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29 pages, 2409 KiB  
Article
Enhancing Hierarchical Sales Forecasting with Promotional Data: A Comparative Study Using ARIMA and Deep Neural Networks
by Mariana Teixeira, José Manuel Oliveira and Patrícia Ramos
Mach. Learn. Knowl. Extr. 2024, 6(4), 2659-2687; https://doi.org/10.3390/make6040128 - 19 Nov 2024
Viewed by 356
Abstract
Retailers depend on accurate sales forecasts to effectively plan operations and manage supply chains. These forecasts are needed across various levels of aggregation, making hierarchical forecasting methods essential for the retail industry. As competition intensifies, the use of promotions has become a widespread [...] Read more.
Retailers depend on accurate sales forecasts to effectively plan operations and manage supply chains. These forecasts are needed across various levels of aggregation, making hierarchical forecasting methods essential for the retail industry. As competition intensifies, the use of promotions has become a widespread strategy, significantly impacting consumer purchasing behavior. This study seeks to improve forecast accuracy by incorporating promotional data into hierarchical forecasting models. Using a sales dataset from a major Portuguese retailer, base forecasts are generated for different hierarchical levels using ARIMA models and Multi-Layer Perceptron (MLP) neural networks. Reconciliation methods including bottom-up, top-down, and optimal reconciliation with OLS and WLS (struct) estimators are employed. The results show that MLPs outperform ARIMA models for forecast horizons longer than one day. While the addition of regressors enhances ARIMA’s accuracy, it does not yield similar improvements for MLP. MLPs present a compelling balance of simplicity and efficiency, outperforming ARIMA in flexibility while offering faster training times and lower computational demands compared to more complex deep learning models, making them highly suitable for practical retail forecasting applications. Full article
(This article belongs to the Section Data)
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<p>A three-level hierarchical structure.</p>
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<p>Hierarchical structure of Pingo Doce sales data by SKU, illustrating three levels: total, regional (A, B), and store-level sales.</p>
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<p>Hierarchical daily sales data for a representative SKU from 2012 to 2015, illustrating total, regional, and store-level sales with seasonal patterns. Different colors represent distinct aggregation levels and the individual time series within each level.</p>
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<p>Rolling-window approach for forecasting with 120 rolling steps. The training set is represented by dark-red bars and the testing set by light-red bars. At each step, the training set is incrementally extended by one day, producing forecasts for a 7-day horizon.</p>
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<p>Huber loss (blue) and mean absolute error (MAE, red) during MLP training for a typical SKU, comparing the standard MLP (<b>left</b>) and an MLP with regressors (<b>right</b>).</p>
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<p>Actual and forecasted sales for a representative SKU, comparing ARIMA, ARIMAX, MLP, and MLP with regressors models (red: actual; blue: forecast).</p>
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31 pages, 10786 KiB  
Article
Forecasting Visitor Arrivals at Tourist Attractions: A Time Series Framework with the N-BEATS for Sustainable Tourism
by Ke Xu, Junli Zhang, Junhao Huang, Hongbo Tan, Xiuli Jing and Tianxiang Zheng
Sustainability 2024, 16(18), 8227; https://doi.org/10.3390/su16188227 - 21 Sep 2024
Viewed by 1702
Abstract
Contemporary techniques built on deep learning technologies enable precise forecasting of tourism demand, particularly for the relaunch of sustainable tourism following COVID-19. We developed a novel framework to forecast visitor arrivals at tourist attractions in the post-COVID-19 period. To this end, a time-based [...] Read more.
Contemporary techniques built on deep learning technologies enable precise forecasting of tourism demand, particularly for the relaunch of sustainable tourism following COVID-19. We developed a novel framework to forecast visitor arrivals at tourist attractions in the post-COVID-19 period. To this end, a time-based data partitioning module was first pioneered. The N-BEATS algorithm with multi-step strategies was then imported to build a forecasting system on historical data. We imported visualization of curve fitting, metrics of error measures, wide-range forecasting horizons, different strategies for data segmentations, and the Diebold–Mariano test to verify the robustness of the proposed model. The system was empirically validated using 1604 daily visitor volumes of Jiuzhaigou from 1 January 2020 to 13 May 2024 and 1459 observations of Mount Siguniang from 1 October 2020 to 18 May 2024. The proposed model achieved an average MAPE of 39.60% and MAAPE of 0.32, lower than the five baseline models of SVR, LSTM, ARIMA, SARIMA, and TFT. The results show that the proposed model can accurately capture sudden variations or irregular changes in the observations. The findings highlight the importance of improving destination management and anticipatory planning using the latest time series approaches to achieve sustainable tourist visitation forecasts. Full article
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<p>The designed experimental framework.</p>
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<p>Daily tourist arrivals of Jiuzhaigou. The dotted lines in different colors indicate the four splitting strategies of the training (including validation) and test datasets (hereinafter the same).</p>
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<p>Daily tourist arrivals of Mount Siguniang.</p>
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<p>Fitting curves of real and forecasted tourist volume in Jiuzhaigou. (<b>a</b>) a composite graph of all methods. (<b>b</b>) the fitting curve by use of SVR. (<b>c</b>) the fitting curve by use of LSTM. (<b>d</b>) the fitting curve by use of ARIMA. (<b>e</b>) the fitting curve by use of SARIMA. (<b>f</b>) the fitting curve by use of TFT. (<b>g</b>) the fitting curve by use of N-BEATS.</p>
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<p>Scatters of real and forecasted tourist volume in Jiuzhaigou. Please note that the x-axes of (<b>a</b>,<b>d</b>–<b>f</b>) were truncated for aesthetic purposes. (<b>a</b>) a composite graph of all methods. (<b>b</b>) the scatter points and the best-fit line by use of SVR. (<b>c</b>) the scatter points and the best-fit line by use of LSTM. (<b>d</b>) the scatter points and the best-fit line by use of ARIMA. (<b>e</b>) the scatter points and the best-fit line by use of SARIMA. (<b>f</b>) the scatter points and the best-fit line by use of TFT. (<b>g</b>) the scatter points and the best-fit line by use of N-BEATS.</p>
