Analyzing and Forecasting Laboratory Energy Consumption Patterns Using Autoregressive Integrated Moving Average Models

Abstract

This study applied ARIMA modeling to analyze the energy consumption patterns of laboratory equipment over one month, focusing on enhancing energy management in the laboratory. By explicitly examining AC and DC equipment, this study obtained detailed daily operating cycles and periods of inactivity. Advanced differencing and diagnostic checks were used to verify model accuracy and white noise characteristics through enhanced Dickey–Fuller testing and residual analysis. The results demonstrate the model’s accuracy in predicting energy consumption, providing valuable insights into the use of the model. This study highlights the adaptability and validity of the ARIMA model in laboratory environments, contributing to more competent laboratory energy management practices.

1. Introduction

Laboratories, essential scientific and technological advancement hubs, require substantial energy to operate specialized equipment and maintain controlled environments [1,2]. This high energy demand is driven by various laboratory activities such as heating, cooling, ventilation, and the continuous operation of high-power instruments [3]. As energy costs and environmental concerns rise, improving energy efficiency in laboratories has become a key focus in academic and industrial research [4].

However, laboratory energy consumption is significant and complex to predict and manage due to laboratory workflows’ diverse and sometimes unpredictable nature [5]. Unlike commercial or residential spaces, where energy usage patterns are relatively stable, laboratories face fluctuating power demands based on factors such as the frequency of equipment use, the type of research being conducted, and specific experimental requirements [6,7]. As a result, developing effective strategies to analyze and predict laboratory power consumption is critical for optimizing energy usage, reducing operational costs, and minimizing the environmental impact of laboratory operations [8,9].

In recent years, machine learning (ML) has emerged as a powerful tool for predictive analysis in various fields, including energy consumption [10,11,12,13]. By leveraging historical energy data and real-time monitoring, machine learning models can accurately identify patterns and forecast energy demand [14,15,16]. Applying ML techniques to laboratory energy consumption analysis offers the potential to predict demand based on various features, such as equipment usage schedules, environmental conditions, and experiment type [17,18]. This predictive capability could enable laboratories to implement data-driven energy management strategies, ultimately enhancing energy efficiency and promoting sustainable practices within research institutions.

Despite the high energy demands of laboratory environments, managing and optimizing power consumption remains challenging due to the variability in energy usage and the diversity of laboratory activities [19]. Traditional energy monitoring systems often provide historical data but lack the predictive capability to proactively manage energy consumption [20]. This inability to predict demand accurately leads to inefficiencies, such as overconsumption during low-use periods or under-provisioning when energy demand spikes unexpectedly [21]. Given the rising costs of energy and increasing awareness of sustainability, there is a pressing need for tools and methods to forecast laboratory energy usage with precision and reliability.

Furthermore, laboratory power consumption is influenced by numerous factors, such as equipment usage patterns, environmental conditions, and the nature of experimental activities [22]. The complexity of these interdependent variables makes it difficult to establish straightforward predictive models using conventional methods [23]. Therefore, a more advanced approach, leveraging machine learning to capture and analyze these patterns, is essential for effective energy management in laboratories.

This study aimed to develop a machine learning-based approach to analyze and predict power consumption in a laboratory environment. It sought to identify and evaluate the key factors affecting energy consumption in laboratories and develop predictive models that use historical and real-time energy data to forecast power demand accurately. By achieving these goals, this research aspires to provide a scalable and adaptable forecasting framework that enhances energy efficiency. The study supports sustainability goals by enabling laboratories to better understand their energy usage patterns, which can contribute to reducing carbon footprints and promoting responsible resource management.

2. Literature Review

Energy consumption analysis has recently received increased attention due to rising operational costs and environmental concerns. Various approaches have been used to monitor, analyze, and predict energy usage, particularly in commercial and industrial buildings. However, the unique energy demands and variability in laboratory environments present distinct challenges for traditional energy management techniques.

Historically, rule-based systems and statistical methods have been applied to model energy consumption. These methods use predetermined rules or linear regression models based on past energy usage trends to estimate future demand. While rule-based systems are relatively simple to implement and interpret, their effectiveness is often limited in dynamic environments like laboratories, where energy consumption is subject to frequent fluctuations [24]. Similarly, linear regression and other statistical models can capture basic trends but struggle with complex patterns influenced by multiple interacting factors, such as equipment usage and environmental conditions [11].

