A Sustainable Development for Building Energy Consumption Based on Improved Rafflesia Optimization Algorithm with Feature Selection and Ensemble Deep Learning

Abstract

Buildings emit a great deal of carbon dioxide and use a lot of energy. The study of building energy consumption is useful for the sustainable development of multi-energy planning and energy-saving strategies. Therefore, a sustainable development for building energy consumption based on the improved rafflesia optimization algorithm (ROA) with feature selection and ensemble deep learning is proposed in this paper. This method can explore data on building energy usage, assess prediction accuracy, and address concerns that building energy usage research must address. The proposed model first uses an improved self-organizing map with a new neighborhood function to select important features. After that, it uses ensemble deep learning to accurately anticipate the building’s energy usage. In addition, the improved ROA is used to fine-tune parameters for feature selection and ensemble deep learning. This research uses the dataset of the American Society of Heating, Refrigerating, and Air Conditioning Engineers (ASHRAE) to compare the performance of several modeling approaches. It identifies the top five most important features based on the model’s results. Furthermore, the proposed model can be successfully applied to a real-world application. They both have the lowest root mean squared errors among the approaches examined. The proposed model indeed provides the benefits of feature selection and ensemble deep learning with the improved ROA for the prediction of building energy consumption.

1. Introduction

Due to the rise in global temperatures, extreme climate change has become a serious threat to the progress and safety of contemporary human civilization. The basis of extreme climate change is carbon peaking, and the answer to this issue is carbon neutrality. Buildings are a major source of energy consumption and carbon dioxide emissions. As the economy develops, carbon emissions continue to climb, as does building energy usage [1]. Forecasting building energy usage is thus one of the most critical areas for reaching carbon peaking and carbon neutrality. It is expected to develop various energy-saving and energy-optimized control strategies to achieve carbon peaking and carbon neutrality goals. Building energy consumption prediction is a direct reflection of the distributions and trends of a building’s energy use. Such information is crucial for accomplishing the sustainable development of predicting energy use.

Building energy consumption research started in the mid-to-late twentieth century, and its primarily focused on gathering data on energy use, creating databases, analyzing energy use, etc. [2]. Connecting data from sensors to servers was proposed by Cao et al. to make it possible to collect and transmit building energy consumption data [3]. Piette et al. increased the degree of energy consumption research in buildings through the collection and analysis of energy use data [4]. Chen et al. designed an indoor environmental monitoring network based on sensors, base stations, and data management applications [5]. Mishra constructed an energy consumption database based on data from 638 village energy consumption surveys administered by different organizations in India from 1985 to 1989 [6]. Steadman et al. established a database on energy usage in non-residential buildings in the UK [7]. Recently, machine learning has been applied to assess and predict building energy use. Machine learning is widely used because it offers numerous advantages in analyzing and modifying building energy usage data. Idowu et al. used heating datasets from ten residential and commercial buildings in Sweden to conduct energy consumption analysis and forecasting models [8]. Artificial neural networks (ANNs) were shown by Karatasou et al. to be useful in estimating building energy use [9]. Their results show that an ANN is more energy efficient and has fewer errors than regression trees. Xia et al. improved on the classic ANN and developed a building energy consumption prediction model that outperformed the ANN and other models [10]. Cerqueira et al. recommended using feature selection and integrated learning methods to improve performance [11]. Ericks et al. also proposed the use of a self-organizing map (SOM) for feature selection [12]. However, how to properly adjust suitable neighborhoods and parameters to generate valuable features is still a problem. Somu et al. hypothesized that deep learning could be used for building energy consumption and achieved remarkable results [13]. Dong et al. presented a prediction strategy for building energy consumption based on ensemble learning and energy consumption pattern classification [14]. The current status of this research field shows that researchers have actively explored building energy consumption technology, but most of the research results are relatively difficult to apply to a “ubiquitous perception” environment. They do not fully solve the problem of implementing integrated learning of building energy consumption data that is multi-dimensional, diverse, and dynamically optimized. Recently, deep learning has achieved a good nonlinear approximation ability through layer-by-layer neural network processing and has been widely used for nonlinear regression in the transportation, power, and medicine fields, among others [15,16]. Ensemble deep learning integrates the learning abilities of various deep neural networks (DNNs) to construct a model that enhances the performance of the original model. It can adapt to the sample problem and increase prediction accuracy, yielding better outcomes than single deep learning. However, maintaining sample variety in each deep learning model in an ensemble DNN is difficult. The number of neurons, for example, is highly related to performance. If the selection is poor, network fluctuations can occur, and the deep learning model is then easily drawn into local optimization. As a result, optimizing deep learning and successfully enhancing prediction accuracy is an issue worth investigating. To properly adjust parameters and enhance the predicting performance, improving the prediction of building energy consumption using feature selection and ensemble deep learning with the ROA is described in this paper. In the proposed model, the improved ROA is used to fine-tune the parameters to achieve the best performance. The model can address the aforementioned problems of building energy consumption prediction.