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<p>Fitting curves of real and forecasted tourist volume in Mount Siguniang. (<b>a</b>) a composite graph of all methods. (<b>b</b>) the fitting curve by use of SVR. (<b>c</b>) the fitting curve by use of LSTM. (<b>d</b>) the fitting curve by use of ARIMA. (<b>e</b>) the fitting curve by use of SARIMA. (<b>f</b>) the fitting curve by use of TFT. (<b>g</b>) the fitting curve by use of N-BEATS.</p>
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<p>Scatters of real and forecasted tourist volume in Mount Siguniang. Please note that the x-axes of (<b>a</b>,<b>c</b>,<b>e</b>) were truncated for aesthetic purposes. (<b>a</b>) a composite graph of all methods. (<b>b</b>) the scatter points and the best-fit line by use of SVR. (<b>c</b>) the scatter points and the best-fit line by use of LSTM. (<b>d</b>) the scatter points and the best-fit line by use of ARIMA. (<b>e</b>) the scatter points and the best-fit line by use of SARIMA. (<b>f</b>) the scatter points and the best-fit line by use of TFT. (<b>g</b>) the scatter points and the best-fit line by use of N-BEATS.</p>
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<p>Line charts showing the rankings of the MAPE, RMSE, and MAAPE performance of different models across different data partitions and forecast horizons in Jiuzhaigou and Mount Siguniang. (<b>a</b>) the MAPE performance of different models in Jiuzhaigou. (<b>b</b>) the RMSE performance of different models in Jiuzhaigou. (<b>c</b>) the MAAPE performance of different models in Jiuzhaigou. (<b>d</b>) the MAPE performance of different models in Mount Siguniang. (<b>e</b>) the RMSE performance of different models in Mount Siguniang. (<b>f</b>) the MAAPE performance of different models in Mount Siguniang.</p>
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<p>Line charts showing the rankings of the MAPE, RMSE, and MAAPE performance of different models across different data partitions and forecast horizons in Jiuzhaigou and Mount Siguniang. (<b>a</b>) the MAPE performance of different models in Jiuzhaigou. (<b>b</b>) the RMSE performance of different models in Jiuzhaigou. (<b>c</b>) the MAAPE performance of different models in Jiuzhaigou. (<b>d</b>) the MAPE performance of different models in Mount Siguniang. (<b>e</b>) the RMSE performance of different models in Mount Siguniang. (<b>f</b>) the MAAPE performance of different models in Mount Siguniang.</p>
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21 pages, 15716 KiB  
Article
A Novel Wind Power Prediction Model That Considers Multi-Scale Variable Relationships and Temporal Dependencies
by Zhanyang Xu, Hong Zhao, Chengxi Xu, Hongyan Shi, Jian Xu and Zhe Wang
Electronics 2024, 13(18), 3710; https://doi.org/10.3390/electronics13183710 - 19 Sep 2024
Viewed by 1046
Abstract
Wind power forecasting is a critical technology for promoting the effective integration of wind energy. To enhance the accuracy of wind power predictions, this paper introduces a novel wind power prediction model that considers the evolving relationships of multi-scale variables and temporal dependencies. [...] Read more.
Wind power forecasting is a critical technology for promoting the effective integration of wind energy. To enhance the accuracy of wind power predictions, this paper introduces a novel wind power prediction model that considers the evolving relationships of multi-scale variables and temporal dependencies. In this paper, a multi-scale frequency decomposition module is designed to split the raw data into high-frequency and low-frequency parts. Subsequently, features are extracted from the high-frequency information using a multi-scale temporal graph neural network combined with an adaptive graph learning module and from the low-frequency data using an improved bidirectional temporal network. Finally, the features are integrated through a cross-attention mechanism. To validate the effectiveness of the proposed model, extensive comprehensive experiments were conducted using a wind power dataset provided by the State Grid. The experimental results indicate that the MSE of the model proposed in this paper has decreased by an average of 7.1% compared to the state-of-the-art model and by 48.9% compared to the conventional model. Moreover, the improvement in model performance becomes more pronounced as the prediction horizon increases. Full article
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<p>Wind turbine workflow.</p>
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<p>The overall framework of the proposed model.</p>
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<p>Framework diagram of MSF-Decomp module.</p>
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<p>The primary structure of MST-GCN.</p>
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<p>Overall architecture diagram of Bi-TGCN.</p>
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<p>Bidirectional architecture diagram of three-layer TCN.</p>
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<p>Data distribution of power and wind speed.</p>
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<p>Scatter plot of power versus wind speed and direction.</p>
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<p>Correlation analysis results.</p>
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<p>Prediction accuracy comparison.</p>
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<p>Visualization of forecast results in wind farm site 1. The section within the red circle in <a href="#electronics-13-03710-f011" class="html-fig">Figure 11</a>a is magnified and displayed in <a href="#electronics-13-03710-f011" class="html-fig">Figure 11</a>b.</p>
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<p>PCC scatter plot of predicted and true values in wind farm site 1.</p>
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<p>Visualization of forecast results in wind farm site 4. The section within the red circle in <a href="#electronics-13-03710-f013" class="html-fig">Figure 13</a>a is magnified and displayed in <a href="#electronics-13-03710-f013" class="html-fig">Figure 13</a>b.</p>
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<p>Voilin plots of predicted and true values in wind farm site 4.</p>
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21 pages, 6438 KiB  
Article
Weighted Averages and Polynomial Interpolation for PM2.5 Time Series Forecasting
by Anibal Flores, Hugo Tito-Chura, Victor Yana-Mamani, Charles Rosado-Chavez and Alejandro Ecos-Espino
Computers 2024, 13(9), 238; https://doi.org/10.3390/computers13090238 - 18 Sep 2024
Viewed by 537
Abstract
This article describes a novel method for the multi-step forecasting of PM2.5 time series based on weighted averages and polynomial interpolation. Multi-step prediction models enable decision makers to build an understanding of longer future terms than the one-step-ahead prediction models, allowing for more [...] Read more.
