks starting from 8 July 2020 [26].On 2 August 2020, a state of disaster was declared, and Stage 4 restrictions were implemented in Metropolitan Melbourne for six weeks [27].This lockdown was later extended to 28 October 2020.Following an outbreak at the Holiday Inn, Victoria entered a sudden five-day lockdown, known as Vic lockdown 3, from 13 February 2021 to 17 February 2021, reverting to Stage 4 restrictions [28].Lockdown number 4 was another seven-day circuit breaker lockdown that was imposed on 28 May 2021, to combat an outbreak, which was later extended to 10 June 2021 [29].Victoria then entered a sudden five-day lockdown from 16 July 2021 to 20 July 2021 [28] after the number of Delta variant cases reached 18.This lockdown was later extended until 27 July 2021 [30].Just nine days after the easing of restrictions from the fifth lockdown, Victoria entered its sixth lockdown to combat a surge in Delta variant cases.The announcement was made on 5 August, and the lockdown initially lasted seven days.However, it was later extended until 17 September 2021 [31].With improvements in the situation, the restrictions were gradually eased, allowing for a return to a semblance of normalcy.However, sporadic outbreaks led to localized lockdowns in different states and territories, with swift and targeted responses to contain the virus.The vaccine rollout gained momentum, offering hope for the future.By late 2021, Australia transitioned from a suppression strategy to living with the virus, adopting a nuanced approach to restrictions and focusing on vaccination rates, setting the stage for postpandemic recovery.
The COVID-19 pandemic has introduced unprecedented and rapidly changing circumstances that have had significant implications for energy consumption patterns.As a result, the necessity of employing highly data-driven models, such as long short-term memory (LSTM), for energy consumption forecasting has become increasingly evident.The pandemic has led to nonlinear and dynamic changes in energy consumption due to various factors, including lockdowns, remote working, and shifts in industrial and commercial activities.LSTM, as a type of recurrent neural network (RNN), is well suited to capturing complex temporal dependencies and nonlinear patterns in data, making it effective in modeling and forecasting these dynamic changes.LSTM can capture both short-term and long-term dependencies in time-series data.This is crucial in the context of COVID-19, where sudden and short-term changes (e.g., immediate lockdown effects) as well as longerterm trends (e.g., evolving work-from-home practices) have impacted energy consumption.LSTM's ability to remember information over varying time intervals makes it adept at handling such scenarios.Compared with the traditional neural network, LSTM possesses the capability to transmit information from previous time steps to subsequent ones through backpropagation.Based on this feature, LSTM emerges as a natural choice for handling sequential data, such as building loads.In essence, the COVID-19 situation necessitates the utilization of highly data-driven models like LSTM for energy consumption forecasting due to the model's capacity to handle complex, dynamic, and uncertain patterns in data.