The rest of this paper is structured as follows: Section 2 discusses the basis of the proposed model. Section 3 describes the proposed model. Section 4 summarizes the findings and compares the proposed model to other previous approaches in detail. Section 5 contains the conclusions.

2. The Basis of the Proposed Model

In this section, the basis of the proposed model is briefly described. The ROA is founded on the actions of the rafflesia flower, from the initial stages of blossoming to the distribution of its seeds [17]. Three steps have been distinguished for the ROA: insect attraction, insect consumption, and dispersal of seeds. During the insect attraction phase, the ROA employs two techniques. The first technique focuses on the interaction between freshly attracted insects and non-rafflesia flying insects. The second technique is to keep track of the insects that migrate to the rafflesia. The individual position $P_i$ is carried out as follows in the first technique:

$$P_{i_k}=P_{{best}_k}+dist·\mathit{sin}{\alpha }_k\mathit{cos}{\beta }_k$$

(1)

$$dist=\sqrt{{\sum }_{k=1}^D{(P_{i_k}-P_{{best}_k})}^2}$$

(2)

$$P_{{worst}_i}=P_i$$

(3)

where k (k = 1, 2,…, D) and D represent the population’s dimension and index, dist is the distance between $P_i$ and $P_{best},$ $P_{best}$ is the best individual position in the population, $P_{worst}$ represents the worst individual position in the population, ${\alpha }_k$ is a random value between [0, π/2], and ${\beta }_k$ is a random value between [0, π]. In the second technique, the main emphasis is modifying the individual’s position. The vectorial sum of a flying insect’s rotational and translational velocities determines its velocity.

$$\stackrel{⃑}{v_1}={\displaystyle \frac{w_0}{2}}\sqrt{E^2{\sin }^2\left(w_{0}t+\theta \right)+F^2{\cos }^2(w_{1}t+\theta )}$$

(4)

$$\stackrel{⃑}{v_2}=\stackrel{⃑}{v_2}{w}_0\cos (w_{0}t+\theta +\varnothing )$$

(5)

where $\stackrel{⃑}{v_1}$ and $\stackrel{⃑}{v_2}$ represent the translation velocity and rotation velocity, E denotes the amplitude of wing flapping, F represents the lateral offset, $w_0$ is the flapping frequency period, $w_1$ stands for the lateral flapping frequency period, θ signifies the phase, $\varnothing$ indicates the phase difference between rotation and translation, and t denotes time. The formula for updating the insect’s velocity is as follows.

$$\stackrel{⃑}{v}=\stackrel{⃑}{v_1}+\stackrel{⃑}{v_2}$$

(6)

While the individual position is adjusted using the velocity update formula, the globally optimal individual also has an impact. The position update formula for the insect individual is generated by incorporating this influence into the individual motion.