This article describes a novel method for the multi-step forecasting of PM2.5 time series based on weighted averages and polynomial interpolation. Multi-step prediction models enable decision makers to build an understanding of longer future terms than the one-step-ahead prediction models, allowing for more timely decision-making. As the cases for this study, hourly data from three environmental monitoring stations from Ilo City in Southern Peru were selected. The results show average RMSEs of between 1.60 and 9.40 ug/m3 and average MAPEs of between 17.69% and 28.91%. Comparing the results with those derived using the presently implemented benchmark models (such as LSTM, BiLSTM, GRU, BiGRU, and LSTM-ATT) in different prediction horizons, in the majority of environmental monitoring stations, the proposed model outperformed them by between 2.40% and 17.49% in terms of the average MAPE derived. It is concluded that the proposed model constitutes a good alternative for multi-step PM2.5 time series forecasting, presenting similar and superior results to the benchmark models. Aside from the good results, one of the main advantages of the proposed model is that it requires fewer data in comparison with the benchmark models. Full article
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<p>The 20-day correlation of Pacocha station.</p>
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<p>The 20-day correlation of Bolognesi station.</p>
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<p>The 20-day correlation of Pardo station.</p>
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<p>How matrix <span class="html-italic">M</span> is used to make predictions.</p>
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<p>The 24 predicted hours with the weighted average equation.</p>
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<p>Multi-step predictions of WA and WA + PI.</p>
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<p>The WA + PI algorithm.</p>
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<p>Web application for PM2.5 forecasting.</p>
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<p>Architectures of the benchmark models: (<b>a</b>) LSTM, (<b>b</b>) GRU, (<b>c</b>) BiLSTM, (<b>d</b>) BiGRU, and (<b>e</b>) LSTM−ATT.</p>
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<p>The 72 predicted hours for Pacocha station.</p>
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<p>The 72 predicted hours for Bolognesi station.</p>
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<p>The 72 predicted hours for Pardo station.</p>
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24 pages, 9114 KiB  
Article
Real-Time Prediction of Multi-Degree-of-Freedom Ship Motion and Resting Periods Using LSTM Networks
by Zhanyang Chen, Xingyun Liu, Xiao Ji and Hongbin Gui
J. Mar. Sci. Eng. 2024, 12(9), 1591; https://doi.org/10.3390/jmse12091591 - 9 Sep 2024
Cited by 1 | Viewed by 562
Abstract
This study presents a novel real-time prediction technique for multi-degree-of-freedom ship motion and resting periods utilizing Long Short-Term Memory (LSTM) networks. The primary objective is to enhance the safety and efficiency of shipborne helicopter landings by accurately predicting heave, pitch, and roll data [...] Read more.
This study presents a novel real-time prediction technique for multi-degree-of-freedom ship motion and resting periods utilizing Long Short-Term Memory (LSTM) networks. The primary objective is to enhance the safety and efficiency of shipborne helicopter landings by accurately predicting heave, pitch, and roll data over an 8 s forecast horizon. The proposed method utilizes the LSTM network’s capability to model complex nonlinear time series while employing the User Datagram Protocol (UDP) to ensure efficient data transmission. The model’s performance was validated using real-world ship motion data collected across various sea states, achieving a maximum prediction error of less than 15%. The findings indicate that the LSTM-based model provides reliable predictions of ship resting periods, which are crucial for safe helicopter operations in adverse sea conditions. This method’s capability to provide real-time predictions with minimal computational overhead highlights its potential for broader applications in marine engineering. Future research should explore integrating multi-model fusion techniques to enhance the model’s adaptability to rapidly changing sea conditions and improve the prediction accuracy. Full article
(This article belongs to the Special Issue Advances in Marine Engineering Hydrodynamics)
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<p>Geodetic coordinate system and accompanying ship coordinate system.</p>
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<p>Schematic diagram of direct multi-step output prediction.</p>
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<p>LSTM neurons.</p>
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<p>Model training process.</p>
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<p>The actual engineering scenario simulated in this paper.</p>
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<p>Real-time online prediction.</p>
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<p>Numerical offset in normalization.</p>
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<p>Prediction set normalization.</p>
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<p>Results display and comparison.</p>
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<p>Condition 1 data comparison.</p>
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<p>Condition 2 data comparison.</p>
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<p>Condition 3 data comparison.</p>
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<p>Condition 4 data comparison.</p>
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<p>Condition 5 data comparison.</p>
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<p>Condition 6 data comparison.</p>
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<p>Condition 7 data comparison.</p>
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<p>Condition 8 data comparison.</p>
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<p>Condition 9 data comparison.</p>
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<p>Condition 10 data comparison.</p>
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4 pages, 558 KiB  
Proceeding Paper
Cascade Machine Learning Approach Applied to Short-Term Medium Horizon Demand Forecasting
by Bruno Brentan, Ariele Zanfei, Martin Oberascher, Robert Sitzenfrei, Joaquin Izquierdo and Andrea Menapace
Eng. Proc. 2024, 69(1), 42; https://doi.org/10.3390/engproc2024069042 - 3 Sep 2024
Viewed by 280
Abstract
This work proposes a cascade model incorporating Long–Short-Term Memory (LSTM) and Multi-Layer Perceptron (MLP), which offers a more reliable model to forecast short-term (hourly) and medium horizon (week) water demand. The MLP model integrates the previously forecasted demand with exogenous variables, functioning as [...] Read more.