Impact of COVID-19 on Australian Higher Education
Following the World Health Organization's declaration of COVID-19 as a global pandemic on 11 March 2020, various countries have experienced significant economic, social, and political disruptions.The pandemic has particularly affected countries where universities played a crucial role in the export industry, such as Australia, leading to considerable disruptions and financial challenges for many universities.According to the Department of Education, Skills and Employment (DESE), the total number of international students enrolled in Australian courses in 2021 was 572,349, indicating a 17% decrease compared with the same period in 2020 [32].The pandemic's impact on Australian universities is evident through the loss of over 17,000 jobs reported in 2021, as per data from Universities Australia [33].Even in 2023, the repercussions of the pandemic persist, with universities in Western Australia still suffering financial losses, evident from their 2022 financial reports, which are considerably lower than their figures from 2021 [34].For Swinburne University of Technology, following a warning issued by the vice-chancellor back in June 2020 [35], the university scrapped more than 100 jobs to address the impacts of COVID-19 on its financial sustainability and declining international student enrolment [36].Despite the drastic measures, Swinburne University reported a deficit of $48.55 million in its annual report for 2020 [37].By late 2021, as restrictions were gradually eased in Victoria, Swinburne welcomed international students back to campus [38]; as stated in the 2021 annual report released in 2022, the university finished 2021 with a modest surplus of $11.8 million.This financial result was a good foundation for continued recovery after a disrupted two years, as stated by the Vice-Chancellor and President, Professor Pascale Quester [39].
In addition to the energy consumption in three commercial buildings every 15 min, the daily COVID-19 case from its state (i.e., Victoria) was employed for better forecasting.Australia has faced a series of challenging lockdown measures in response to the COVID-19 pandemic.On 16 March 2020, Victoria declared a state of emergency; urged the public to practice social distancing, avoid nonessential contacts, and work from home; and prohibited nonessential gatherings and travel [25].Subsequently, more rigorous measures were introduced on 31 March 2020, when Victoria implemented Stage 3 restrictions across the state [28].Stage 3 restrictions were gradually eased on 13 May 2020, and further relaxed on 1 June 2020.
Due to a sharp increase in COVID-19 cases and breaches in hotel quarantine, Stage 3 restrictions were reintroduced in Metropolitan Melbourne and Mitchell Shire.The announcement was made on 7 July 2020, and the second lockdown, known as Vic lockdown 2, was scheduled to last for six weeks starting from 8 July 2020, in order to contain the spread [26].On 2 August 2020, Victoria declared a state of disaster, in addition to the existing state of emergency, and implemented Stage 4 restrictions in Metropolitan Melbourne for six weeks [27].However, this lockdown was extended until 28 October 2020.Following an outbreak at the Holiday Inn involving 13 cases of the U.K .Strain of COVID-19, Victoria entered a sudden five-day lockdown from 13 February 2021 to 17 February 2021, reverting to Stage 4 restrictions [28].On 28 May 2021, Victoria imposed another seven-day circuit breaker lockdown to combat the outbreak, reimposing Stage 4 restrictions and stay-at-home orders reminiscent of the previous lockdowns [29].The fourth lockdown was extended by seven days and lasted until 10 June 2021.As a result of the Delta variant outbreak in Sydney and the irresponsible actions of interstate delivery drivers from Sydney, Melbourne experienced its own Delta outbreak.When the number of cases in Victoria reached 18, the state entered a sudden five-day lockdown from 16 July 2021 to 20 July 2021 [28].This lockdown was later extended until 27 July 2021 [30].Just nine days after the easing of restrictions from the fifth lockdown, Victoria entered its sixth lockdown to combat a surge in Delta cases.The announcement was made on 5 August, and the lockdown initially lasted for seven days.However, it was later extended until 17 September 2021 [31].
As the situation improved, restrictions were gradually eased, allowing for a return to a semblance of normalcy.However, sporadic outbreaks led to localized lockdowns in various states and territories, with swift and targeted responses to contain the virus.The vaccine rollout gained momentum, providing hope for the future.By late 2021, Australia began transitioning from a suppression strategy to living with the virus, adopting a more nuanced approach to restrictions, and focusing on vaccination rates, paving the way for a postpandemic recovery.

Methodology
In this section, we describe the proposed model, that is, mv-M-LSTM-CI.An overview of the proposed model is shown in Figure 4.The model aims to forecast the energy used every 15 min by commercial buildings during the COVID-19 period.The model has three main phases, namely, data preprocessing, model training, and evaluation.The data preprocessing phase involves the preparation of the input data by applying various preprocessing techniques, such as data differencing, time labeling, data accumulation, and normalization.This step ensures that the data are in a suitable format for further analysis.Next, the model training phase focuses on training the proposed mv-M-LSTM-CI model to capture the complex relationships and dependencies present in the data, enabling accurate predictions.Once the model is trained, the evaluation phase assesses its performance and effectiveness.Various evaluation metrics and techniques are employed to measure the model's accuracy.