$$\stackrel{⃑}{L}=G·\stackrel{⃑}{v}·t+(P_{best}-P_i)·(1-G)·rand$$

(7)

where $G$ denotes the influencing factor, with its value ranging between −1 and 1, and $rand$ refers to a random number between 0 and 1. Ultimately, the individual’s position is updated after each iteration according to the following formula:

$$P_i=P_i+\stackrel{⃑}{L}$$

(8)

During the consumption phase of the algorithm, the primary objective is to exclude the individuals that are least suited to the environment, thereby guaranteeing the quality of the optimal population. A predetermined number of iterations is carried out during this phase, and the population size is reduced by one following each iteration. The rafflesia is positioned in the seed spreading phase according to the best individual position at the end of the two phases that came before it. The seed with the best chance of surviving during this period becomes the new definition of the optimal individual. In the meantime, other individuals look for appropriate growth conditions at random. Below is the updated formula for this phase:

$$P_{i_k}=P_{{best}_k}+R_a·\exp \left({\displaystyle \frac{iter}{{max}_{iter}}}-1\right)·sign(rand-0.5)$$

(9)

where $R_a=rand\ast \left(ub-lb\right)+lb$ denotes the individual’s distribution range, $lb$ and $ub$ mark the upper and lower boundaries of the individual distribution range,${max}_{iter}$ denotes the maximum iteration, and $iter$ represents the iteration.

Kohonen proposed that the SOM conforms to the model of unsupervised learning networks [18]. The learning paradigm is appropriate for the SOM as long as it contains inherent clustering principles, as shown in Figure 1. There are two layers in the SOM network: the input layer and the output layer. The input layer consists of a single layer of neural configurations that are fully weight-connected to the neurons in the output layer. The number of neurons in the input layer is determined by the dimensionality of the sample. It relies on neurons competing with each other to iteratively optimize networks using competitive learning methods. Iteratively traversing each neuron in the competitive layer to calculate the distance between data x(t) and each one in the SOM. The winning node will select the neurons with the lowest distance, commonly known as the best matching unit (BMU). Equation (10) describes the learning rule.

$$w_i\left(t+1\right)=w_i\left(t\right)+\beta \left(t\right)·N_{i,bmu}\left(t\right)·(x\left(t\right)-w_i\left(t\right))$$

(10)

where $w_{ij}\left(t\right)$ denotes the weight of the ith neuron at time t, $\beta \left(t\right)$ denotes the learning rate at time t, $N_{i,bmu}\left(t\right)$ denotes the neighborhood function between the ith neuron and BMU at time t, and $x\left(t\right)$ denotes the sample data at time t. Traditionally, the neighborhood function could be described as Equation (11).

$$N_{i,bmu}\left(t\right)=N_0·exp\left(-{\displaystyle \frac{t}{\tau }} \right)$$

(11)

where $N_0$ is the initial value of $N_{i,bmu}\left(t\right)$ and $\tau$ is the total iteration time.

DNN is a kind of ANN composed of many layers of interconnected neurons and intends to learn and predict complicated data patterns and relationships [19]. Each layer is made up of a collection of neurons that process the incoming data and pass the results on to the layer below it. When the neurons in a given layer connect with those in the next layer, they form a neural network made up of interconnected nodes. Figure 2 illustrates a DNN with four layers.

A neuron, known as a node, is a fundamental unit in DNNs. Neurons receive inputs, apply weights to those inputs, perform an activation function, and produce an output. The output of neuron j is described in Equation (12).

