Deep learning ensemble for solar and wind power forecasting with feature engineering optimization (swift-net)

Abstract

To compensate for the massive variations in power output brought on by unpredictability, enormous quantities of pricy battery storage or power reserve capacity are required. Precise prediction of the Solar Wind Power Forecasting system improves energy conversion efficiency, reduces the risk of overloading the system, and optimizes unit commitment. In this paper, design a SWIFT-Net (Solar & Wind Integrated Forecasting Technology Network) model for precise solar and wind energy forecasting. Unlike existing models, SWIFT-Net uniquely integrates a deep learning ensemble framework with a dual-stage hybrid feature engineering mechanism using Hybrid Kookaburra Optimization and Botox Optimization, which has not been previously applied in this context. This ensures the selection of the most impactful features and enhances generalization across variable weather conditions. The weighted averaging method is employed to combine solar and wind power predictions. Finally, the designed model gained results are validated with existing classifiers in terms of MSE, RMSE, and MAE, ensuring continual refinement for enhanced forecasting accuracy, reliability.

Keywords

solar wind power forecasting SWIFT-net hybrid kookaburra optimization and Botox optimization multi-head attention and long short-term memory

Introduction

The primary means of addressing the global warming issue is becoming more and more focused on Renewable Energy Sources (RES). Researchers are paying more and more consideration to RES and sustainable energy sources, including wind, solar, wave, and tidal energy because fossil fuels are becoming scarcer and have negative environmental effects (AlKandari and Ahmad, 2020). Because of this, the use of RES has grown significantly in recent years and is predicted to grow considerably more in the ensuing decades (Carneiro et al., 2022). This poses a new issue because solar and wind energy systems only produce electricity when sunlight and wind are present. Because the primary RES are stochastic, their proper integration depends on precise and dependable forecasts (Rosa De Jesus et al., 2020). However, both physically and temporally integrating RES into the electrical system is difficult, and the cost of doing so remains high. The two most widely utilized RES are solar and wind (Kumari and Toshniwal, 2021; Wu and Wang, 2021). One distinctive quality of consumable electricity is that it is produced and consumed with little to no storage. Conventional electricity is produced in response to consumer demand from businesses, industries, and residences (Singla et al., 2022). The main issue in integrating RES into the electricity grid is their unpredictable character, such as the sporadic nature of wind speed (Massaoudi et al., 2021). In addition, the power output of individual wind turbines inside a wind farm varies according to the wind direction and turbine placement. The haze effect, solar elevation angle, and cloud cover all affect solar irradiation (Mora et al., 2021; Ribeiro et al., 2022). Cloud cover and haze impact are stochastic, but the sun elevation angle is theoretically determinant (Malhan and Mittal, 2022).

Inconsistent power sources interfere with traditional techniques of energy system planning and operation presenting challenges for power generation (Chakraborty et al., 2023). Grid operators are forced to modify their day-ahead, hour-ahead, minute-ahead, and real-time operations procedures due to the variability and fluctuation of renewable electricity output on numerous time scales (Xing and He, 2023). The building and organizing of wind and solar (W&S) power frameworks, the creation of electricity markets, and the planning and execution of power generation are only a few of the issues that depend on the accuracy and dependability of the prediction models for these energy sources (Marndi et al., 2020). However, given that errors in W&S power forecasting are inevitable, predictive modeling is a crucial tool for assessing risk in power systems, quantifying the unpredictability of traditional point predictions, and providing insightful data (Tarek et al., 2023). For this reason, load forecasting and immediate RES (such as W&S power) are essential in modern power plants for scheduling servicing, generating planning, and security evaluation (Guermoui et al., 2022).

Huge amounts of expensive battery storage or power reserve capacity are needed to smooth out the huge fluctuations in power outputs caused by unpredictability. It is possible to decrease these reserves by increasing forecasting accuracy (Devaraj et al., 2021). Accurate forecasting of the W&S power system enhances unit commitment optimization, lowers the danger of system overloading, and increases the efficiency of energy conversion. Power systems need accurate W&S power predictions because this RES has the potential to enhance both the economy and the environment (Jalali et al., 2021; Ma et al., 2020).

In response to these challenges, this paper suggesting a new deep learning ensemble framework, SWIFT-Net, which is the first attempt to combine hybrid optimization and multi-modal deep learning networks to improve the forecasting of solar and wind. In contrast to the traditional models, SWIFT-Net has a number of novel contributions that contribute to the significant improvement of accuracy, robustness, and interpretability. The following are the paper’s primary contributions:

• To effectively extract the features, the BOA optimization is hybrid with the KOA optimization method. The hunting approach of the KOA is improved using the mean value of the BOA algorithm.

• Utilizes LSTM network with an optimized MA mechanism to capture sequential data patterns effectively. By allowing the model to concentrate on pertinent elements of the input data, the attention mechanism improves the model’s capacity to identify significant temporal correlations.

• Integrates Inceptionv2 for efficient feature extraction from the input images, enabling the model to incorporate additional relevant information. Utilizes Efficient Capsule Networks for robust feature representation, improving the model’s capability to represent intricate spatial relationships in the information.

• Combines the forecasts from O-MA-LSTM and I2EMv2-E-CapsNet using a weighted averaging approach. By utilizing both models’ advantages, this integration method creates a forecasting system that is more reliable and accurate.

• All these contributions make SWIFT-Net stand out among the current forecasting models that incorporate a hybrid metaheuristic optimization, temporal attention modeling, and advanced feature fusion techniques. The obtained model shows better forecasting ability when tested against conventional measures of MSE, RMSE, and MAE.

The manuscript’s remaining section is arranged as follows: Section 2 lists the publications that are currently available on the solar and wind forecasting. In Section 3, the architecture of the proposed model is described. The experimental findings for the suggested method are shown in Section 4. Section 5 serves as the conclusion.

Related works

Wu and Wang (2021) created an ensemble neural network system for W&S power forecasting in China using LSTM, SVM, BP neural network, and ELM. To lessen the negative consequences of the original series’ fluctuation, VMD first breaks down unstable W&S power time series to smooth portions. Then, four fundamental models that are optimized using the EOSSA method are utilized to forecast W&S power based on the deconstructed subsequences. Ultimately, weighing the predictions from the four designs, the ENN prediction results were rebuilt.

Cannizzaro et al. (2021) offer a brand-new approach for both short- and long-term time frame Global Horizontal Irradiance (GHI) solar forecasting. It examines real-world datasets containing various time-series weather information, including GHI. Next, employ Random Forest (RF) with LSTM in conjunction with two Convolutional Neural Networks (CNN) and Variational Mode Decomposition (VMD). The creation of more precise energy management policies is aided by GHI forecasting.