Data Preprocessing
The data preprocessing phase has two main subphases: (i) processing of the energy consumption and time and (ii) processing of COVID-19 data.There are three main input data, i.e timeline, energy consumption, and the daily COVID-19 cases.The timeline refers to a sequence of time points, each spaced in 15 min intervals, forming the temporal framework for the data collection and analysis.Energy consumption signifies the quantification of the energy consumed within each 15 min interval, offering insights into the patterns and fluctuations of energy usage.Daily COVID-19 cases represents the count of COVID-19 cases reported on a daily basis, serving as an additional variable for analysis and potential correlation with energy consumption trends.
(i) Processing of energy consumption and time.This subphase has 4 steps, i.e., data differencing, time labeling, row concatenation, and widow slicing.These steps align with the techniques previously introduced by Tan et al. [40].Data differencing involves calculating the differences between consecutive observations in a time series.The changes between data points are computed instead of using the raw values to make the data stationary.Stationary data are typically easier to model and predict accurately than dynamic data.Peak and nonpeak times could reveal underlying trends in the data.Understanding the patterns during these times enables the capture of the variations in and the adjustment of the forecasting model accordingly.In this paper, 8:00 to 21:00 are referred to as the peak hours, and the others are referred to as the nonpeak hours.
(ii) Processing of the COVID-19 data.During the COVID-19 period, the mobility of people was normally influenced by the number of COVID-19 cases.More restrictions were imposed on people's movement as the number of COVID-19 cases increased, particularly when accessing commercial buildings.Therefore, the energy consumption in these buildings tended to decrease.Figure 3 illustrates a correlation between the cumulative number of COVID-19 cases in the past 14 days and the corresponding decrease in energy consumption the Hawthorn Campus-ATC Building.This relationship suggests that as the COVID-19 cases accumulated, a noticeable decline in energy usage occurred within the specified timeframe.The observed trend serves as valuable insight into the impact of COVID-19 on the energy consumption patterns at the mentioned location.Consequently, incorporating these data into forecasting models would be advantageous for accurate predictions.Therefore, two main steps are involved, namely, COVID-19 case cumulation and data normalization.In COVID-19 case cumulation, the cumulative number of COVID-19 cases in the past 14 days is calculated.Then, the data are clipped to the 0 to 10,000 range.Clipping helps maintain the data within a reasonable and meaningful range while addressing potential anomalies or extreme values that might skew the model's behavior.By rescaling the values to this common range, variations in the magnitude of the COVID-19 case counts are eliminated.This normalization process enables fair comparisons between different timesteps and ensures that no single feature dominates the learning process due to its larger magnitude.The normalization formulation is presented in Equation (1).
where ĉi represents the cumulation of COVID-19 cases in the previous 14 days for each time step c i in the 0 to 1 range, and c max and c min are the maximum and minimum COVID-19 cases, respectively.

Forecasting Model
As shown in Figure 4, the proposed mv-M-LSTM-CI model contains two flows of input, namely, (i) energy consumption and labeled time and (ii) normalized COVID-19 data.
The first input flow focuses on the creation of a specialized multivariate LSTM architecture that is tailored to effectively extract and capture valuable information in the labeled time embedded within the time-series energy consumption.Two consecutive LSTM layers exist.LSTM is a type of recurrent neural network (RNN) layer that is specifically designed to capture and model the long-term dependencies and patterns in sequential data [41].The LSTM layer consists of memory cells that can store and retrieve information over extended sequences.Each memory cell has three main components: an input gate (in), a forget gate ( f o), and an output gate (ou).These gates regulate the flow of information within the LSTM layer and produce a hidden state (h) and a cell state (c).For details, with each jth cell at the kth layer, the input gate, forget gate, and output gate are calculated using Equations ( 2)- (4).
where  5), that regulates information flow, counteracts the vanishing gradient issue, control smemory cell updates, and enables meaningful output generation.
After the calculation, the update function (up) in Equation ( 6) with the corresponding weights controls the flow of information in and out of the LSTM cell with the tanh function.The tanh function is formulated in Equation (7).
At the final calculation of each LSTM cell, the cell state (c k j ) and the hidden state (h k j ) are produced using Equations ( 8) and ( 9), respectively.
Within the second input flow, the COVID-19 data are channelled into a dense layer to extract pertinent information that contributes to the overall analysis.This intermediate step helps distil meaningful insights from the COVID-19 data.The resulting output from the dense layer is then combined with the last hidden state of the second LSTM layer, serving as a knowledge injection mechanism.
After two input flows are processed, the outputs of these two sources are concatenated along a column.Therefore, the model is expected to gain access to both the learned representations from the LSTM layers and the specific COVID-19-related insights.Subsequently, the combination is directed into a series of dense layers and a batch normalization layer positioned in the middle to generate the final decision.
The objective function is one of the main factors in achieving a high-performing model.Various objective functions are employed for model training.In this research, Huber loss was employed because it is commonly utilized in forecasting tasks due to its robustness against outliers [42] and can strike a balance between the mean absolute error and the mean squared error.This objective function is particularly useful in situations where extreme values may exist, such as in time-series forecasting or in datasets affected by anomalous events, like the COVID-19 pandemic.The formulation of Huber loss for each prediction ŷi and the corresponding actual value y i are presented in Equation (10).
where δ determines the threshold at which the loss function transitions from the quadratic region to the linear region.The value of δ was set to 1 for both the proposed and the comparison models employed in this study.
The combination of the proposed data-processing techniques and model architecture was designed to ensure robust performance not only during the COVID-19 pandemic but also in similar crisis situations.The models have the potential to accurately capture and forecast key patterns and trends, providing valuable insights and aiding in effective decision making.The adaptability of the proposed model extends beyond the current pandemic: the model offers a promising solution for accurate forecasting and decision support in the face of further pandemics.