$$y_j=f({\sum }_{i=1}^n{w}_{ij} x_i-{\theta }_j)$$

(12)

where $y_j$ is the output of the jth neuron, $x_i$ is the ith input, $w_{ij}$ is the weight for the ith input and jth neuron, n is the total number of inputs, ${\theta }_j$ is the threshold of the jth neuron, and f is the activation function. The activation function is used at the outputs of specific neurons, which enables the network to recognize intricate patterns and make precise predictions. Based on the weighted sum of a neuron’s inputs, activation functions assist in deciding whether or not it should be activated. To minimize the gap between its expected output and the desired output, a DNN adjusts its internal parameters, called weights. The weights are iteratively modified using gradient descent, relying on the estimated gradients of the gap. The root mean squared error (RMSE) is a commonly preferred option. Furthermore, incorporating several hidden layers can notably enhance the generalizability of the model. DNNs, in general, have shown an outstanding capability to tackle complicated problems and have become a cornerstone of modern machine learning and artificial intelligence research. Ensemble learning is a machine learning method in which numerous separate learners are combined to create predictions [20]. The network structure can also fully map nonlinear data and increase prediction skills, increasing the accuracy of data analysis and forecasting. Ensemble DNNs can aid in improving generalization, prevent overfitting, and improve the ensemble’s overall predictive power [21].

3. The Proposed Model

An ROA for predicting building energy consumption using feature selection and ensemble deep learning is proposed in this paper. Our goal is to create a cutting-edge model that will increase the predictability of building energy usage. The proposed model’s procedure is depicted in Figure 3. In Figure 3, the dataset of ASHRAE is imported first, and then the data are preprocessed. Data preprocessing is the process of re-examining and calibrating data to correct existing errors and provide data consistency. Then, an improved SOM is proposed to process feature selection. When the feature selection is completed, the ensemble deep learning is performed to improve its performance. In the proposed model, ROA is used to fine-tune the parameters of the improved SOM and ensemble deep learning to obtain the best prediction. The proposed model continues to run until the stop criterion is reached.

In this research, the ASHRAE energy consumption dataset is imported along with building information and historical weather data [22]. These two datasets are described in

Table 1. The dataset of building information.

No.	Feature	Characterization
1	building_id	The building identification.
2	meter	The identification code was 0 as electricity, 1 as chilled water, 2 as steam, and 3 as hot water.
3	timestamp	The time that the measurement was made.
4	meter_reading	The output label that means energy consumption in kWh (or equivalent).
5	site_id	The site identification.
6	primary_use	Indicator of the main category of construction activities.
7	square_feet	The overall area of the structure.
8	year_built	The construction year.
9	floor_count	The total number of floors in the structure.

and

Table 2. The dataset of weather.

No.	Feature	Characterization
1	site_id	The site identification.
2	timestamp	The time that the measurement was made.
3	air_temperature	Temperature in Celsius.
4	cloud_coverage	A portion of the sky was cloudy.
5	dew_temperature	It means that the temperature at which the atmosphere is saturated with water vapor in Celsius.
6	precip_depth_1_hr	It describes hourly precipitation in millimeters.
7	sea_level_pressure	It is the weight of a column of air per unit area from sea level to the upper boundary of the atmosphere in millimeters.
8	wind_direction	Direction on a compass (0–360). It is defined as the direction that the wind is coming from.
9	wind_speed	Seconds per meter.

. The primary_use feature of the building information dataset is the indicator of the main category of construction activities, as shown in Figure 4. It appears that education is the category with the greatest amount of construction. The features of sea_level_pressure and wind_direction are depicted in Figure 5. As shown in Figure 6, there are four different forms of metering, with 0 denoting electricity, 1 denoting chilled water, 2 denoting steam, and 3 denoting hot water. The highest amount is seen in Figure 6 to be associated with electricity.

For preprocessing the data, the data are performed as follows: It first performs data cleaning and then it performs data transformation and feature scaling as shown in Figure 7. Data cleaning is the process of removing or filling missing values from a dataset. Data transformation is to regularize data into a range to compare it more accurately. Feature scaling standardizes the range of independent variables in the dataset, ensuring that all features contribute equally to the model training process. In this paper, the features of floor_count and year_built have too many missing values in the building information dataset. These features refer to the actual number of floors in the structure and the year of the building, respectively. Due to the lack of real-world data, these two features are removed from the preprocessing data. However, the median value is used to fill in the missing values for the weather dataset. The features of air_temperature and dew_temperature are shown in Figure 8 in Celsius. The dew_temperature feature means the temperature at which the atmosphere is saturated with water vapor. The figure shows that the dew_temperature feature is slightly skewed. The meter_reading feature is the output label, and it means energy consumption in kWh (or equivalent). The meter_reading feature is shown in Figure 9. As can be seen, the meter_reading is extremely skewed to the left, so log transformation is applied to fix the skewness. Thereafter, normalization is used to scale features into a range between 0 and 1. It prevents certain features from dominating the model training due to their larger scales, promoting better model performance and convergence.