Massaoudi et al. (2021) offer an accurate and dependable ensemble learning framework for short-term PV power generation prediction to address the significant volatility of PV electricity. The forecasting tool that is being presented includes layers of both base and meta-models. To obtain excellent predicting accuracy, the tree-structured Parzen estimators’ method is used to tune the hyper-parameters of the suggested stacking ensemble. The suggested approach outperforms the current forecasting techniques with the lowest Mean Absolute Percentage Error (MAPE) of 2.30%, as confirmed by the simulation outcomes.

For W&S power forecasting, Ahmad et al. (2021) introduced the ensemble-based k-nearest neighbor (KNN) model. This method’s nonlinear modeling problem in W&S energy allows for a more precise assessment of the spatial characteristics of wind and solar power. Specifically, the technique known as KNN was trained and optimized using Makowski metric evaluation. The chi-square distance was employed to evaluate the k-nearest neighbor method’s theoretical goodness of fit among observed and predicted values. The 5-fold cross-validation technique was used for extremely complex solar/wind data to ascertain the precise lasso-penalty strength.

To forecast solar energy, Khan et al. (2022) suggested an enhanced stacked ensemble method (DSEXGB) that utilizes two DL techniques: LSTM and Artificial Neural Network (ANN). To improve the forecast accuracy of solar power production, an extreme gradient boosting technique is used that integrates forecasts from the basic models. Furthermore, the designed study employed the shapely additive explanation paradigm to offer a more profound understanding of the algorithm’s learning process. The suggested model’s effectiveness was assessed by contrasting the prediction outcomes with those of individual ANN, LSTM, and bagging.

For wind speed ensemble prediction, Ibrahim et al. (2021) suggested an Adaptive Dynamic Particle Swarm System (AD-PSO) for machine learning in combination with the Guided Whale Optimization Algorithm (Guided WOA). The best hyperparameter variable for the LSTM DL system is chosen by the AD-PSO-Guided WOA method to anticipate wind speed. The outcomes showed that compared to multiple comparative efficiency and DL techniques, the AD-PSO-Guided WOA method performs well and offers excellent accuracy.

Lee et al. (2020) ensemble learning-based techniques to forecast time-dependent characteristics of the wind power data to build a method to estimate wind power output with an acceptable level of accuracy based on a variety of criteria. In essence, ensemble learning techniques pool the knowledge of several learners to provide predictions that are better than those of traditional standalone learners. The ensemble algorithms’ prediction performance with two regression techniques is contrasted. Comparing the ensemble approaches against the solo models, experimental data demonstrate that the latter is less accurate in predicting the output of wind power.

Suárez-Cetrulo et al. (2022) presents a novel method that accounts for constraints like curtailment and turbine deterioration to anticipate generating electricity at high frequencies 1 day ahead of schedule. Conducted an initial investigation to examine the correlation between all possible combinations of electrical power, predicted wind, and observed wind. Second, to evaluate the levels of predictability of various algorithms and geographies, a broad range of machine learning methods were applied to each site. In comparison to existing Machine Learning methods that estimate wind power 1 day in advance, our study and experimental findings demonstrate how enhancing ensembles is a more cost-effective approach in terms of runtime.

Peng et al. (2020) created a high-accuracy Wavelet Soft Threshold Denoising (WSTD) technique to forecast wind speed. Furthermore, a brand-new DL technique called the Gated Recurrent Unit (GRU) has been effectively created and used in conjunction with WSTD to forecast the wind speed series. The ensemble WSTDGRU approach uses WSTD to remove unnecessary details from the initial wind speed series data, and GRU to forecast later multi-step wind speed numbers. GRU is very useful for learning features when working in conjunction with WSTD. Ultimately, the test results confirm this methodology’s great performance, good flexibility, and reasonably high accuracy.

De Jesús et al. (2020) offer a new DL ensemble-based wind power prediction technique with very short forecast periods. To forecast wind power, a number of hybrid DL techniques—including CNN, LSTM, and HDNN—are integrated. To arrive at the ultimate wind power estimate, the suggested method uses ensemble averaging to take past wind speed data into account. An actual wind farm in Texas is used to simulate the stated approach and show that it produces a greater degree of very short-term wind power prediction precision.

Although these methods have been developed, several limitations remain many models consider solar or wind power but not both, little use is made of deep feature interactions between weather and energy variables, metaheuristic optimization is seldom combined. Furthermore, the combination of a high-level temporal attention module and spatial feature extraction is not well studied. The proposed SWIFT-Net addresses these issues by proposing a hybrid feature selection approach (HKOBO), combining attention-enhanced LSTM and Inceptionv2-CapsNet blocks and employing ensemble averaging to make robust predictions. This single architecture captures multimodal dependencies well and it performs better than both traditional and new ensemble models in terms of forecasting accuracy.

Problem definition

It is still difficult to forecast daily, weekly, monthly, seasonal, and yearly information for several sites with various observation/data sample sizes while utilizing an identical forecasting method. Data-driven methods offer a chance to enhance solar generation prediction because of the increased granularity of data available (Banik et al., 2020). Power systems with high wind penetration, experience increased security and stability with the invention and implementation of efficient forecasting of wind speed technology. Accurate W&S power forecasting is quite difficult because of the wind’s erratic and unstable characteristics. For this reason, several methods were put forth to raise the forecasting dependability threshold. These days, bidding procedures require estimates at the minute level 1 day ahead of time, which presents an additional challenge for many energy markets. It is crucial for safety to predict wind speed and efficiency of the power system’s functioning (Jalali et al., 2022). Three characteristics of wind speed—randomness, volatility, and unpredictability make reliable wind speed forecasting still difficult. Even though decomposition-based pre-processing techniques have been extensively researched in the past, their use in actual prediction is challenging since the values of the first decomposed segments would be significantly impacted by the recently received data.

Proposed methodology

The suggested approach starts with careful data gathering and pre-processing, filling in any missing values and using normalization to make sure all the features are the same. To reveal underlying links, feature extraction uses statistical measures, time-based indicators, frequency-based features, and metrics based on entropy correlation. Robust characteristics are chosen by hybrid optimization techniques such as Botox and Hybrid Kookaburra optimizations. For effective feature representation, the model architecture consists of an O-MA-LSTM and I2EMv2-E-CapsNet. Forecasts are incorporated using weighted averaging. Splitting data, training models, and adjusting hyperparameters are all part of training. The accuracy and dependability of the SWIFT-Net model, which has been verified against other classifiers, are demonstrated by the results, highlighting its potential to improve energy systems and facilitate sustainable energy transitions. The block diagram of the proposed solar and wind energy prediction model is shown in Figure 1.

Figure 1.

Block diagram of the proposed energy prediction model.