Experiments 4.1. Data
This study utilized a dataset comprising energy consumption measurements recorded every 15 min in three buildings: the Hawthorn Campus-ATC Building (referred to as DatasetS1), the Hawthorn Campus-AMDC Building (referred to as DatasetS2), and the Wantirna Campus-KIOSC Building (referred to as DatasetS3).Additionally, the dataset includes records of COVID-19 cases in Victoria state in 2020 and 2021.
For all the models, the training set spanned from January 2020 to the end of June 2021, while the test set covered the period from July 2020 to the end of December 2021.In the experimental phase, the target variable was predicted based on the 96 immediate previous data points.

Baseline Model
In this study, we compared the proposed model with four baseline models, namely, linear regression (LR), LSTM, M-LSTM, Bi-LSTM, and SVM.
Linear Regression: LR is a popular statistical model used for forecasting.In the context of forecasting, LR aims to establish a linear relationship between the input features and the target variable.The model assumes that this relationship can be represented by a straight line.The goal is to find the best-fitting line that minimizes the difference between the predicted and actual values of the target variable.The model calculates the predicted value of the target variable on the basis of the linear equation, allowing the forecast of future outcomes.
Long Short-term Memory: The LSTM model for forecasting refers to an RNN architecture that consists of a single LSTM layer.This type of model is commonly used to capture temporal dependencies and patterns in sequential data.The energy consumption in the previous sequence of time steps is fed into the LSTM layer, which processes the data over multiple time steps.The LSTM layer contains memory cells that allow the model to retain and utilize the energy information from previous time steps, enabling the capture of long-term dependencies in the data.
Multivariate Multilayered LSTM: In this study, we compared the proposed model with the M-LSTM model proposed by Tan et al. [40].The M-LSTM model architecture comprises an input layer, followed by two LSTM layers, and a dense layer at the end.It takes two types of input: energy consumption data recorded every 15 min and labeled time information.
Bidirectional Long Short-term Memory: The Bi-LSTM model for forecasting is an RNN architecture that consists of a single Bi-LSTM layer.In this model, the input sequence is bidirectionally processed [43].The Bi-LSTM layer incorporates both forward and backward LSTMs, allowing the model to simultaneously capture information from past and future time steps.This bidirectional processing enables the model to have a comprehensive understanding of the temporal patterns in the data.The Bi-LSTM model can capture complex temporal dependencies and has been widely employed in various forecasting tasks.
Support Vector Machine: SVM with the radial basis function (RBF) kernel is a popular machine learning model used for forecasting tasks [44].SVMs are effective in capturing nonlinear relationships and have been widely applied in various fields, including timeseries forecasting.The RBF between two data points (x, and x ) is presented in Equation (11), with γ as the parameter that controls the width of the Gaussian curve.
During the training phase, the SVM with RBF kernel adjusts its parameters by solving an optimization problem to find the hyperplane that maximizes the margin and minimizes the errors.This process involves tuning the hyperparameters, such as the kernel parameter (γ), to achieve the best generalization performance.