This work proposes a cascade model incorporating Long–Short-Term Memory (LSTM) and Multi-Layer Perceptron (MLP), which offers a more reliable model to forecast short-term (hourly) and medium horizon (week) water demand. The MLP model integrates the previously forecasted demand with exogenous variables, functioning as a filter to enhance the accuracy of the LSTM estimation. The LSTM model estimates, utilizing a univariate approach, the hourly forecasting of water demand for the entire available dataset and the minimum night flow. The algorithm considers various time series sizes for each DMA and predicts the water demand values for each hour throughout the week. Having forecasted all timesteps with the LSTM, a virtual online process can be implemented to enhance forecasting quality. Full article
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<p>Results of the proposed methodology in weekly water demand forecasting on the 10 DMAs.</p>
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18 pages, 4812 KiB  
Article
On the Exploration of Temporal Fusion Transformers for Anomaly Detection with Multivariate Aviation Time-Series Data
by Bulent Ayhan, Erik P. Vargo and Huang Tang
Aerospace 2024, 11(8), 646; https://doi.org/10.3390/aerospace11080646 - 9 Aug 2024
Viewed by 1345
Abstract
In this work, we explored the feasibility of using a transformer-based time-series forecasting architecture, known as the Temporal Fusion Transformer (TFT), for anomaly detection using threaded track data from the MITRE Corporation’s Transportation Data Platform (TDP) and digital flight data. The TFT architecture [...] Read more.
In this work, we explored the feasibility of using a transformer-based time-series forecasting architecture, known as the Temporal Fusion Transformer (TFT), for anomaly detection using threaded track data from the MITRE Corporation’s Transportation Data Platform (TDP) and digital flight data. The TFT architecture has the flexibility to include both time-varying multivariate data and categorical data from multimodal data sources and conduct single-output or multi-output predictions. For anomaly detection, rather than training a TFT model to predict the outcomes of specific aviation safety events, we train a TFT model to learn nominal behavior. Any significant deviation of the TFT model’s future horizon forecast for the output flight parameters of interest from the observed time-series data is considered an anomaly when conducting evaluations. For proof-of-concept demonstrations, we used an unstable approach (UA) as the anomaly event. This type of anomaly detection approach with nominal behavior learning can be used to develop flight analytics to identify emerging safety hazards in historical flight data and has the potential to be used as an on-board early warning system to assist pilots during flight. Full article
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<p>Temporal Fusion Transformer (TFT) architecture. Reproduced from [<a href="#B19-aerospace-11-00646" class="html-bibr">19</a>].</p>
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<p>Forecasting-based anomaly detection via nominal behavior learning with the TFTs.</p>
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<p>Averaged RMSE profiles as a function of “time before touchdown” resulting from various TFT models for the nominal flight data in the test split with speed as the target output.</p>
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<p>Feature importance rankings for the three TFT models trained with different input feature combinations with speed as the target (<b>a</b>) TFT-1, (<b>b</b>) TFT-2, and (<b>c</b>) TFT-3.</p>
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<p>Averaged RMSE profiles for TFT-2 and TFT-select.</p>
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<p>Averaged RMSE profiles from speed predictions for the TFTs trained to jointly predict speed and altitude (multi-output) in comparison to the single-output TFT model (speed).</p>
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<p>Averaged RMSE profiles from altitude predictions for the TFTs trained to jointly predict speed and altitude (multi-output) in comparison to the single-output TFT model (altitude).</p>
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<p>Averaged RMSE profiles for speed and altitude using the TFT-2 single-output models (speed and altitude modeled separately).</p>
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<p>Fisher’s score for various TFT models as a function of time before touchdown.</p>
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<p>RMSE values of the test split (nominal and UA flight data) for the single output TFT models (speed and altitude outputs) at the 26 timesteps before touchdown—zoomed in for better visualization.</p>
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<p>ROC curve for visualizing the detection performance of the RMSE-threshold-based anomaly detection at the identified time point when used with single outputs and two outputs together.</p>
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25 pages, 2970 KiB  
Article
Impact of PV and EV Forecasting in the Operation of a Microgrid
by Giampaolo Manzolini, Andrea Fusco, Domenico Gioffrè, Silvana Matrone, Riccardo Ramaschi, Marios Saleptsis, Riccardo Simonetti, Filip Sobic, Michael James Wood, Emanuele Ogliari and Sonia Leva
Forecasting 2024, 6(3), 591-615; https://doi.org/10.3390/forecast6030032 - 31 Jul 2024
Viewed by 991
Abstract
The electrification of the transport sector together with large renewable energy deployment requires powerful tools to efficiently use energy assets and infrastructure. In this framework, the forecast of electric vehicle demand and solar photovoltaic (PV) generation plays a fundamental role. This paper studies [...] Read more.
The electrification of the transport sector together with large renewable energy deployment requires powerful tools to efficiently use energy assets and infrastructure. In this framework, the forecast of electric vehicle demand and solar photovoltaic (PV) generation plays a fundamental role. This paper studies the impact of forecast accuracy on total electric cost of a simulated electric vehicles (EVs) charging station coupled with true solar PV and stationary battery energy storage. The optimal energy management system is based on the rolling horizon approach implemented in with a mixed integer linear program which takes as input the EV load forecast using long short-term memory (LSTM) neural network and persistence approaches and PV production forecast using a physical hybrid artificial neural network. The energy management system is firstly deployed and validated on an existing multi-good microgrid by achieving a discrepancy of state variables below 10% with respect to offline simulations. Then, eight weeks of simulations from each of the four seasons show that the accuracy of the forecast can increase operational costs by 10% equally distributed between the PV and EV forecasts. Finally, the accuracy of the combined PV and EV forecast matters more than single accuracies: LSTM outperforms persistence to predict the EV load (−30% root mean squared error), though when combined with PV forecast it has higher error (+15%) with corresponding higher operational costs (up to 5%). Full article
(This article belongs to the Special Issue Feature Papers of Forecasting 2024)
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<p>Experimental setup and control architecture considered in this case.</p>
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<p>Operational scheduling for a considered week using LSTM forecast: experimental results (<b>left</b>) and offline results with the simulator (<b>right</b>).</p>
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<p>Offline results of the operational scheduling of the two weeks of spring using persistence (<b>left</b>) and LSTM (<b>right</b>) forecasts.</p>
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<p>Second layer block scheme.</p>
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<p>Common architecture of the LSTM cell.</p>
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20 pages, 4689 KiB  
Article
Extending Multi-Output Methods for Long-Term Aboveground Biomass Time Series Forecasting Using Convolutional Neural Networks
by Efrain Noa-Yarasca, Javier M. Osorio Leyton and Jay P. Angerer
Mach. Learn. Knowl. Extr. 2024, 6(3), 1633-1652; https://doi.org/10.3390/make6030079 - 17 Jul 2024
Viewed by 1273
Abstract
Accurate aboveground vegetation biomass forecasting is essential for livestock management, climate impact assessments, and ecosystem health. While artificial intelligence (AI) techniques have advanced time series forecasting, a research gap in predicting aboveground biomass time series beyond single values persists. This study introduces RECMO [...] Read more.