Another common approach to energy prediction is time series analysis, which includes techniques like autoregressive integrated moving average (ARIMA) models and seasonal decomposition methods. Time series models are effective at capturing temporal dependencies and seasonal trends in energy data, making them useful for certain predictive applications [18]. However, they typically assume that future patterns closely follow historical trends, which can be challenging in laboratory settings due to unpredictable experimental demands and variable operating schedules [12]. While this study employs the ARIMA model to explore its applicability in such environments, it acknowledges these limitations and suggests the need for future research to integrate more flexible models or additional variables to better accommodate deviations from historical trends.

Simulation techniques, such as energy modeling software (e.g., EnergyPlus 24.2.0 or TRNSYS Version 18), allow researchers to create detailed models of energy usage in controlled environments. These methods can account for a wide range of variables, including heating, ventilation, air conditioning, and equipment use [25]. While effective in large-scale buildings, simulation models are typically labor-intensive to set up and require extensive data on the specific equipment and laboratory processes. Additionally, simulations are static once built and may not adapt well to ongoing changes in laboratory activities or new usage patterns [26].

Preliminary research has demonstrated the effectiveness of machine learning (ML) techniques in energy consumption prediction across various sectors, including residential, commercial, and industrial settings. Techniques such as decision trees, artificial neural networks (ANNs), support vector regression (SVR), and ensemble methods like random forests and gradient boosting have shown promise in capturing nonlinear relationships within energy data. These models learn from historical data to predict energy usage based on various input features [27,28]. While ML has proven to be a powerful tool for predicting energy consumption, existing studies often focus on environments where usage patterns are more stable and predictable, such as commercial or industrial settings. In contrast, laboratory environments present unique challenges due to their highly variable and often unpredictable energy consumption patterns [29]. There is limited research applying ML models specifically to laboratories, highlighting a gap in the literature that this study aimed to address. For instance, ANNs have been effectively employed to predict energy demand in large office buildings, leveraging their ability to model nonlinear relationships and complex dependencies within energy data [30]. Studies employing ensemble methods like random forests and gradient boosting have also shown promise, as these techniques reduce the risk of overfitting and improve robustness in dynamic settings [12].

Additionally, time series models based on recurrent neural networks (RNNs) and long short-term memory (LSTM) networks have gained popularity for energy forecasting, especially in environments where temporal patterns play a significant role [23]. LSTM-based models, for example, have shown superior performance in predicting energy loads in smart buildings due to their ability to handle long-term dependencies in sequential data.

While ML applications in energy prediction are advancing, most studies focus on commercial or industrial contexts with relatively stable energy usage patterns. Research specifically targeting laboratories—where power consumption is highly variable and influenced by the diverse nature of experiments, equipment, and environmental conditions—remains limited.

3. Methods

3.1. Data Collection

To validate the feasibility of the machine learning approach, this study focused on collecting real-time energy consumption data from alternating-current (AC) and direct-current (DC) electrical equipment commonly used in biochemistry research environments to construct the dataset.

The energy consumption data were collected from laboratory equipment at Universiti Sains Malaysia, including high-power AC equipment such as centrifuges, PCR machines, refrigerators, fume hoods, and air conditioning units. DC equipment, such as laboratory stirrers, incubators, and gel electrophoresis systems, were also included. Because different laboratory equipment types have different power requirements, smart meters and IoT sensors were installed and calibrated to ensure accurate readings. The power rating of each piece of equipment (as shown in

Table 1. Energy consumption of AC electrical equipment.

Equipment Type	Voltage (V)	Current (A)	Rated Power (W)	Quantity	Total Power (W)
Centrifuge	240	1.2	288	2	576
PCR Machine	240	0.8	192	1	192
Refrigerator	240	1.0	240	1	240
Fume Hood	240	0.6	144	1	144
Air Conditioner	240	2.5	600	1	600
Total					1752

and

Table 2. Energy consumption of DC electrical equipment.