Data collection and pre-processing

Pre-processing data is essential for fixing missing value issues and enhancing data quality. While min-max scaling is employed to normalize the data and ensure that each characteristic has a uniform scale, interpolation is employed to fill in the missing values. Figure 2 shows the pre-processing process in a diagrammatic representation.

Figure 2.

Step by step procedure of the pre-processing phase.

Missing values handling

Two methods of interpolation quadratic and linear are employed in this stage for estimating the missing values (Noor et al., 2014).

Linear interpolation

Making a straight-line connection between two data points is the most basic type of interpolation. Equation (1) depicts the linear interpolation function

{\overset{\leftrightarrow}{F}}_{1} (X) = B_{0} + B_{1} (X - X_{0})

(1)

Let, $X$ is denoted as the independent value, $X_{0}$ is the independent variable’s known value and ${\overset{\leftrightarrow}{F}}_{1} (X)$ is considered a dependent variable value for an independent variable $X$ . Next, equations (2) and (3) are derived from equation (1)

B_{0} = \overset{\leftrightarrow}{F} (X_{0})

(2)

And

B_{1} = \frac{\overset{\leftrightarrow}{F} (X_{1}) - \overset{\leftrightarrow}{F} (X_{0})}{X_{1} - X_{0}}

(3)

Data normalization

To make sure that all of the characteristics are scaled similarly, standardize the data using methods such as min-max scaling.

Min-max normalization

The values of a feature are scaled to lie between 0 and 1 using this method. This is achieved by subtracting the lowest value of the feature from each value and dividing the resulting number by the width of the feature. This data normalization process involves a linear transformation of the original data. The next equation (4) modifies each value after retrieving the minimum and maximum values of the data

N^{'} = \frac{o - \min (a)}{\max (a) - \min (a) (n e w_\max (a) + n e w_\min (a))}

(4)

Let,

a

is denoted as attribute data,

\min (a)

\max (a)

are considered as minimum and maximum absolute values of

a

N^{'}

is denoted as the new value for every data insertion,

o

is denoted as the previous value of every data input,

n e w_\max (a)

, and

n e w_\min (a)

are denoted as new boundary ranges of the max and min value.

Feature extraction

Extraction of pertinent features, such as statistical, time-, frequency-, entropy-, and correlation-based features, are done from the gathered data.

Statistical features

Mean

It calculates the data points’ average values, which are given in equation (5)

M = \frac{1}{n} \sum_{i = 1}^{n} z_{i}

(5)

Standard deviation

Equation (6) is utilized to compute the dispersion or spread of the given collection of values

S D = \sqrt{\frac{1}{n - 1}} \sum_{i = 1} n {(Z_{i} - M)}^{2}

(6)

Minimum and maximum

It measures the highest and lowest values in the collected dataset using equation (7)

M^{-} = \min (z_{1}, z_{2}, . . . . ., z_{n}) M^{+} = \max (z_{1}, z_{2}, . . . . ., z_{n})

(7)

Percentiles of solar irradiance and wind speed

If the value is below the given percentage, the values mean the observation falls and is measured using equation (8)

q^{t h} p e r c e n t i l e = \frac{q}{100} (n + 1)

(8)

Time-based features

Seasonality indicators

Time-based seasonality indicators, like the month, days, and hour of the day, are retrieved, representing the monthly, weekly, and hourly aspects of the data’s seasonality.

Time lags

Retrieve historical values for the wind speed and sun irradiance variable. For instance, the solar radiance value is $S_{t}$ at time $t$ , then the time lag of $n$ hours be $S_{t - n}$ .

Moving averages

It calculates rolling averages over a given period. If the wind power’s moving average over the last $k$ hours using equation (9)

M o_{v} (t) = \frac{1}{k} \sum_{i = t - k + 1}^{t} S_{i}

(9)

Frequency-based features

Wavelet transform is used to retrieve features from various frequency ranges. It is a mathematical transformation that allows frequency analysis by breaking down a signal into different frequency components. Furthermore, wavelet transform is used to extract features from various frequency bands.

Entropy and correlation-based features

Determine possible relationships by calculating the correlation and entropy between different features.

Entropy

Equation (10) is used to determine the dataset’s randomness and variability

E (z) = - \sum_{i = 1}^{n} p (z_{i}) \log_{2} (p (z_{i}))

(10)

Let, $p (z_{i})$ is denoted as the probability of $i^{t h}$ value occurrences.

Correlation

It establishes the two factors’ linear relationship’s intensity and direction. The correlation-based features are extracted using equation (11), which is the Pearson correlation coefficient (PCC) method

ρ (a, b) = \frac{c o v (a, b)}{σ_{a} σ_{b}}

(11)

Let, $c o v (a, b)$ is denoted as the covariance of $a$ and $b$ , $σ_{a}$ , and $σ_{b}$ are considered the standard deviation of $a$ and $b$ . Then the extracted features are updated to the feature selection process to select the best features.

Feature selection

Use a hybrid optimization called HKOBO at this phase to determine which features are most important for model performance. The Kookaburra Optimization Algorithm (KOA) (Dehghani et al., 2023) assesses feature combinations according to prediction accuracy by imitating the Kookaburra bird’s hunting technique. A swarm intelligence method called the Botox Optimization Algorithm (BOA) (Hubálovská et al., 2024) assists in determining the best feature subsets. Hybrid Kookaburra–Botox feature selection strategy aims to improve the performance of the model in terms of efficiency and accuracy by choosing the most relevant features of high-dimensional input data. This strategy combines the global search ability of KOA with local exploitation capability of BOA. KOA, based on the intelligent foraging behavior of kookaburras, is able to explore the various areas of the search space well and avoid premature convergence. Conversely, BOA emulates the muscle-relaxation mechanism of botulinum toxin in biological systems, which allows it to carry out fine-tuning of results locally around good solutions. These two algorithms are hybridized to achieve a balanced trade-off between exploration and exploitation in feature selection. Consequently, the strategy discovers a small subset of features that are informative, minimizing the computational complexity and still retaining essential information that is needed in subsequent learning. The input to the SWIFT-Net ensemble model is then the selected features in order to achieve better predictive performance.