Accurate aboveground vegetation biomass forecasting is essential for livestock management, climate impact assessments, and ecosystem health. While artificial intelligence (AI) techniques have advanced time series forecasting, a research gap in predicting aboveground biomass time series beyond single values persists. This study introduces RECMO and DirRecMO, two multi-output methods for forecasting aboveground vegetation biomass. Using convolutional neural networks, their efficacy is evaluated across short-, medium-, and long-term horizons on six Kenyan grassland biomass datasets, and compared with that of existing single-output methods (Recursive, Direct, and DirRec) and multi-output methods (MIMO and DIRMO). The results indicate that single-output methods are superior for short-term predictions, while both single-output and multi-output methods exhibit a comparable effectiveness in long-term forecasts. RECMO and DirRecMO outperform established multi-output methods, demonstrating a promising potential for biomass forecasting. This study underscores the significant impact of multi-output size on forecast accuracy, highlighting the need for optimal size adjustments and showcasing the proposed methods’ flexibility in long-term forecasts. Short-term predictions show less significant differences among methods, complicating the identification of the best performer. However, clear distinctions emerge in medium- and long-term forecasts, underscoring the greater importance of method choice for long-term predictions. Moreover, as the forecast horizon extends, errors escalate across all methods, reflecting the challenges of predicting distant future periods. This study suggests advancing hybrid models (e.g., RECMO and DirRecMO) to improve extended horizon forecasting. Future research should enhance adaptability, investigate multi-output impacts, and conduct comparative studies across diverse domains, datasets, and AI algorithms for robust insights. Full article
(This article belongs to the Section Network)
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<p>Time series of aboveground vegetation biomass (kg/ha) derived from calibrated PHYGROW model simulations at six rangeland locations in Kenya. Each subfigure (<b>a</b>–<b>f</b>) represents time series data from a representative location.</p>
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<p>Conversion of time series data into a supervised dataset. Blue squares: predictor subsequences inputted to the model (window size w). Orange squares: predicted values.</p>
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<p>Overview of the examined and prospective forecasting methods. Blue squares: predictor subsequences inputted to the model (window size w). Orange squares: predicted values.</p>
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<p>Architecture of the Convolutional Neural Network.</p>
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<p>Average RMSE values across different forecasting methods for aboveground vegetation biomass (kg/ha) across a horizon (<span class="html-italic">H</span>) of 24. Each subfigure from (<b>a</b>–<b>f</b>) displays the results of each time series data from a representative study location.</p>
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<p>Relative RMSE values of aboveground vegetation biomass (kg/ha) across different forecasting methods in relation to forecast horizons. Relative RMSE is calculated as a percentage by dividing the average RMSE by the time series mean.</p>
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29 pages, 953 KiB  
Article
Multi-Step Internet Traffic Forecasting Models with Variable Forecast Horizons for Proactive Network Management
by Sajal Saha, Anwar Haque and Greg Sidebottom
Sensors 2024, 24(6), 1871; https://doi.org/10.3390/s24061871 - 14 Mar 2024
Viewed by 975
Abstract
The ISP (Internet Service Provider) industry relies heavily on internet traffic forecasting (ITF) for long-term business strategy planning and proactive network management. Effective ITF frameworks are necessary to manage these networks and prevent network congestion and over-provisioning. This study introduces an ITF model [...] Read more.
The ISP (Internet Service Provider) industry relies heavily on internet traffic forecasting (ITF) for long-term business strategy planning and proactive network management. Effective ITF frameworks are necessary to manage these networks and prevent network congestion and over-provisioning. This study introduces an ITF model designed for proactive network management. It innovatively combines outlier detection and mitigation techniques with advanced gradient descent and boosting algorithms, including Gradient Boosting Regressor (GBR), Extreme Gradient Boosting (XGB), Light Gradient Boosting Machine (LGB), CatBoost Regressor (CBR), and Stochastic Gradient Descent (SGD). In contrast to traditional methods that rely on synthetic datasets, our model addresses the problems caused by real aberrant ISP traffic data. We evaluated our model across varying forecast horizons—six, nine, and twelve steps—demonstrating its adaptability and superior predictive accuracy compared to traditional forecasting models. The integration of the outlier detection and mitigation module significantly enhances the model’s performance, ensuring robust and accurate predictions even in the presence of data volatility and anomalies. To guarantee that our suggested model works in real-world situations, our research is based on an extensive experimental setup that uses real internet traffic monitoring from high-speed ISP networks. Full article
(This article belongs to the Section Sensor Networks)
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<p>High-level framework of proposed model.</p>
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<p>Feature extraction.</p>
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<p>Chain multi-output regression model.</p>
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<p>Rolling-based cross-validation.</p>
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<p>Original traffic vs. outlier mitigated traffic.</p>
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<p>Empirical Cumulative Distribution Function (ECDF) plot of our traffic data.</p>
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<p>Average execution time of our proposed models for different forecast length.</p>
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<p>A comparison among different feature subset performances regarding average prediction accuracy for six-step forecasting. The average accuracy is calculated as the mean of each step’s individual prediction accuracy.</p>
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<p>A comparison among different feature subset performances regarding average prediction accuracy for nine-step forecasting. The average accuracy is calculated as the mean of each step’s individual prediction accuracy.</p>
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<p>A comparison among different feature subset performances regarding average prediction accuracy for twelve-step forecasting. The average accuracy is calculated as the mean of each step’s individual prediction accuracy.</p>
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20 pages, 2481 KiB  
Article
Tackling Uncertainty: Forecasting the Energy Consumption and Demand of an Electric Arc Furnace with Limited Knowledge on Process Parameters
by Vanessa Zawodnik, Florian Christian Schwaiger, Christoph Sorger and Thomas Kienberger
Energies 2024, 17(6), 1326; https://doi.org/10.3390/en17061326 - 10 Mar 2024
Viewed by 1187
Abstract
The iron and steel industry significantly contributes to global energy use and greenhouse gas emissions. The rising deployment of volatile renewables and the resultant need for flexibility, coupled with specific challenges in electric steelmaking (e.g., operation optimization, optimized power purchasing, effective grid capacity [...] Read more.