Equipment Type	Voltage (V)	Current (A)	Rated Power (W)	Quantity	Total Power (W)
Laboratory Mixer	12	1.5	18	3	54.0
Incubator (DC-powered)	5	2.0	10	2	20.0
Gel Electrophoresis System	3.3	3.0	9.9	2	19.8
Power Supply for Small Equipment	0–32	3.2	102.4	1	102.4
Laboratory Mixer	12	1.5	18	3	54.0
Total					196.2

) was used as a reference during calibration to verify the accuracy of the readings.

Energy data were recorded at 5 min intervals to capture detailed consumption patterns. All energy consumption data were stored in a secure cloud database to ensure data integrity and accessibility. Ultimately, the collected data formed a dataset for energy consumption analysis and predictive modeling.

3.2. Data Sources

Smart meters or IoT sensors connected to each device can automatically collect voltage, current, and runtime data. The energy consumption data are summarized as a time series based on timestamps that represent the total electricity consumption over a period of time. The calculation was carried out as follows:

$$\mathrm{Energy}\mathrm{Consumption}=\mathrm{Voltage}\times \mathrm{Current}\times \mathrm{Operating}\mathrm{Duration}\times \mathrm{Quantity}$$

(1)

3.3. Machine Learning Models

Considering the time-series nature of the data, the ARIMA (autoregressive integrated moving average) model was chosen in this study to analyze and predict the energy consumption patterns of laboratories, which is capable of capturing time dependencies and providing reliable short-term forecasts.

The ARIMA model consists of three parameters—AR (autoregressive), I (integrated), and MA (moving average)—that enable it to model a wide range of time series properties.

• The AR component represents the relationship between observations and a certain number of lagged observations;
• The I component represents the degree of differencing required to make the series smooth;
• The MA component captures the dependence between observations and the residual errors of lagged observations.

After fitting the ARIMA model, residuals (differences between observed and predicted values) were analyzed to ensure they exhibit white noise characteristics, meaning they have no significant autocorrelation.

3.4. Evaluation Metrics

There are three commonly used smoothness tests. One is the autocorrelation coefficient (ACF) and partial autocorrelation coefficient (PACF) plots, and the other is the augmented Dickey–Fuller (ADF) test.

The ACF describes the correlation of a time series at different numbers of lags (Lag), i.e., the degree of linear correlation between the series and its own lagged values. It measures the relationship between current and past values. In practice, sample data are used to estimate the autocorrelation function and obtain the sample autocorrelation coefficient:

$$\mathrm{r}\left(\mathrm{k}\right)\mathrm{ }=\mathrm{ }{\displaystyle \frac{{\sum }_{\mathrm{t}=\mathrm{k}+1}^{\mathrm{N}}\left(Y_t\mathrm{ }-\mathrm{ }\overline{Y}\right)\left(Y_{t-k}\mathrm{ }-\mathrm{ }\overline{Y}\right)\mathrm{ }}{{\sum }_{\mathrm{t}=1}^{\mathrm{N}}{\left(Y_t\mathrm{ }-\mathrm{ }\overline{Y}\right)}^2\mathrm{ }}}$$

(2)

where $\mathrm{N}$ is the sample capacity, which is the number of data points; and $\overline{Y}$ is the sample mean, calculated as $\overline{Y}={\displaystyle \frac{1}{N}}{\sum }_{t=1}^N{Y}_t$.

When $r\left(k\right)\mathrm{ }>0$, it means that the current value is positively correlated with the value of the lag k periods; when $\mathrm{r}\left(\mathrm{k}\right)\mathrm{ }<0$, it means that the current value is negatively correlated with the value of the lag k periods. The larger the absolute value of $\mathrm{r}\left(\mathrm{k}\right)$, the stronger the correlation.