Process of the HKOBO

The kookaburra’s instinctive hunting habits, which involve striking their prey with trees to kill it, are far more fascinating than any scientific explanation. The clever techniques used in the architecture to choose the greatest features are these innate kookaburra habits. Equation (12) is used to represent the KOA population matrix, which is made up of kookaburras combined

X = [\begin{array}{c} \begin{array}{c} X_{1} \\ ⋮ \\ X_{i} \end{array} \\ ⋮ \\ X_{n_{-} n \times m} \end{array}] = {[\begin{array}{c} \begin{array}{c} \begin{array}{c} X_{1, 1} & \dots & X_{1, j} \end{array} \\ \begin{array}{l} ⋮ & ⋱ & ⋮ \end{array} \\ \begin{array}{c} X_{i, 1} & \dots & X_{i, j} \end{array} \end{array} & \begin{array}{c} \dots \\ ⋱ \\ \dots \end{array} & \begin{array}{c} X_{1, m} \\ ⋮ \\ X_{i, m} \end{array} \\ \begin{array}{c} ⋮ & ⋱ & ⋮ \end{array} & ⋱ & ⋮ \\ \begin{array}{c} X_{n, 1} & \dots & X_{n, j} \end{array} & \dots & X_{n, m} \end{array}]}_{n \times m}

(12)

Using equation (13), the starting arbitrary position of the kookaburras during KOA installation is determined

x_{i, k} = {L B}_{k} + q ({U B}_{k} - {L B}_{k})

(13)

Let, $X$ is denoted as the population matrix of the KOA, $X_{i}$ is considered as the candidate solution of the $i^{t h}$ kookaburra, $X_{i, k}$ is considered as decision variables of the search space in $k^{t h}$ dimension, $n$ is denoted as the number of kookaburras, $q$ is denoted as an arbitrary value inside the range (0, 1), $m$ is considered as the number of variables used in decision-making, $U B_{k}$ , and $L B_{k}$ are the upper and lower bounds of the $k^{t h}$ dimension.

Equation (14) states that the set of examined values for the problem’s goal function and is expressed as a vector

f = {[\begin{array}{c} \begin{array}{c} f_{1} \\ ⋮ \\ f_{i} \end{array} \\ ⋮ \\ f_{n} \end{array}]}_{n \times 1} = {[\begin{array}{c} \begin{array}{c} f (X_{1}) \\ ⋮ \\ f (X_{1}) \end{array} \\ ⋮ \\ f (X_{n}) \end{array}]}_{n \times 1}

(14)

Let, $f$ is denoted as a vector representing the assessed objective value and $f$ is denoted as an assessed objective function with $i^{t h}$ kookaburra.

The proposed KOA approach modifies kookaburra locations in the two separate phases of exploration and exploitation through an iterative process based on modeling real kookaburra actions in the wild. Provided next is the procedure for upgrading the KOA population in finding space.

Hunting approach (Exploration)

The way kookaburras choose and attack their prey causes them to move significantly in position. In this strategy, the term “exploration” refers to the method of closely examining the problem-solving space in order to identify the primary optimal area without becoming entangled in the local ideal. This procedure represents the global search.

Each kookaburra imitates its companions’ hunting approach by designating its position in the KOA mechanism as the prey location, since it has a higher goal value. Equation (15) is used to identify the possible prey set for every kookaburra based on the contrast of the function’s goal values

C (p_{i}) = {X_{d} : f_{d} < f_{i}} where i = 1, 2, \dots ., n, and d \in {1, 2, . . . . n}

(15)

Let $C (p_{i})$ be represented as a set of possible kookaburra victims, and $X_{d}$ be regarded as kookaburra with a higher value for the primary purpose than the kookaburra, $f_{d}$ denoting the value of a goal function.

Each kookaburra is thought to choose its target at random and attack it according to the KOA design. Equation (16) is used to identify the kookaburra’s updated position, which simulates the movement of the reptile toward its target in the hunting method

x_{i, k}^{p 1} = x_{i, k} + q . ({s c p}_{i, k} - 1 x_{i, k}) i = 1, 2, 3, . . . . ., n, k = 1, 2, 3, . . ., m

(16)

During this step, update the Botox optimization variables as ${\overset{X}{\leftrightarrow}}_{m e a n}$ and ${\overset{X}{\leftrightarrow}}_{b e s t}$ in the position updating phase to enhance the performance of the feature selection process. In this instance, according to equation (17), if the target function’s result is improved, the new location replaces the linked kookaburra’s previous position

X_{i} = {\begin{cases} X_{m e a n} - X_{i}^{p 1}, f_{i}^{p 1} < f_{i} \\ X_{b e s t} - X_{i} e l s e \end{cases}}

(17)

Let, $X^{p 1}$ is denoted as $i^{t h}$ kookaburra updated the position on the KOA’s exploratory phase, $x_{i, k}^{p 1}$ is denoted as $k^{t h}$ dimension, $q$ is an arbitrary number in the interval (0, 1) with an average distribution, $1$ is considered a random number from the set {1, 2}, $f_{i}^{p 1}$ is considered an objective function value, $s c p_{i, k}$ is denoted as a selection of prey in $k^{t h}$ dimension for $i^{t h}$ kookaburra, $X_{m e a n}$ is denoted as the average population position, and $X_{b e s t}$ is considered as greatest member of the population, $n$ is considered the quantity of kookaburra, and $m$ is denoted as the number of parameters used in decision-making.

Making certain the prey is killed (Exploitation)

After assaulting its prey, kookaburras carry the victim with them and ensure that it dies by repeatedly striking it against trees. This is their second distinguishing trait. The kookaburra eats its meal after crushing it with its powerful claws. Kookaburras exhibit this behavior near their hunting grounds, which causes slight shifts in their location. This procedure, which embodies the idea of exploitation in local search, speaks to the method’s capacity to produce superior results close to discovered solutions and areas of potential. Equation (18) is used to determine an arbitrary location in the KOA architecture, which mimics kookaburra behavior based on where they travel about the hunting region

x_{i, k}^{p 2} = x_{i, k} + (1 - 2 q) . \frac{({U B}_{k} - {L B}_{k})}{t}, i = 1, 2, 3, \dots . ., n, k = 1, 2, 3, \dots, m, and t = 1, 2, \dots ., T

(18)

If every kookaburra’s updated position improves the value of the goal function as determined by equation (19) then it substitutes the prior position

X_{i} = {\begin{cases} X_{m e a n} - X_{i}^{p 2}, f_{i}^{p 2} < f_{i} \\ X_{b e s t} - X_{i} e l s e \end{cases}}

(19)

Let, $X_{i}^{p 2}$ is denoted as $i^{t h}$ kookaburra fresh plan predicated on KOA exploitation, $X_{i, k}^{p 2}$ is denoted as $k^{t h}$ dimension, $f_{i}^{p 2}$ is considered as the value of the objective function, $t$ is denoted as an iteration counter, and $T$ is denoted as a maximum number of iterations. Finally, the developed technique selects the best features using their seeking and hunting behavior of hybrid optimization.