The iron and steel industry significantly contributes to global energy use and greenhouse gas emissions. The rising deployment of volatile renewables and the resultant need for flexibility, coupled with specific challenges in electric steelmaking (e.g., operation optimization, optimized power purchasing, effective grid capacity monitoring), require accurate energy consumption and demand forecasts for electric steel mills to align with the energy transition. This study investigates diverse approaches to forecast the energy consumption and demand of an electric arc furnace—one of the largest consumers on the grid—considering various forecast horizons and objectives with limited knowledge on process parameters. The results are evaluated for accuracy, robustness, and costs. Two grid connection capacity monitoring approaches—a one-step and a multi-step Long Short-Term Memory neural network—are assessed for intra-hour energy demand forecasts. The one-step approach effectively models energy demand, while the multi-step approach encounters challenges in representing different operational phases of the furnace. By employing a combined statistic–stochastic model integrating a Seasonal Auto-Regressive Moving Average model and Markov chains, the study extends the forecast horizon for optimized day-ahead electricity procurement. However, the accuracy decreases as the forecast horizon lengthens. Nevertheless, the day-ahead forecast provides substantial benefits, including reduced energy balancing needs and potential cost savings. Full article
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<p>Representative energy demand for two heats of the investigated EAF.</p>
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<p>Forecast model classification scheme.</p>
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<p>Impact area of different forecast horizons.</p>
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<p>Model execution flow of O-LSTM NN (<b>A</b>) and M-LSTM NN (<b>B</b>).</p>
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<p>Workflow of statistic–stochastic model.</p>
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<p>Heat-wise EAF energy consumption based on inserted scrap mass using linear regression (regression line: grey line; whole dataset: transparent data points; representative sample of one week: solid data points).</p>
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<p>Energy demand forecast of Sample 1 (<b>A</b>) and 2 (<b>B</b>) with O-LSTM NN.</p>
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<p>Energy demand forecast of Sample 3 (<b>A</b>) and 4 (<b>B</b>) with M-LSTM NN.</p>
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<p>Comparison of real data with the forecast (<b>A</b>) and the standard load profile (<b>B</b>) of the day-ahead electricity consumption for Sample 1.</p>
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30 pages, 2439 KiB  
Article
Automated Model Selection Using Bayesian Optimization and the Asynchronous Successive Halving Algorithm for Predicting Daily Minimum and Maximum Temperatures
by Dilip Kumar Roy, Mohamed Anower Hossain, Mohamed Panjarul Haque, Abed Alataway, Ahmed Z. Dewidar and Mohamed A. Mattar
Agriculture 2024, 14(2), 278; https://doi.org/10.3390/agriculture14020278 - 8 Feb 2024
Viewed by 1641
Abstract
This study addresses the crucial role of temperature forecasting, particularly in agricultural contexts, where daily maximum (Tmax) and minimum (Tmin) temperatures significantly impact crop growth and irrigation planning. While machine learning (ML) models [...] Read more.
This study addresses the crucial role of temperature forecasting, particularly in agricultural contexts, where daily maximum (Tmax) and minimum (Tmin) temperatures significantly impact crop growth and irrigation planning. While machine learning (ML) models offer a promising avenue for temperature forecasts, the challenge lies in efficiently training multiple models and optimizing their parameters. This research addresses a research gap by proposing advanced ML algorithms for multi-step-ahead Tmax and Tmin forecasting across various weather stations in Bangladesh. The study employs Bayesian optimization and the asynchronous successive halving algorithm (ASHA) to automatically select top-performing ML models by tuning hyperparameters. While both the Bayesian and ASHA optimizations yield satisfactory results, ASHA requires less computational time for convergence. Notably, different top-performing models emerge for Tmax and Tmin across various forecast horizons. The evaluation metrics on the test dataset confirm higher accuracy, efficiency coefficients, and agreement indices, along with lower error values for both Tmax and Tmin forecasts at different weather stations. Notably, the forecasting accuracy decreases with longer horizons, emphasizing the superiority of one-step-ahead predictions. The automated model selection approach using Bayesian and ASHA optimization algorithms proves promising for enhancing the precision of multi-step-ahead temperature forecasting, with potential applications in diverse geographical locations. Full article
(This article belongs to the Special Issue Application of Machine Learning and Data Analysis in Agriculture)
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<p>Study area indicating the positioning of the weather stations.</p>
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<p>PACF plots of the <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> data.</p>
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<p>Flow diagram of the proposed automatic model selection scheme.</p>
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<p>Performance of the best models on test dataset in terms of forecasting maximum temperatures (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math>) under various forecast horizons at the weather stations.</p>
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<p>Performance of the best models on test dataset to forecast minimum temperatures (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math>) under various forecast horizons at the weather stations.</p>
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18 pages, 4156 KiB  
Article
Deep Learning Model Effectiveness in Forecasting Limited-Size Aboveground Vegetation Biomass Time Series: Kenyan Grasslands Case Study
by Efrain Noa-Yarasca, Javier M. Osorio Leyton and Jay P. Angerer
Agronomy 2024, 14(2), 349; https://doi.org/10.3390/agronomy14020349 - 8 Feb 2024
Cited by 2 | Viewed by 1647
Abstract
Timely forecasting of aboveground vegetation biomass is crucial for effective management and ensuring food security. However, research on predicting aboveground biomass remains scarce. Artificial intelligence (AI) methods could bridge this research gap and provide early warning to planners and stakeholders. This study evaluates [...] Read more.