Metrics
To assess the performance of the model, it was evaluated by generating a set of predictions ŷ = { ŷ1 , ŷ2 , . . ., ŷn } and comparing them with the corresponding known actual values Y = {y 1 , y 2 , . . ., y n }, where n represents the size of the test set.Three commonly used metrics were employed to measure the overall disparity between these two sets: MAPE, NRMSE, and the R-squared (R 2 ) score.These metrics provide insights into the accuracy and performance of the model's predictions compared with the actual values.

MAPE
The MAPE calculation involves taking the absolute difference between the predicted and actual values, dividing it by the actual value, and then computing the average of these values across the entire dataset, as depicted in Equation ( 12).This computation yields a single numerical value that represents the average percentage difference between the predicted and actual values.The lower the MAPE value, the better the performance of the model, because it signifies a smaller average percentage deviation between the predicted and actual values.

NRMSE
The NRMSE is a performance metric utilized to assess the accuracy of a prediction model.This metric quantifies the normalized average magnitude of the residuals or errors between the predicted and actual values, as indicated in Equation (13).By calculating the square root of the MSEs and normalizing them, the NRMSE provides a measure of the overall deviation between the predicted and actual values, considering the scale of the data.A low NRMSE value signifies a good fit of the model to the data, indicating high accuracy in the predictions.
The R 2 score, also referred to as the coefficient of determination, is a statistical metric that quantifies the proportion of the variability in the dependent variable that can be explained by the independent variables in a regression model, as depicted in Equation ( 14).y * is the mean of the actual values and serves as an indicator of the model's fitness and its ability to accurately predict the target variable.A high R 2 score signifies a good fit of the model, implying that a large portion of the variability in the dependent variable can be accounted for by the independent variables.Figure 5 shows the performance of the proposed model on the training and test sets from three buildings.For DatasetS1, the MPAE, NRMSE, and R 2 values are higher for the test set than for the training set by approximately 0.01, 0.03, and 0.03 respectively.For DatasetS2, the MPAE, NRMSE, and R 2 are higher for the test set than the test set by approximately 0.03, 0.03, and 0.07, respectively.For DatasetS3, the MPAE and NRMSE are higher for the test set than the test set by approximately 0.02 and 0.000727344, respectively, and R 2 is slightly larger for the test set by approximately 0.02.The MPAE, NRMSE, and R 2 values demonstrate a consistent trend across all three datasets, indicating relatively minor discrepancies between the training and test sets.Overall, the proposed model consistently exhibits superior forecasting performance across all datasets and evaluation metrics, outperforming the M-LSTM, Bi-LSTM, LR, and SVM models by substantial margins.These numerical comparisons demonstrate the accuracy of the proposed model in predicting future and reinforce its potential practical applicability in real-world forecasting scenarios.
To enhance visual comparison, instead of showing line graphs for every 15 min interval, we chose to present Figures 7-9.These visual representations depict the daily line graphs of the energy consumption forecasts spanning from 15 July 2021 to 15 October 2021 for DatasetS1, DatasetS2, and DatasetS3.The proposed model mv-M-LSTM-CI consistently demonstrates the highest level of accuracy and alignment with the actual data in the three datasets, as illustrated in the figures.Furthermore, the proposed model exhibits greater stability in its predictions, particularly in the challenging context of the COVID-19 period.