SWIFT-net: DL ensemble model

SWIFT-Net is a deep learning ensemble model, which incorporates the processing of temporal and visual data to increase the accuracy of forecasting. The model is based on two essential elements O-MA-LSTM and I2EMv2-E-CapsNet. The O-MA-LSTM module is used to learn sequential patterns in time-series data with the use of a multi-attention mechanism that selectively highlights the most relevant input features in various time steps. This increases the interpretability and the predictive power of the temporal model. In addition to this, the I2EMv2-E-CapsNet module is specialized in extracting and representing features of images of sky conditions. It integrates the multi-scale feature extraction properties of Inceptionv2 and the powerful spatial representation of Enhanced Capsule Networks (E-CapsNet) which enables it to preserve the hierarchical relationship in the visual input. To obtain the final output, SWIFT-Net uses weighted averaging approach to combine the predictions of the two sub-models, with the weights being computed using validation performance. Such ensemble strategy allows SWIFT-Net to obtain more consistent and generalizable predictions on a wide range of data modalities.

O-MA-LSTM model

To identify sequential data sequences and concentrate on pertinent elements of the input, this model makes use of an LSTM network with an improved MA strategy. The attention mechanism’s primary goal is to draw attention to a particular weight differential. The attention layer increased by the final representation, aids in the strategy performance improvement. By detecting sequential data patterns, the study’s improved MA system using LSTM predicts the W&S power (Zhao et al., 2021).

LSTM model

The memory gate in an LSTM cell is used to update the cell state and remove unnecessary information from the previous instant. The updating method makes use of the output of the previously buried layer as well as the present moment’s input. Several structures have been suggested to enhance the performance of LSTM. The trials’ findings indicate that the attention gate improves how well LSTM models are trained. Therefore, to capture consecutive data trends and concentrate on pertinent features of the input, the study updates the LSTM in the MA approach, shown in Figure 3.

Figure 3.

Architecture of the LSTM model.

Optimized MA

Their research identified the benefits of various attention heads for the queries, values, and keys by using an attention mechanism as a way to connect a variety of key-value pairings and a query to the outcomes. The multi-headed focus layer performs better than single-head attentive by computing the undetectable data by exponentially mapping the context vectors into several subspaces. Weighted numbers are calculated by the proposed framework using queries and their corresponding keys to determine the output. Equations (20) and (21), when applied to single-head attention, yield the attention time-dimension computation for attention weighting

d_{t} = s o f t \max (A_{l} \times {(A_{o} \times Q_{t})}^{g}), A_{l} \in R^{b, 1, z}

(20)

A_{t} = d_{t} \times A_{l}, A_{l} \in R^{b, 1, z}, d_{t} \in R^{b, 1, t}

(21)

Let, $d_{t}$ is considered as temporal dimension’s attention score, $g$ is denoted as a transpose operator, $A_{l}$ is considered as the last time output, $A_{o}$ is denoted as batch size, $A_{o}$ is denoted as all-time output, and $t$ is the number of time intervals, $z$ is the dimension of features, parameter $1$ is denoted as the last time step, $Q_{t}$ is denoted as a parameter matrix, and $A_{t}$ is represented as the output of the attention layer with temporal dimensions. Two kinds of LSTM output are used by the designed method for attention. Because it includes all LSTM output data, the output of every moment is crucial. The last-time phase output was selected because, out of all the time steps, it has the greatest amount of redundant data. We also select the two output kinds for multi-head time-dimension attention computation to compute the queries, keys, and values, as indicated by equations (22), (23), and (24)

X_{i} = Q_{i, x} \times A_{o} + b_{i, x}, X_{i} \in R^{b, t, \frac{z}{n}}, Q_{i, x} \in R^{z, \frac{z}{n}}, b_{i, x} \in R^{\frac{z}{n}}

(22)

Y_{i} = Q_{i, y} \times A_{o} + b_{i, y}, Y_{i} \in R^{b, t, \frac{z}{n}}, Q_{i, y} \in R^{z, \frac{z}{n}}, b_{i, y} \in R^{\frac{z}{n}}

(23)

Z_{i} = Q_{i, z} \times A_{l} + b_{i, z}, Z_{i} \in R^{b, 1, \frac{z}{n}}, Q_{i, z} \in R^{z, \frac{z}{n}}, b_{i, z} \in R^{\frac{z}{n}}

(24)

Let, $X$ , $Y$ , and $Z$ be the value, key, and query, respectively. Furthermore, $b$ is regarded as biased and $n$ is the MA. To enhance the prediction results, the weight and bias of the MA-LSTM are optimized using the HKOBO model. Equations (25) to (27) are utilized for the computation of MA ratings and context vectors

d_{i} = s o f t \max (Z_{i} \times X_{i}^{g}), d_{i} \in R^{b, 1, t}

(25)

C o n_{t e x t (i)} = d_{i} \times Y_{i}, C o n_{t e x t (i)} \in R^{b, 1, \frac{z}{n}}

(26)

c v = c o n c a t ([c o n_{t e x t} (1), c o n_{t e x t} (1), . . ., c o n_{t e x t} (1)]), c v \in R^{b, 1, z}

(27)

Let, $d_{i}$ is denoted as a MA score based on temporal dimensions and $C o n_{t e x t (i)}$ depicts the context variables from every subspace in reduced dimension. Subsequently, the connection layer as a whole receives the context vector. The softmax layer receives the output after that for the ultimate forecast.

I2EMv2 and efficient-CapsNet (I2EMv2-E-CapsNet)

This approach integrates Efficient Capsule Networks for reliable feature representation with Inceptionv2 for effective feature extraction on sky condition photos (if available).

I2EMv2

To accomplish the classification job, the I2EMv2 model (Wu et al., 2023) stacks successive convolution blocks to increase the receptive area and capture deep semantic data. The deep separable convolution feature, which splits the standard convolution into depth-wise and pointwise convolutions and significantly reduces the number of parameter values and calculations while maintaining accuracy, is the main innovation of the I2EMv2 system.

• Inverted inception

The inception module is the basis for the inverted inception layout concept, which expands on it by employing a range of size convolution kernels to produce distinct responsive fields, enhancing the network’s width, and enhancing the model’s susceptibility to forecast W&S power. The inverted inception increases the feature information by using a 1 × 1 convolution opposite dimension grow, extracts features using a variety of convolution kernels, and fully employs the two pooling techniques—maximum pooling and average pooling—to boost feature richness and enhance network expansion capabilities. 1 × 1 convolution reduction in dimension matching is performed after multi-scale feature fusion. After convolution, BN layer batch standardization is applied to remove gradient distribution, prevent network saturation, and speed up convergence.