The improved SOM algorithm is configured as follows:

• Step 1: Initialize the weights.
• Step 2: Input the data.
• Step 3: Apply the new neighborhood function to calculate the amplitude of the respective updates of the neighborhood function.
• Step 4: Neurons in the winning neighborhood have their weights updated.
• Step 5: Return to Step 2 after finishing the iteration until the stop criterion is met.

The amplitude of the update increases with proximity to the BMU. The new neighborhood function $N_{i,bmu}\left(t\right)$ is calculated using Equation (13).

$$N_{i,bmu}\left(t\right)=\left\{\begin{array}{c} 1 if t\le {\Omega }_1,\\ {\displaystyle \frac{{\Omega }_2-\Omega }{{\Omega }_2-{\Omega }_1}} if {\Omega }_1\le t<{\Omega }_2,\\ 0 \mathrm{others}\end{array}\right.$$

(13)

where ${\Omega }_1$ and ${\Omega }_2$ are fine-tuned by the ROA. The ensemble deep learning uses cross-validation to divide the original data into $k$-folds. The $k$ numbers of the DNN are then generated while maintaining the same functionality for ensemble deep learning. Each DNN has three hidden layers, one output layer, and one input layer as its structure. The activation functions of the three hidden layers and the input layer are all set to relu functions. The activation is configured as a linear function for the output layer. The ensemble output L(t) is calculated as an averaged RMSE with the overall $k$ numbers of DNNs, as shown in Equation (14).

$$L(t)={\displaystyle \frac{1}{k}}{\sum }_{i=1}^k{L}_i\left(t\right)$$

(14)

where $L_i\left(t\right)$ is the RMSE of the ith DNN at time t. The information of the ensemble output is used as the penalized error function $E_i\left(t\right)$, and $E_i\left(t\right)$ is to be minimized as follows:

$$E_i\left(t\right)={\displaystyle \frac{1}{2}}{(L_i\left(t\right)-L_{low}(t\left)\right)}^2-\gamma (L_i\left(t\right)-L(t))$$

(15)

where $L_{low}$ is the lowest RMSE for all DNNs, and $0\le \gamma <1$ is an adjustable strength parameter. These $k$ numbers in the DNN assess the validity outcomes by averaging the final RMSE. The prediction is output once the average RMSE reaches the stop criterion. Otherwise, $\alpha$ neurons are added to the hidden layers to improve learning across all samples. Note that $\alpha ,k$, and $\gamma$ are fine-tuned by the ROA in the DNN. The ensemble deep learning is configured as follows:

• Step 1: Create $k$ numbers of DNN after $k$-folding the original data.
• Step 2: Obtain $L_i\left(t\right)$ and calculate $L\left(t\right)$ in Equation (14).
• Step 3: Apply Equation (15) to calculate the penalized error function $E_i\left(t\right)$.
• Step 4: If the stop criterion is matched, the prediction is output. Otherwise, add $\alpha$ neurons in hidden layers from ROA and return to Step 2.