Conclusions
In summary, this paper presented a novel forecasting model that aims to provide a generic framework that can be adapted to future pandemic scenarios and other comparable crisis situations.As the results obtained from the testing were promising, the proposed model is thought to be sufficient to be applied to the data of any pandemic.Due to the availability of testing data, the study specifically focused on predicting the energy consumption of three buildings located on the Hawthorn and Wantirna campuses.The analysis covered the energy consumption data recorded every 15 min during the COVID-19 period from January 2021 to December 2021.Furthermore, the paper proposed a datapreprocessing tailored to the COVID-19 data, enhancing the understanding of the relationships between the independent variables and the target variables.The results of this study emphasize the notable improvement in performance achieved by the proposed model for energy consumption forecasting with knowledge injection.These findings will play a crucial role in effectively addressing the challenges presented by future pandemics.They should be implemented in energy management systems within commercial buildings to improve building management control and enable more advanced and efficient operations.The experimental results demonstrate that the proposed model, along with the suggested data-preprocessing technique, outperforms baseline models including LSTM, Bi-LSTM, LR, and SVM.This superior performance is evident in three widely used metrics: MPAE, NRMSE, and R 2 score.In particular, for DatasetS1, the proposed mv-M-LSTM-CI model demonstrates the best performance, achieving the lowest MPAE (0.061) and NRMSE (0.047) and the highest R 2 (0.931).This performance can also be seen on DatasetS2 and DatasetS3, with the mv-M-LSTM-CI model having the lowest MPAE and NRMSE and the highest R 2 at 0.093, 0.062, and 0.729 for DatasetS2 and 0.158, 0.033, and 0.895 for DatasetS3.The model mv-M-LSTM-CI demonstrates superior performance, achieving the lowest MPAE values of 0.061, 0.093, and 0.158 for datasets from the three different buildings, respectively.This accomplishment is of significant importance for efficient energy management and conservation within commercial buildings.This approach can be extended to other commercial buildings that exhibit similar energy consumption patterns, rendering it a feasible solution for energy management in this sector.Additional investigation could focus on evaluating the efficacy of the suggested preprocessing method and models in forecasting energy consumption across diverse building types or larger datasets.Exploring alternative techniques, like seasonal decomposition or time-series analysis, to incorporate temporal information into the models may yield valuable findings.Further expansion of the research can involve incorporating a 24 h ahead electrical load forecast, which can be used as day-ahead electrical load information.In addition to the inclusion of additional input features, such as occupancy and equipment-level information (e.g., the thermostat setpoint, the brightness of the lighting system, and the number of devices connected to plug loads), historical load data and weather information can be included to enhance the accuracy of electrical load forecasting.These advances in energy consumption forecasting have the potential to generate substantial cost savings and environmental advantages, particularly within commercial buildings.

Figure 1 .
Figure 1.Statistics of final energy consumption by end users in Australia from 2016 to 2021 [4].

Figure 3 .
Figure 3. Analysis of the trend in daily energy consumption on the basis of the cumulative number of COVID-19 cases over the previous 14 days from February 2020 to January 2021 at the Hawthorn Campus-ATC Building.Note that the cumulation of COVID-19 cases is restricted to the range of 0 to 10,000, and both data are normalized to fit within the range of 0 to 1.

Figure 4 .
Figure 4. Overview of the proposed model.
and w in,k , w f o,k , w ou,k , b in , b f o , b ou ∈ R are the weights to be updated during the training process.σ is a sigmoid function, as shown in Equation (

) 4 . 4 . Results 4 . 4 . 1 .
Performance of the Proposed Model on the Training and Test Sets

Figure 5 .
Figure 5. Performance of the proposed mv-M-LSTM-CI model on training and test sets in terms of three metrics: MPAE, NRMSE, and R 2 (or R2 as shown in image), on three datasets: (a) DatasetS1, (b) DatasetS2, and (c) DatasetS3.

Figure 6
Figure 6 showcases the forecast generated by the proposed model, specifically for DatasetS1.The outcomes obtained for the remaining datasets follow a similar pattern.The line plot visually demonstrates the model's fitness and provides a clear representation of how well it aligns with the test set.