The PACF is used to measure the pure correlation between the current value $Y_t$ in the time series and the value $Y_{t-k}$ with a lag of $\mathrm{k}$ periods, excluding the interference of all intermediate lag terms $\left(Y_{t-1},Y_{t-2},\dots ,Y_{t-k+1}\right)$ in between. For lag order $\mathrm{k}$, the definition of the partial autocorrelation function $\varnothing \left(k\right)$

$$\varnothing \left(k\right)=\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\left(Y_t-P_{k-1}\left(Y_t\right),Y_{t-k}-P_{k-1}\left(Y_{t-k}\right)\right)$$

(3)

where $P_{k-1}\left(Y_t\right)$ is the least squares prediction of $Y_t$ based on $\left(Y_{t-1},Y_{t-2},\dots ,Y_{t-k+1}\right)$ least squares-predicted values; similarly $Y_{t-k}-P_{k-1}\left(Y_{t-k}\right)$ is the least squares prediction of $Y_{t-k}$ based on $\left(Y_{t-1},Y_{t-2},\dots ,Y_{t-k+1}\right)$; $\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}$ denotes the correlation coefficient.

The ADF test is a statistical test used to assess the stationarity of time series data. Stationarity, a key assumption in ARIMA modeling, implies that the data’s mean and variance remain constant over time. The ADF test examines whether unit roots are present in the series, indicating non-stationarity. A low p-value (typically below 0.05) suggests that the data are stationary and essential for accurate ARIMA forecasting.

4. Results and Discussion

To verify the effectiveness of the method, one month’s worth of electricity consumption data from the laboratory were collected, and a dataset was constructed with a time stamp of every five minutes. The dataset was then used for ARIMA analysis.

The augmented Dickey–Fuller (ADF) test was conducted to assess the stationarity of the time series data for total power usage. This test helps determine whether differencing is necessary to stabilize the mean and eliminate trends in the data.

Table 3. ADF inspection table.

Variable	Differencing Order	t-Statistic	p-Value	AIC	Critical Value
					1%	5%	10%
Total Power Usage	0	−8.332	0.000 ***	−39,326.282	−3.431	−2.862	−2.567
	1	−25.576	0.000 ***	−39,259.07	−3.431	−2.862	−2.567
	2	−28.622	0.000 ***	−39,014.79	−3.431	−2.862	−2.567

*** represent the significance level of 1%, respectively. t-statistic: an indicator that measures the stationarity of a time series; p-value: the probability of the significance of the test result; AIC: an indicator of model quality.

below summarizes the test statistics at different levels of differencing.

Original Data (Differencing Order 0): The t-statistic is −8.332 with a p-value of 0.000, which is highly significant at the 1% level. This result suggests that even the original series is stationary. However, given the high t-statistic, further differencing may still be explored for stability.

First Differencing (Differencing Order 1): The t-statistic improves significantly to −25.576, confirming stationarity with even stronger evidence. The p-value remains 0.000, indicating that the first-differenced data are stationary.

Second Differencing (Differencing Order 2): The t-statistic further decreases to −28.622, with continued significance at the 1% level. This implies that the second-differenced series is also stationary.

The ADF test consistently showed high significance across all differencing levels, indicating that the series achieved stationarity even at the original level. However, the improved t-statistics with differencing suggest that applying at least first-order differencing stabilizes the series, providing a robust basis for modeling. The results confirm that the data are suitable for ARIMA modeling without additional transformations.

Figure 1 shows a regular pattern of peaks and declines, indicating increased and decreased activity or usage periods. This pattern indicates periodic or intermittent behavior in the data, which is common in applications where usage is erratic throughout the day. A consistent pattern throughout the timeframe indicates that the differencing stabilized the mean, eliminated trends, and smoothed the data. This suggests that the chosen order of differencing effectively captured the variability in the data, making it suitable for ARIMA modeling.

As shown in Figure 2, the autocorrelation function (ACF) of the differenced data shows a gradual decline, indicating that although the differencing has stabilized the series, some correlation still exists. The partial autocorrelation function (PACF) shows a significant peak at the first lag and then rapidly declines, suggesting that the AR (1) model is appropriate because of its strong correlation with recent past values. The ACF and PACF plots of the model residuals do not show significant autocorrelation or partial autocorrelation, indicating that the residuals exhibit white noise properties. This lack of correlation confirms that the ARIMA model effectively captured the underlying patterns in the data. The analysis suggests that the model is well specified and suitable for prediction because it fully accounts for the autocorrelation structure, leaving uncorrelated residuals.

Table 4. ARIMA model (0,1,0) test.