To refine solutions and improve exploitation capabilities for the ROA, the simulated annealing (SA) technique is combined into Equation (9). SA is a probabilistic optimization algorithm inspired by the process of annealing in metallurgy. The algorithm starts with an initial solution and iteratively explores neighboring solutions. At each iteration, it considers moving to a neighboring solution. It is always accepted if the neighboring solution is better than the current one. If the neighboring solution is worse, it may still be accepted with a certain probability that decreases over time. The probability of accepting a worse solution is determined by a parameter called the “temperature”, which is gradually decreased according to a cooling schedule. The parameter of $T_0$ represents the initial temperature in the SA algorithm. A higher initial temperature allows for more solution space exploration, while a lower initial temperature focuses on exploitation. Initially, the temperature is high, allowing the algorithm to accept worse solutions more easily, which helps in escaping local optima. As the temperature decreases, the algorithm becomes more selective, focusing on refining the solution towards the global optimum. In SA, the parameter μ represents the cooling rate or temperature reduction factor applied at each iteration to decrease the temperature. In SA, the value of μ typically lies between 0 and 1, where μ determines the rate at which the temperature is reduced during the optimization process. SA is particularly useful for optimization problems where the search space is complex and rugged, with many local optima. The pseudo-code of SA is shown as follows (Algorithm 1) [23].

Algorithm 1. Procedure: SA algorithm

$iter$ = 0; Set the initial temperature $T_0$ and the parameter $\mu$ ($0<\mu <1)$; While ($T_{iter}\ge$ $T_{min}$) do $\omega$ = 0; While (the stop criterion has not been reached) do Generate a new solution from Equation (9) to be the current solution; ΔE = the fitness of the current solution—the fitness of the new solution; $P_{\omega }=\exp (-\Delta E/T_{iter}$); If $P_{\omega }$>= $rand$ then Accept the new solution; Set the new solution as the current solution; $\omega =\omega$ + 1; End; Update the obtained best solution; $T_{iter+1}=T_{iter}\ast \mu$; $iter$ = $iter$ + 1;  End.

For the improved ROA, it first initializes the parameters for ROA before randomly generating the positions of the insects. Stop the process if the $iter$ exceeds the ${max}_{iter}$. Otherwise, it will calculate insect fitness, sort individuals based on fitness, and update the best individual. Following that, the insect attraction, insect consumption, and seed spreading phases will be completed in the order listed. The improved ROA is set up as follows:

• Step 1: Initialize the parameters of ROA.
• Step 2: Generate the positions of the insects at random.
• Step 3: If the $iter>{max}_{iter}$, the procedure is terminated and the prediction is output. Otherwise, proceed to Step 4.
• Step 4: Determine the fitness of the insects.
• Step 5: Sort individuals based on fitness and update the best individual.
• Step 6: If the first technique is used during the insect attraction phase, the individuals are updated according to Equations (1)–(3). Otherwise, it updates the individuals using Equations (4)–(8).
• Step 7: During the insect consuming phase, it will eliminate the individual with the lowest fitness.
• Step 8: During the seed spreading phase, the individual will be updated with Equation (9) and the SA technique.

The choices of ROA, SOM, and DNN in the context of predicting energy consumption play significant roles in improving predictive accuracy. In the context of energy consumption prediction, ROA can be used to optimize the parameters of predictive models. By efficiently exploring the solution space, ROA can help in finding the best set of model parameters that capture the basic trends in energy consumption data. This optimization process can lead to more accurate predictions by fine-tuning the model to fit the data more effectively. When applied to energy consumption prediction, the SOM can help in feature selection. It can identify relationships and structures within the data that may not be obvious initially. This can lead to more accurate predictions by capturing the basic trends and dependencies in the data. In the context of energy consumption prediction, the DNN can learn intricate patterns and nonlinear relationships within the data. By leveraging the deep architecture of the DNN, it can make accurate predictions based on the learned representations. The combination of the ROA, SOM, and DNN can significantly contribute to improving the predictive accuracy of energy consumption.