Figure 6 .
Figure 6.Prediction of the proposed model on DatasetS3 from 15 July 2021 to 1 January 2022, every 15 min with a step size of 96.In summary, the findings indicate that the proposed model achieves significant optimization when trained on the training set and demonstrates a strong generalization ability when applied to the test set, particularly in the context of the unstable conditions prevailing during the COVID-19 period.4.4.2.Comparison

Figure 7 .
Figure 7. Prediction for energy consumption every day of forecasting models on DatasetS1.

Figure 8 .
Figure 8. Prediction for energy consumption every day of forecasting models on DatasetS2.

Figure 9 .
Figure 9. Prediction for energy consumption every day of forecasting models on DatasetS3.In summary, the proposed model consistently outperformed the other models on all three datasets in terms of three metrics: MPAE, NRMSE, and R 2 .The model obtained lower MPAE and NRMSE values and higher R 2 values than the other models.The results of the proposed model indicate a strong fit and good performance in terms of better capturing the underlying information, especially considering the challenging conditions during the COVID-19 period, which was facilitated by the incorporation of COVID-19 knowledge.

Table 1 .
Summary of different forecasting models for load forecasting in commercial buildings.

Table 2
presents a comprehensive comparison of the forecasting models on the three distinct datasets using three evaluation metrics: MPAE, NRMSE, and R 2 .For dataset DatasetS1, the proposed model exhibits the best performance across all models.It achieves the lowest MPAE of 0.061, outperforming the M-LSTM model (0.103) by approximately 40.8%, the Bi-LSTM model (0.365) by approximately 83.3%, the LR model (0.396) by approximately 84.5%, and the SVM model (0.179) by approximately 65.1%.Additionally, the proposed model demonstrates the lowest NRMSE of 0.047, indicating an enhancement over the M-LSTM model by approximately 50.0%, the Bi-LSTM model by roughly 46.8%, the LR model by about 67.8%, and the SVM model by 56.6%.Additionally, the proposed model achieves the highest R-squared (R 2 ) value of 0.931, surpassing that of the M-LSTM model by about 16.0%, the Bi-LSTM model by roughly 18.3%, the LR model by approximately 60.7%, and the SVM model by around 31.1%.

Table 2 .
Comparison of forecasting models in terms of three metrics on three datasets.The best values are marked in bold.DatasetS2, the mv-M-LSTM-CI consistently demonstrates its superiority over the baseline models.It achieves the minimum MPAE of 0.093, showcasing its superiority over the M-LSTM model by approximately 5.1%, the Bi-LSTM model by about 55.9%, the LR model by around 65.6%, and the SVM model by roughly 29.0%.Furthermore, the NRMSE of the proposed model, which stands at 0.062, marks a notable improvement of about 36.7% compared with the M-LSTM model (0.098), 23.2% compared with the Bi-LSTM model (0.077), 71.9% compared with the LR model (0.196), and 52.7% compared with the SVM model (0.101).Moreover, the proposed model achieves an R-squared (R 2 ) value of 0.729, indicating a remarkable enhancement of around 125.7% over the M-LSTM model (0.323), 19.7% over the Bi-LSTM model (0.588), and 154.2% over the LR model (−0.699).It is worth noting that the SVM model's R 2 value (0.286) is comparatively lower than that of the proposed model.Finally, in dataset DatasetS3, the proposed model remains the best performer.It achieves an MPAE of 0.158, which is approximately 121.8% better than that of the M-LSTM model (0.711), 83.3% better than that of the Bi-LSTM model (0.946), 82.9% better than that of the LR model (0.926), and 59.5% better than that of the SVM model (0.389).The proposed model's NRMSE of 0.033 is approximately 68.6% better than that of the M-LSTM model (0.105), 48.0% better than that of the Bi-LSTM model (0.064), 69.5% larger than that of the LR model (0.110), and 51.2% better than that of the SVM model (0.068).Additionally, the proposed model demonstrates a significantly higher R 2 value of 0.895, outperforming the M-LSTM model (0.676) by approximately 32.3%, the Bi-LSTM model (0.603) by approximately 48.6%, the LR model (−0.169) by approximately 630.2%, and the SVM model (0.550) by approximately 38.5%.