• Efficient excitation and filtering bottleneck

By using mask vectors to apply weights to characteristic channels, the attention mechanism simulates the link of dependency among crucial information in features and channels, avoids internal data in channels, and enhances the efficacy of semantic features. As opposed to a fully linked layer learning channel weights, the ECANet utilizes 1 × 1 convolution to prevent information loss that results from dimension reduction followed by dimension increase. 1 × 1 convolution has fewer parameters than fully linked layers, making it appropriate for creating lightweight convolutional neural networks. Equation (28) defines the ECA formula

ϖ = \bar{σ} (c 1 d_{d} (a v g_p o o l (Z)))

(28)

Let, $Z$ is denoted as an input feature, $a v g_p o o l$ is denoted as adaptive average pooling, $c 1 d$ is denoted as a convolution in one dimension, $\bar{σ}$ is considered a sigmoid function, and $ϖ$ is denoted as an attention vector. Equation (29) dictates that the one-dimensional convolution’s size needs to be dynamically changed

d = ψ (ς) = {| \frac{\log_{2} (ς)}{φ} + \frac{B}{φ} |}_{o d d}

(29)

Let, $d$ symbolizes the convergence kernel’s size, $ς$ denotes the number of feature channels, and odd stands for the odd quantity of $d$ , $φ$ . Moreover, $d$ , $φ$ , are employed to alter the proportion of feature channels to the total feature channels $ς$ , and the convolution kernel’s size $d$ , $φ$ , is set to 1 and 2. To create EEFB, ECA attention is incorporated into the residual connection using a stride of 1. This lowers the channel weight to eliminate redundant characteristics and suppresses the description of the channel features to accomplish the filtering goal. Additionally, EFFB makes use of max pooling, which determines the maximum number in the local data while keeping significant features and eliminating unnecessary ones. Figure 4 shows the block diagram of I2EMv2 model.

Figure 4.

Block diagram of the I2EMv2 model.

E-CapsNet

E-CapsNet consists of three components: the main capsule layer, the convolution layer, and the self-attention mechanism-based routing (Mazzia et al., 2021). To get ready to create the capsule, the input is converted to a more complex space in the convolution layer using BN and multi-layer convolution. In the second section, depth separable convolution is used to map the features with high dimensions. Comprehensive convolution: the number of input channels and the amount of feature map layers are identical. Each channel is associated with a convolution kernel. Point-by-point convolution is used to convert the generated feature map into channels, with each input channel denoting a filter. By using point-by-point convolution, the depth layer’s output is merged sequentially, and the channel from the previous layer’s depth convolution output is projected into the new channel space. The self-attention method is used in the last phase to route the first capsule to the broad target object. It is possible to obtain each layer’s trained feature distribution using equations (30), (31), and (32), respectively

χ_{l} = λ_{l} {\hat{z}}_{l} + η_{l}

(30)

λ_{l} = \sqrt{v a r [z_{l}]}

(31)

η_{l} = \sqrt{E (z_{l})}

(32)

Let,

z_{l}

is a l-layer normalization is applied to the input,

λ

and

η

are two parameters that are taught and introduced alongside the parameters of the framework. During the convolution process, to lower the amount of

λ

and

η

parameters created throughout the transformation and rebuilding phase, the entire feature map is handled as a neuron, and the batch standardized layer adopts a similar weight-sharing technique. Because of this, a batch normalization phase is positioned in between each of the Efficient-CapsNet’s 4 convolution levels to ensure that the data is distributed equally among them.

The routing portion of the self-attention system is comparable to a fully connected network. The input to the top capsule is the weighted sum of all the “forecasting matrix” from the bottom capsule, and every Wind and power category is represented by an output capsule. The network’s squeezing f unction is distinct from CapsNet’s. An implementation of the squeeze function variation described in equation (33), aimed at preventing the network from becoming convergent due to an initial vector length of 0

S_{q} (s_{l}^{n}) = (1 - \frac{1}{e^{‖ s_{l}^{n} ‖}}) \frac{s_{l}^{n}}{‖ s_{l}^{n} ‖}

(33)

Let, $s_{l}^{n}$ is denoted as a single capsule with individual entries. The requisite two qualities are satisfied by the capsule-wise squash coefficient, which also boosts the gradient throughout the training phase because it is considerably more sensitive to minor changes near zero. Every category amount in the multi-classification challenge corresponds to the number of capsules produced. Each capsule’s length indicates both the likelihood that the target thing exists and the presence of all of its properties. The likelihood that the target thing exists increases with the length of the capsule and vice versa.

Final forecasting

Initially, generate prediction results of both techniques O-MA-LSTM and I2EMv2-E-CapsNet, and normalize the prediction values into the mean of 0 and standard deviation of 1. Apply weight to both models based on the performance. Assign higher weights to the model that historically performs better or has more credibility. Finally, calculate the weighted average by multiplying both prediction results based on the sum and weight to form a combined forecasting. The calculation of the weighted average technique is detailed in equation (34)

F_{c o m b i n e} = W_{1} * F_{\mod e l 1} + W_{2} * F_{\mod e l 2}

(34)

Let, $W_{1}$ and $W_{2}$ are denoted as assigned weights of both models, $F_{\mod e l 1}$ , and $F_{\mod e l 2}$ are forecasts generated by the O-MA-LSTM and I2EMv2-E-CapsNet models.

Results

This section compares the results of the suggested model with those of other methods. We use the Python platform for the implementation. Two versions of the model must be created in order to train it on a single subgroup and then assess its ability to generalize. Thirty percent goes toward testing, while the remaining 70 percent is used for training. Utilize measures such as Explained Variance Score (EVS), Mean Squared Error (MSE), Mean Percentage Error (MPL), Mean Squared Logarithmic Error (MSLE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Root Mean Squared Error (RMSE) to assess the performance of the ensemble model.

Dataset description

The SWIFT-Net model suggested is trained and validated on the publicly accessible Renewable Energy and Weather Conditions dataset provided by Kaggle (https://www.kaggle.com/datasets/samanemami/renewable-energy-and-weather-conditions/code). The data set consists of about 42,000 records measured at an hourly frequency with a time span between January 2016 and December 2020. It has 17 features altogether, including various meteorological and energy related variables, including temperature, pressure, humidity, wind speed, precipitation (rain and snow), cloud cover, solar radiation (GHI), and energy consumption delta (Energy delta (Wh)). There are also other attributes like availability of sunlight (isSun), time of sunlight, length of day, and SunlightTime/dayLength, as well as weather_type, hour, and month, which assist in temporal and categorical modeling. Preprocessing entailed missing value imputation through linear interpolation, continuous feature normalization with the Min–Max method, and categorical variables one-hot encoding. The data was divided into training and testing data with the ratio of 80:20, which was chosen due to the hyperparameter tuning to maximize the performance and minimize the overfitting. Despite the completeness of the data, it seems to be geographically limited to a particular area in Europe, that be a limitation when it comes to generalizing the results to other climatic regions.