Timely forecasting of aboveground vegetation biomass is crucial for effective management and ensuring food security. However, research on predicting aboveground biomass remains scarce. Artificial intelligence (AI) methods could bridge this research gap and provide early warning to planners and stakeholders. This study evaluates the effectiveness of deep learning (DL) algorithms in predicting aboveground vegetation biomass with limited-size data. It employs an iterative forecasting procedure for four target horizons, comparing the performance of DL models—multi-layer perceptron (MLP), long short-term memory (LSTM), gated recurrent unit (GRU), convolutional neural network (CNN), and CNN-LSTM—against the traditional seasonal autoregressive integrated moving average (SARIMA) model, serving as a benchmark. Five limited-size vegetation biomass time series from Kenyan grasslands with values at 15-day intervals over a 20-year period were chosen for this purpose. Comparing the outcomes of these models revealed significant differences (p < 0.05); however, none of the models proved superior among the five time series and the four horizons evaluated. The SARIMA, CNN, and CNN-LSTM models performed best, with the statistical model slightly outperforming the other two. Additionally, the accuracy of all five models varied significantly according to the prediction horizon (p < 0.05). As expected, the accuracy of the models decreased as the prediction horizon increased, although this relationship was not strictly monotonic. Finally, this study indicated that, in limited-size aboveground vegetation biomass time series, there is no guarantee that deep learning methods will outperform traditional statistical methods. Full article
(This article belongs to the Topic Advances in Crop Simulation Modelling)
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<p>Aboveground vegetation biomass time series generated from calibrated PHYGROW model simulations across five representative rangeland sites in Kenya. (<b>a</b>) Time series 1 (TS1), (<b>b</b>) Time series 2 (TS2), (<b>c</b>) Time series 3 (TS3), (<b>d</b>) Time series 4 (TS4), and (<b>e</b>) Time series 5 (TS5).</p>
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<p>Using a sliding window to configure time series as a supervised data set.</p>
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<p>Long short-term memory network architecture.</p>
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<p>Gated Recurrent Unit network architecture.</p>
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<p>Model architecture overview: CNN with MLP hidden layer, CNN-LSTM with LSTM hidden layer.</p>
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<p>Performance of DL and statistical models in aboveground vegetation biomass time series forecasting over four horizons. (<b>a</b>–<b>e</b>) correspond to time series TS1 to TS5, respectively.</p>
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18 pages, 3639 KiB  
Article
Photovoltaic Power Generation Forecasting with Hidden Markov Model and Long Short-Term Memory in MISO and SISO Configurations
by Carlos J. Delgado, Estefanía Alfaro-Mejía, Vidya Manian, Efrain O’Neill-Carrillo and Fabio Andrade
Energies 2024, 17(3), 668; https://doi.org/10.3390/en17030668 - 30 Jan 2024
Cited by 5 | Viewed by 1256
Abstract
Photovoltaic (PV) power generation forecasting is an important research topic, aiming to mitigate variability caused by weather conditions and improve power generation planning. Climate factors, including solar irradiance, temperature, and cloud cover, influence the energy conversion achieved by PV systems. Long-term weather forecasting [...] Read more.
Photovoltaic (PV) power generation forecasting is an important research topic, aiming to mitigate variability caused by weather conditions and improve power generation planning. Climate factors, including solar irradiance, temperature, and cloud cover, influence the energy conversion achieved by PV systems. Long-term weather forecasting improves PV power generation planning, while short-term forecasting enhances control methods, such as managing ramp rates. The stochastic nature of weather variables poses a challenge for linear regression methods. Consequently, advanced, state-of-the-art machine learning (ML) approaches capable of handling non-linear data, such as long short-term memory (LSTM), have emerged. This paper introduces the implementation of a multivariate machine learning model to forecast PV power generation, considering multiple weather variables. A deep learning solution was implemented to analyze weather variables in a short time horizon. Utilizing a hidden Markov model for data preprocessing, an LSTM model was trained using the Alice Spring dataset provided by DKA Solar Center. The proposed workflow demonstrated superior performance compared to the results obtained by state-of-the-art methods, including support vector machine, radiation classification coordinate with LSTM (RCC-LSTM), and ESNCNN specifically concerning the proposed multi-input single-output LSTM model. This improvement is attributed to incorporating input features such as active power, temperature, humidity, horizontal and diffuse irradiance, and wind direction, with active power serving as the output variable. The proposed workflow achieved a mean square error (MSE) of 2.17×107, a root mean square error (RMSE) of 4.65×104, and a mean absolute error (MAE) of 4.04×104. Full article
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<p>Workflow used to build a machine learning model.</p>
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<p>Time series signal before removal of outliers. (<b>a</b>) Power generation vs. measures are classified as outliers with class label 1 (green dots) or normal values with class labels 0 and 2 (blue and orange dots) for HMM. (<b>b</b>) <span class="html-italic">Diff</span> variable vs. measures classified from HMM.</p>
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<p>Timeseries signal after the outlier removal step. (<b>a</b>) Power generation vs. measures are classified as outliers with class label 1 (green dots) or normal values with class labels 0 and 2 (blue and orange dots) for HMM. (<b>b</b>) <span class="html-italic">Diff</span> variable vs. measures classified from HMM.</p>
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<p>LSTM cell components.</p>
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<p>Correlation analysis between features.</p>
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<p>Optimization function vs. epochs in Experiment 3.</p>
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<p>Optimization function vs. epochs, zoomed in.</p>
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<p>Signal comparison using the model trained in Experiment 3.</p>
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<p>Outlier references DKA Solar Center Dataset. Normalized active power is on the vertical axis, and the number of measures is on the horizontal axis.</p>
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<p>Outlier references Ambient Weather Network—CID. Normalized solar irradiance is on the vertical axis, and the number of measures is on the horizontal axis.</p>
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26 pages, 3861 KiB  
Article
Predictive Analytics of Air Temperature in Alaskan Permafrost Terrain Leveraging Two-Level Signal Decomposition and Deep Learning
by Aymane Ahajjam, Jaakko Putkonen, Emmanuel Chukwuemeka, Robert Chance and Timothy J. Pasch
Forecasting 2024, 6(1), 55-80; https://doi.org/10.3390/forecast6010004 - 9 Jan 2024
Cited by 1 | Viewed by 1886
Abstract
Local weather forecasts in the Arctic outside of settlements are challenging due to the dearth of ground-level observation stations and high computational costs. During winter, these forecasts are critical to help prepare for potentially hazardous weather conditions, while in spring, these forecasts may [...] Read more.