4. Results and Discussions

In the proposed model, ROA involves initializing the population of solutions with random values from the specified search space. Evaluate the fitness of each solution in the population using the fitness function. Perform pollination activities to create new solutions by combining the best aspects of existing ones. Terminate the optimization process with a halting criterion. It sets up the SOM and provides random weights to the neurons. Iteratively display input data to the SOM and alter neuron weights in response to input patterns. Cluster similar input patterns together using neuron weights. Determine the topological links between clusters in the SOM. Ensemble deep learning sets up the architecture of each DNN model in the ensemble, such as the number of layers, activation functions, and the error function. Describe the ensemble technique used and how individual model predictions are merged to yield the final prediction. Specify the hyperparameters used to train the models, as well as the penalized error function used for model optimization and regularization. Detail the evaluation criteria used to measure model performance, as well as the process for creating k numbers of the DNN after k-folding the original data.

The target variable in this study is meter_reading, which represents energy usage in kWh. The initial structure of the DNN is shown in

Table 3. The initial structure of the DNN.

Layer	Output Shape
Layer No. 0	1024
Layer No. 1	512
Layer No. 2	256
Layer No. 3	128
Layer No. 4	1

. In Table 3, Layer No. 0 is the input layer. Layer No. 1, No. 2, and No. 3 are hidden layers. Layer No. 4 is the output layer as the output variable.

To ensure that the experimental results are comparable, all algorithms are set to the same conditions. For SA, the parameters are set as T₀ = 500, $T_{min}$ = 0.5, and µ = 0.9 [23]. For ROA, certain parameters within the aforementioned equations are set as follows: E, F, $w_1$, $w_0$, and $\varnothing$ are, respectively, set to 2.5, 0.1, 0.025, 0.025, and −0.78545. The range for the site is (0, $\mathsf{\pi }$), and the initial value for $\stackrel{⃑}{v_2}$ is defined between 0 and 2$\mathsf{\pi }$, the maximum number of iterations is ${max}_{iter}=$ 500, the population size is 50, and the representation of the solution is set as the values of $\alpha ,k,\gamma , {\Omega }_1,{\Omega }_2,\beta \left(t\right), \mathrm{a}\mathrm{n}\mathrm{d} {\theta }_j$. These initial values are randomly generated, and these values are set between 0.0001 and 30. Note that the constraints are that $\alpha \ge 1 \mathrm{a}\mathrm{n}\mathrm{d} k\ge 3$ are integers, $0\le \gamma <1, \mathrm{a}\mathrm{n}\mathrm{d} {\Omega }_1<{\Omega }_2$. For α ≥ 1, it means the number of neurons is added to the hidden layers to improve learning across all samples. The ensemble deep learning uses cross-validation to divide the original data into $k$-folds and $k\ge 3$. The fitness in the ROA is set as Equation (16).

$${Fitness}_i=1/(1+{RMSE}_i)$$

(16)

where ${RMSE}_i$ is the RMSE of the $i$th solution. Because we want to obtain the best selected features and prediction accuracy, we set the stop criterion as the output value that is not further ameliorated after 30 consecutive iterations or reaches the maximum number of iterations. The metric is the RMSE of the log for meter_reading.

Table 4. The compared results for ASHRAE.

Approaches	RMSE
LR [24]	1.381
LR with selected features	1.379
DT [24]	0.609
DT with selected features	0.607
RF	0.593
RF with selected features	0.581
SVR	0.781
SVR with selected features	0.724
DL [24]	0.897
DL with selected features	0.876
Ridge [25]	1.384
Lasso [25]	1.381
SGD regressor [25]	1.381
ElasticNet [25]	1.473
The proposed model	0.439