Overall comparison by varying the train data split

The results on comparison of the performance of the proposed SWIFT-Net model with other models such as KNN (22), ANN + LSTM (23), GRU (27), and EDL (28)) on the basis of various evaluation metrics like EVS, MAE, MAPE, MPL, MSE, MSLE, and RMSE) reveal that the proposed SWIFT-Net model outperforms other models in all evaluation metrics in both training-validation splits (70% and 80%). In particular, SWIFT-Net has the highest explained variance score (EVS), which means that it is better at explaining variance in the data. At the same time, it shows the least values of errors among all the other measures, such as MAE, MAPE, and RMSE, which demonstrates its accuracy and strength. The lower prediction loss (MPL) and smaller values of MSE, MSLE also prove the effectiveness of the model in reducing both small and large errors. These findings confirm the high generalization power and better prediction accuracy of SWIFT-Net to process the complex and multimodal renewable energy data. Figure 5 displays the comparison of various metrics with the proposed method.

Figure 5.

Comparison of various metrics with the proposed method.

An ablation analysis is conducted to evaluate the contribution of the HKOBO hybrid feature optimization strategy. Table 1 shows a comparative evaluation of the proposed SWIFT-Net model under different feature optimization scenarios: with HKOBO, without HKOBO, with only KO, and with only BO. The results show that HKOBO achieves the lowest MSE value of 0.0037, outperforming KO (0.0045), BO (0.0041), and the model without feature optimization (0.005). This indicates that the hybridization of KO and BO significantly enhances the selection of relevant features, leading to more accurate forecasting.

Table 1.

MSE comparison showing improved performance with HKOBO over KO, BO, and no optimization.

Metric	With HKOBO	Without HKOBO	With KO	With BO
MSE	0.0037	0.005	0.0045	0.0041

The comparative analysis of the results of the O-MA-LSTM, I2EMv2-E-CapsNet, and proposed SWIFT-Net model based on the 70:30 and 80:20 data split is conducted as shown in Table 2. SWIFT-Net, which combines both component models, is revealed to be better in all the metrics of evaluation. In particular, it has the greatest EVS and the lowest points with respect to MSE, MAE, and MSLE in both data splits. This means that the use of the ensemble technique of SWIFT-Net is effective in capturing the complex temporal and spatial behaviors, which makes the renewable energy forecasting experiences more accurate and robust than that of the combined parts in itself.

Table 2.

Comparison of O-MA-LSTM, I2EMv2-E-CapsNet, and SWIFT-Net under different data splits. SWIFT-Net shows the best performance across all metrics.

Train data split	Metric	With O-MA-LSTM	With I2EMv2-E-CapsNet	Proposed-SWIFT-Net
70:30	EVS	0.85	0.91	0.9567
	MSE	0.0109	0.055	0.0037
	MAE	0.0234	0.0143	0.0084
	MSLE	0.0042	0.0031	0.0015
80:20	EVS	0.935	0.9421	0.9757
	MSE	0.0062	0.0054	0.002
	MAE	0.0141	0.0107	0.0037
	MSLE	0.0024	0.0029	0.0009

Table 3 reports paired statistical significance tests between the suggested SWIFT-Net model and four baseline models concerning MSE and RMSE. In all comparisons, SWIFT-Net displays considerably lower error metrics as indicated by the negative mean differences. The p-values are all less than 0.05, and the 95% confidence intervals exclude zero, verifying that the gains are statistically significant. This enhances the robustness and validity of the superior performance of the proposed model.

Table 3.

Statistical significance testing of SWIFT-Net vs. existing models (MSE & RMSE).

Compared model	Metric	Mean difference	95% confidence interval	p-value	Significance
KNN (Ahmad et al., 2021)	MSE	−0.0072	(−0.0081, −0.0063)	0.0004	Significant
ANN + LSTM (Khan et al., 2022)	MSE	−0.0015	(−0.0022, −0.0008)	0.0012	Significant
GRU (Peng et al., 2020)	MSE	−0.0033	(−0.0041, −0.0026)	0.0006	Significant
EDL (De Jesús et al., 2020)	MSE	−0.0121	(−0.0143, −0.0101)	0	Significant
KNN (Ahmad et al., 2021)	RMSE	−0.0323	(−0.0360, −0.0287)	0.0001	Significant
ANN + LSTM (Khan et al., 2022)	RMSE	−0.0109	(−0.0143, −0.0075)	0.001	Significant
GRU (Peng et al., 2020)	RMSE	−0.0191	(−0.0224, −0.0158)	0.0007	Significant
EDL (De Jesús et al., 2020)	RMSE	−0.0468	(−0.0511, −0.0425)	0	Significant

Discussion

The high performance of the proposed SWIFT-Net model can be explained by the fact that it combines the hybrid feature optimization (HKOBO), deep time modeling with the attention-enhanced LSTM, and advanced spatial representation with the Inceptionv2 and Capsule Networks. The hybrid optimization assists in the identification of highly relevant features, which minimizes noise and dimensionality. In the meantime, the temporal attention process enables the model to concentrate on the important time durations, which enhances sequence learning. The ensemble design also stabilizes the predictions through the exploitation of the complementary power of the two branches of the model. SWIFT-Net outperforms the baseline models in all metrics of evaluation; this is because the model is capable of capturing complex dependencies in multimodal data as compared to the baseline models. Nevertheless, this improved performance is at the expense of greater computational complexity and more time-consuming training. Also, the model deep architecture can only be used with large datasets to avoid overfitting, and additional research is required to enhance its interpretability. These limitations notwithstanding, SWIFT-Net is a good framework to forecast renewable energy, and the trade-off between performance and model complexity is reasonable. The evaluation is provided using several metrics, such as MSE, RMSE, and MAE, as they measure various properties of errors. It is not guaranteed that the proposed model outperforms in each of the metrics individually, but it consistently performs well and reliably in all of them, which means that it generalizes well. Small variations in scores indicate trade-offs between the sensitivity of the metric and do not compromise the overall performance of the approach.

Conclusion

In conclusion, the paper introduces a comprehensive methodology for forecasting solar and wind power outputs, crucial for efficient energy conversion and system optimization. Through meticulous data handling, feature extraction, and the use of hybrid optimization algorithms like HKOBO, we identify key factors essential for accurate predictions. The proposed SWIFT-Net ensemble model, combining O-MA-LSTM and I2EMv2-E-CapsNet, demonstrates promising results in capturing complex data relationships. By validating the proposed model against established classifiers using MSE, RMSE, and MAE metrics, it ensures the reliability and continual refinement. This approach not only reduces reliance on costly storage solutions but also contributes to the efficient utilization of renewable energy resources, facilitating a sustainable energy transition. Overall, the SWIFT-Net model represents a significant step forward in solar and wind power forecasting, offering a robust framework for optimizing energy systems and supporting a more sustainable energy future.

Footnotes

Acknowledgments

The authors would like to thank the Puducherry Technological University for supporting this work.