Local weather forecasts in the Arctic outside of settlements are challenging due to the dearth of ground-level observation stations and high computational costs. During winter, these forecasts are critical to help prepare for potentially hazardous weather conditions, while in spring, these forecasts may be used to determine flood risk during annual snow melt. To this end, a hybrid VMD-WT-InceptionTime model is proposed for multi-horizon multivariate forecasting of remote-region temperatures in Alaska over short-term horizons (the next seven days). First, the Spearman correlation coefficient is employed to analyze the relationship between each input variable and the forecast target temperature. The most output-correlated input sequences are decomposed using variational mode decomposition (VMD) and, ultimately, wavelet transform (WT) to extract time-frequency patterns intrinsic in the raw inputs. The resulting sequences are fed into a deep InceptionTime model for short-term forecasting. This hybrid technique has been developed and evaluated using 35+ years of data from three locations in Alaska. Different experiments and performance benchmarks are conducted using deep learning models (e.g., Time Series Transformers, LSTM, MiniRocket), and statistical and conventional machine learning baselines (e.g., GBDT, SVR, ARIMA). All forecasting performances are assessed using four metrics: the root mean squared error, the mean absolute percentage error, the coefficient of determination, and the mean directional accuracy. Superior forecasting performance is achieved consistently using the proposed hybrid technique. Full article
(This article belongs to the Section Weather and Forecasting)
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<p>Data from the SNAP dataset [<a href="#B36-forecasting-06-00004" class="html-bibr">36</a>] from three field sites in Nome, Bethel, and Utqiagvik in Alaska. (<b>a</b>) Daily temperature time series over time with distinctions between freezing and thawing temperatures; (<b>b</b>) Map of the three field sites in Alaska.</p>
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<p>Multi-horizon forecasting of the temperature using VMD-WT-InceptionTime.</p>
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<p>Moving window schematic to construct training and testing sets. The testing set period spans between 21 May 2008 and 29 October 2015.</p>
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<p>Spearman correlation results between different inputs and the target output for every location. Different input lengths were considered for each input feature spanning nine weeks.</p>
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<p>Example of temperature sequences sequentially processed using VMD (<math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>) and WT (<math display="inline"><semantics> <mrow> <mi>I</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>). (<b>a</b>) Raw temperature sequence; (<b>b</b>) Resulting VMD decomposed sequences from the temperature sequence; (<b>c</b>) Single-sided amplitude spectrum of the VMD decomposed sequences; (<b>d</b>) Resulting WT decomposed sequences from a single IMF; (<b>e</b>) Single-sided amplitude spectrum of WT decomposed sequences.</p>
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<p>Scatterplots comparing observed and forecast air temperatures in the three field sites using InceptionTime under four approaches: no decomposition, WT decomposition only, VMD only, and the proposed hybrid VMD-WT technique. (<b>a</b>) Nome; (<b>b</b>) Bethel; (<b>c</b>) Utqiagvik.</p>
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<p>Impact of different VMD decomposition levels on the average performance of the proposed hybrid model on the test set in terms of RMSE and <math display="inline"><semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics></math>. (<b>a</b>) Nome; (<b>b</b>) Bethel; (<b>c</b>) Utqiagvik.</p>
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<p>Examples of air temperature forecasts using the optimized proposed forecasting technique (<math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>30</mn> </mrow> </semantics></math> for Nome and Bethel and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>39</mn> </mrow> </semantics></math> for Utqiavik) compared with actual measurements from the test set. Additional forecasts using the proposed technique under a sub-optimal decomposition level (<span class="html-italic">M</span> = 3), no decomposition using InceptionTime, and the historical means are shown for reference. All plots share the same vertical axis limits for comparison reasons. (<b>a</b>) randomly selected sequences. (<b>b</b>) randomly selected sequences. (<b>c</b>) the worst performance.</p>
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<p>Boxplot of per-horizon errors found using the optimized proposed technique under <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>30</mn> </mrow> </semantics></math> for Nome and Bethel and under <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>39</mn> </mrow> </semantics></math> for Utqiagvik on the testing sets.</p>
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<p>RMSE performance distribution of the optimized forecasting technique, segmented by the range of daily air temperature changes. The forecast and observation sequences were binned into intervals of <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>K</mi> </mrow> </semantics></math> by computing the amplitude change between consecutive pairs of days (K/day). It is noteworthy that even under rapid air temperature fluctuations, the technique is capable of producing forecasts with low RMSE values at all three locations.</p>
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