and Figure 10 list the outcomes of various methods for ASHRAE. These contrasted methods include linear regression (LR), decision tree (DT), random forest (RF), support vector regression (SVR), deep learning (DL), Ridge, Lasso, SGD Regressor, ElasticNet, and the proposed model [24,25]. Note that the initial network of the proposed model and DL share the same basic structure. The stop condition is the same for all approaches. From the results, LR, Ridge, Lasso, and SGD Regressor have competitively close RMSE. ElasticNet performed worst out of all compared models, indicating its unsuitability for such a problem. It is demonstrated that the proposed model has the lowest RMSE. In addition, Figure 11 illustrates the results of the top five most essential features. From Figure 11, air_temperature, square_feet, meter, primary_use, and building_id are the selected features. The feature of air_temperature is a crucial factor that directly influences the energy demand for building heating and cooling systems. Variations in external and internal temperatures can affect energy consumption levels. Higher or lower temperatures may require increased heating or cooling efforts, leading to fluctuations in energy usage. The size of a building, represented by the feature of square_feet, plays a significant role in determining energy consumption. Larger buildings typically require more energy to heat, cool, and light space than smaller buildings. Understanding the feature of square_feet helps in assessing the overall energy needs and efficiency of a building. Meter type refers to the specific utility meter measuring energy consumption within a building. Different meter types can track electricity, gas, water, or other utilities. By considering the feature of the meter, the model can account for the specific energy sources and consumption patterns, enabling more accurate predictions of energy usage. The feature of primary_use indicates its intended function, such as office, residential, retail, or educational purposes. Each building type has unique energy consumption patterns based on occupancy, equipment usage, and operational hours. Understanding the feature of primary_use helps tailor energy management strategies and optimize consumption for specific building categories. The feature of building_id serves as a unique identifier for individual buildings in the dataset. By including building_id as a feature, the model can capture site-specific characteristics, such as building design, location, and historical energy usage trends. Analyzing the feature of building_id enables personalized energy consumption predictions based on the building’s unique attributes. It is noted that the air_temperature feature plays the most important role in building energy consumption.

We also utilize another dataset to demonstrate the performance of the proposed model. In this scenario, data were obtained from a university. The data collection instruments include the acquisition terminal, a soil pressure gauge, a water pressure gauge, a rain gauge, a steam gauge, an inclinometer, temperature and humidity sensors, and a static level. There are a total of 35 features obtained from these instruments. There are six features extracted from the proposed model. The comparison of results for this dataset is shown in

Table 5. The compared results for the dataset from a university.

Approaches	RMSE
LR	1.045
LR with selected features	0.992
DT	0.997
DT with selected features	0.985
RF	0.982
RF with selected features	0.943
SVR	0.956
SVR with selected features	0.921
DL	0.972
DL with selected features	0.958
The proposed model	0.809

and Figure 12. From the results of Table 4 and Table 5, the approaches with feature selection have better performance than traditional approaches. It also shows that the proposed model also has the best performance in these compared approaches.

5. Conclusions

The goal of the proposed model is to select important features for decisions and ameliorate the predicted performance. The improved SOM is employed for feature selection in the proposed model, which finally selects five important features and reduces the dimensionality of the complex for the ASHRAE dataset. The ensemble deep learning model aims to provide the diversity of DNNs and it is suitable and capable of great generalization while maintaining accuracy. In addition, the ROA is employed to fine-tune parameters in the proposed improved SOM and ensemble deep learning model.

According to the results, the proposed model has the lowest RMSE among the compared techniques. Incorporating feature selection can provide a more comprehensive understanding of the model’s performance and the features influencing energy consumption in buildings. It was discovered that the air_temperature feature is the most essential characteristic of ASHRAE. People should pay more attention to global temperature. It is an important issue to prevent global warming from the perspective of renewable energy (wind, solar, wave, and biomass) in the making of strategies for sustainable development. In addition, the real-world collected dataset is also used for performance testing of the proposed model. Based on the results, the feature selection indeed plays an important role for both datasets and the proposed model outperformed other approaches in the comparison. This advancement has resulted in the sustainable development for the successful application of building energy consumption forecasts.

The ASHRAE dataset is a valuable resource for building energy consumption prediction models. It is important to acknowledge its limitations that the dataset may not encompass a wide range of features. However, the ASHRAE dataset could serve as a valuable starting point for building energy consumption prediction models, and researchers could take steps to address potential challenges related to model generalization and accuracy in diverse real-world settings.