ORCID iD

Tharwin Kumar Ravikumar

Author’s contributions

Mr R. Tharwin Kumar, He performed the conceptualization, Methodology, Data collection and writing the study. Dr C. Christober Asir Rajan, He analysis the dataset and conceptualization in the study.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

All the data is collected from the simulation reports of the software and tools used by the authors. Data will be made available upon reasonable request. *

References

Ahmad

Manzoor

Zhang

(2021) Forecasting high penetration of solar and wind power in the smart grid environment using robust ensemble learning approach for large-dimensional data. Sustainable Cities and Society 75: 103269.

AlKandari

Ahmad

(2020) Solar Power Generation Forecasting Using Ensemble Approach Based on Deep Learning and Statistical Methods. Applied Computing and Informatics.

Banik

Das

Ray

, et al. (2020) Wind power generation probabilistic modeling using ensemble learning techniques. Materials Today: Proceedings 26: 2157–2162.

Cannizzaro

Aliberti

Bottaccioli

, et al. (2021) Solar radiation forecasting based on convolutional neural network and ensemble learning. Expert Systems with Applications 181: 115167.

Carneiro

Rocha

Carvalho

, et al. (2022) Ridge regression ensemble of machine learning models applied to solar and wind forecasting in Brazil and Spain. Applied Energy 314: 118936.

Chakraborty

Mondal

Barua

, et al. (2023) Computational solar energy–ensemble learning methods for prediction of solar power generation based on meteorological parameters in Eastern India. Renewable Energy Focus 44: 277–294.

de Jesús

DAR

Mandal

, et al. (2020) Deep learning ensemble based new approach for very short-term wind power forecasting. In: 2020 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 1–5.

Dehghani

Montazeri

Bektemyssova

, et al. (2023) Kookaburra optimization algorithm: a new bio-inspired metaheuristic algorithm for solving optimization problems. Biomimetics 8(6): 470.

Devaraj

Madurai Elavarasan

Shafiullah

, et al. (2021) A holistic review on energy forecasting using big data and deep learning models. International Journal of Energy Research 45(9): 13489–13530.

10.

Guermoui

Benkaciali

Gairaa

, et al. (2022) A novel ensemble learning approach for hourly global solar radiation forecasting. Neural Computing & Applications 34: 1–23.

11.

Hubálovská

Hubálovský

Trojovský

(2024) Botox optimization algorithm: a new human-based metaheuristic algorithm for solving optimization problems. Biomimetics 9(3): 137.

12.

Ibrahim

Mirjalili

El-Said

, et al. (2021) Wind speed ensemble forecasting based on deep learning using adaptive dynamic optimization algorithm. IEEE Access 9: 125787–125804.

13.

Jalali

SMJ

Osório

Ahmadian

, et al. (2021) New hybrid deep neural architectural search-based ensemble reinforcement learning strategy for wind power forecasting. IEEE Transactions on Industry Applications 58(1): 15–27.

14.

Jalali

SMJ

Ahmadian

Nakisa

, et al. (2022) Solar irradiance forecasting using a novel hybrid deep ensemble reinforcement learning algorithm. Sustainable Energy, Grids and Networks 32: 100903.

15.

Khan

Walker

Zeiler

(2022) Improved solar photovoltaic energy generation forecast using deep learning-based ensemble stacking approach. Energy 240: 122812.

16.

Kumari

Toshniwal

(2021) Extreme gradient boosting and deep neural network based ensemble learning approach to forecast hourly solar irradiance. Journal of Cleaner Production 279: 123285.

17.

Lee

Wang

Harrou

, et al. (2020) Wind power prediction using ensemble learning-based models. IEEE Access 8: 61517.

18.

Guo

, et al. (2020) Meta learning-based hybrid ensemble approach for short-term wind speed forecasting. IEEE Access 8: 172859–172868.

19.

Malhan

Mittal

(2022) A novel ensemble model for long-term forecasting of wind and hydro power generation. Energy Conversion and Management 251: 114983.

20.

Marndi

Patra

Gouda

(2020) Short-term forecasting of wind speed using time division ensemble of hierarchical deep neural networks. Bulletin of Atmospheric Science and Technology 1(1): 91–108.

21.

Massaoudi

Abu-Rub

Refaat

, et al. (2021) Enhanced deep belief network based on ensemble learning and tree-structured of Parzen estimators: an optimal photovoltaic power forecasting method. IEEE Access 9: 150330–150344.

22.

Mazzia

Salvetti

Chiaberge

(2021) Efficient-capsnet: capsule network with self-attention routing. Scientific Reports 11(1): 14634.

23.

Mora

Cifuentes

Marulanda

(2021) Short-term forecasting of wind energy: a comparison of deep learning frameworks. Energies 14(23): 7943.

24.

Noor

Yahaya

Ramli

, et al. (2014) Filling missing data using interpolation methods: study on the effect of fitting distribution. Key Engineering Materials 594: 889–895.

25.

Peng

, et al. (2020) A novel deep learning ensemble model with data denoising for short-term wind speed forecasting. Energy Conversion and Management 207: 112524.

26.

Ribeiro

MHDM

da Silva

Moreno

, et al. (2022) Efficient bootstrap stacking ensemble learning model applied to wind power generation forecasting. International Journal of Electrical Power & Energy Systems 136: 107712.

27.

Rosa de Jesus

Mandal

, et al. (2020) Deep learning ensemble based new approach for very short-term wind power forecasting. In: 2020 IEEE Power & Energy Society General Meeting (PESGM). IEEE.

28.

Singla

Duhan

Saroha

(2022) An ensemble method to forecast 24-h ahead solar irradiance using wavelet decomposition and BiLSTM deep learning network. Earth Science Informatics 15(1): 291–306.

29.

Suárez-Cetrulo

Burnham-King

Haughton

, et al. (2022) Wind power forecasting using ensemble learning for day-ahead energy trading. Renewable Energy 191: 685–698.

30.

Tarek

Shams

Elshewey

, et al. (2023) Wind power prediction based on machine learning and deep learning models. Computers, Materials & Continua 75(1): 715–732.

31.

Wang

(2021) An ensemble neural network based on variational mode decomposition and an improved sparrow search algorithm for wind and solar power forecasting. IEEE Access 9: 166709–166719.

32.

Luo

(2023) Recognition of pear leaf disease under complex background based on DBPNet and modified mobilenetV2. IET Image Processing 17(10): 3055–3067.

33.

Xing

(2023) Multi-modal multi-step wind power forecasting based on stacking deep learning model. Renewable Energy 215: 118991.

34.

Zhao

Liang

, et al. (2021) Multi-head attention-based long short-term memory for depression detection from speech. Frontiers in Neurorobotics 15: 684037.