Item	Symbol	Value
	Df Residuals	8350
Sample size	N	8353
Q statistic	Q6 (p value)	0.066 (0.798)
	Q12 (p value)	3.566 (0.735)
	Q18 (p value)	35.582 (0.000 ***)
	Q24 (p value)	52.994 (0.000 ***)
	Q30 (p value)	62.055 (0.000 ***)
Information criterion	AIC	−39,514.144
	BIC	−39,486.022
Goodness of fit	R2	0.69

*** represent significance level of 1%, respectively.

illustrates the parameters of the model, the ARIMA (0,1,0) model was selected and evaluated for its effectiveness in capturing trends in total electricity consumption.

Table 4 shows the results of the ARIMA (1,0,1) model selected based on the AIC criteria. The model was fitted using a sample size 8353 with 8350 degrees of freedom. The Q-statistics for lags 6 and 12 have insignificant p-values, indicating that there is no significant autocorrelation at these lags. However, starting at lag 18, the p-value becomes significant, indicating some autocorrelation in the residuals at higher lags.

The model had the AIC and BIC values of −39,514.144 and −39,486.022, respectively, reflecting good model fit where AIC is used to determine the best parameters. The goodness of fit (R² of 0.69) indicates that the model explained 69% of the variance in the data, suggesting that it is well suited to capture the primary dynamics. Overall, the ARIMA (1,0,1) model provided a robust fit to the data.

Table 5. Model check.

	Coefficient	Standard	t	p > |t|	0.025	0.975
constant	0	0	1.163	0.245	0	0.001
ar.L1	0.986	0.003	291.653	0	0.979	0.993
ma.L1	−0.738	0.005	−161.364	0	−0.747	−0.729
sigma2	0.001	0	98.882	0	0.001	0.001

details the results of the ARIMA (1,0,1) model, optimized for total energy consumption (kWh) using the AIC criterion. The model is expressed as

$$y\left(t\right)=0.0+0.986·y(t-1)-0.738·\epsilon (t-1)$$

(4)

The constant coefficient of 0 is statistically insignificant (p = 0.245), indicating that it has no meaningful effect on the model. The AR (1) coefficient (ar.L1) of 0.986, with a p-value of <0.001, shows a strong positive correlation with the previous point in time, highlighting its significance in explaining the behavior of the series. The MA (1) coefficient (ma.L1) of −0.738, with a p-value of <0.001, indicates a strong negative correlation with the previous error term, which is crucial in capturing the moving average component. The Sigma² of 0.001 is highly significant (p < 0.001), indicating variability in the error term. From the significant autoregressive and moving average components, the ARIMA (1,0,1) model effectively captured the dynamics of energy consumption.

Figure 3 illustrates the time series model predictions of total energy consumption (kWh), showing the observed data, fitted values, and predicted values.

The observed data (blue line) show regular fluctuations, suggesting a cyclical consumption pattern. This suggests that the model needs to effectively capture the potential impact of factors such as daily or weekly cycles. The fitted values (green line) closely track the observed data, indicating the effectiveness of the ARIMA (1,0,1) model in capturing the underlying patterns. This suggests that the model accurately reflects both short-term changes and long-term trends in the data. However, it can be seen that its fit to the magnitude of the energy consumption values is always lower than the observed data. The predictions (orange lines and shaded areas) extend beyond the observation period, the confidence intervals indicate the range of potential future values, and this time, a backward prediction of 500 time stamps was set. The predictions indicate that the model can successfully generalize from past data to predict future consumption. However, its confidence intervals also indicate the uncertainty inherent in the predictions, highlighting areas where model improvements may further increase accuracy.

5. Conclusions

This study successfully developed a laboratory energy consumption prediction model using the ARIMA methodology, focusing on AC and DC equipment. Unlike previous methods, this study provides detailed insights into daily operating patterns, demonstrating the model’s ability to capture specific laboratory energy dynamics. ADF tests confirmed the smoothing of the variance series, and the residuals of the model exhibited white noise characteristics, indicating an appropriate model fit. Forecasting using the model was also attempted, but the predictions were average. Future research could improve forecasting accuracy by integrating other variables such as seasonal trends or external environmental factors, thus expanding the applicability and accuracy of the model in different environments.